On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
On 6/26/2026 9:17 AM, olcott wrote:
On 6/26/2026 8:14 AM, dbush wrote:
On 6/26/2026 8:49 AM, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
Given that the following statement is true:
--------------------------------------
There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
And the following statement has an unknown truth value:
--------------------------------------
There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
When put together in the following natural language sentence:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Is the condition "At least one of the following statements is true"
satisfied?
You either are not bright enough to understand
the deep meaning of Disjunction introduction or
you are playing head games. Unless you want an
honest dialogue please fuck off.
Why is it a head game?
On 6/26/2026 9:22 AM, dbush wrote:
On 6/26/2026 9:17 AM, olcott wrote:
On 6/26/2026 8:14 AM, dbush wrote:
On 6/26/2026 8:49 AM, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
Given that the following statement is true:
--------------------------------------
There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
And the following statement has an unknown truth value:
--------------------------------------
There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
When put together in the following natural language sentence:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Is the condition "At least one of the following statements is true"
satisfied?
You either are not bright enough to understand
the deep meaning of Disjunction introduction or
you are playing head games. Unless you want an
honest dialogue please fuck off.
Why is it a head game? It's a simple question:
Is the condition "At least one of the following statements is true"
satisfied?
Not answering this question can only be seen as dishonest. Do you
intend to be dishonest?
Copy/paste error above: the following statement is given as true:
--------------------------------------
Earth is the third planet from the sun. --------------------------------------
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier statements
by a truth-preserving transformation. Or-intrduction
discussed above is a truth-preserving transformation.
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier
statements
Except with Disjunction introduction, that is its problem.
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a statement X
such that the condition "At least one of the following statements is
true" is false.
Name it.
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier >>>>> statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is off-topic.
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>> sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier >>>>>> statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is off-
topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>> other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>> formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier >>>>>>> statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is off-
topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a contradiction is given as true, any statement can be proven as true.
The principle of explosion is a demonstration of *why* a formal system
whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of
explosion is to be able to use a system that has a contradiction.
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>> other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>> formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier >>>>>>> statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is off-
topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a contradiction is given as true, any statement can be proven as true.
The principle of explosion is a demonstration of *why* a formal system
whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of
explosion is to be able to use a system that has a contradiction.
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more
earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a contradiction
is given as true, any statement can be proven as true.
The principle of explosion is a demonstration of *why* a formal system
whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of
explosion is to be able to use a system that has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who >>>>>>>>>>> don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a contradiction
is given as true, any statement can be proven as true.
The principle of explosion is a demonstration of *why* a formal
system whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of
explosion is to be able to use a system that has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non-
contradiction goes away as it looses its basis.
We *want* the principle of explosion because it shows us what can happen when we have a system that can prove a contradiction.
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who >>>>>>>>>>>> don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a
contradiction is given as true, any statement can be proven as true.
The principle of explosion is a demonstration of *why* a formal
system whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of
explosion is to be able to use a system that has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non-
contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction introduction.
We *want* the principle of explosion because it shows us what can
happen when we have a system that can prove a contradiction.
It *is* and actual psychotic break from reality
to prove any damned thing from a contradiction
besides ⊥ falsum.
On 6/27/2026 7:22 PM, olcott wrote:
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who >>>>>>>>>>>>> don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a
contradiction is given as true, any statement can be proven as true. >>>>>
The principle of explosion is a demonstration of *why* a formal
system whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of
explosion is to be able to use a system that has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non-
contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction introduction.
Which you can't do because it's a truth-preserving operation.
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>
statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a
contradiction is given as true, any statement can be proven as true. >>>>>>
The principle of explosion is a demonstration of *why* a formal
system whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of >>>>>> explosion is to be able to use a system that has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non-
contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction introduction.
Which you can't do because it's a truth-preserving operation.
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere >>>>>>>>>>>>>> (as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>>> eachstatement either is a premis or follows from one or >>>>>>>>>>>>> more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a
contradiction is given as true, any statement can be proven as true. >>>>>>>
The principle of explosion is a demonstration of *why* a formal >>>>>>> system whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of >>>>>>> explosion is to be able to use a system that has a contradiction. >>>>>>>
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non-
contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction introduction.
Which you can't do because it's a truth-preserving operation.
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a statement X
such that the condition "At least one of the following statements is
true" is false.
Name it.
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:Which you can't do because it's a truth-preserving operation.
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when >>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>> where eachstatement either is a premis or follows from one >>>>>>>>>>>>>> or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid. >>>>>>>>
Through a series of truth preserving operations, when a
contradiction is given as true, any statement can be proven as >>>>>>>> true.
The principle of explosion is a demonstration of *why* a formal >>>>>>>> system whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle >>>>>>>> of explosion is to be able to use a system that has a
contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non-
contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction introduction. >>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a statement
X such that the condition "At least one of the following statements is
true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:Which you can't do because it's a truth-preserving operation.
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>> where eachstatement either is a premis or follows from >>>>>>>>>>>>>>> one or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid. >>>>>>>>>
Through a series of truth preserving operations, when a
contradiction is given as true, any statement can be proven as >>>>>>>>> true.
The principle of explosion is a demonstration of *why* a formal >>>>>>>>> system whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle >>>>>>>>> of explosion is to be able to use a system that has a
contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non-
contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction introduction. >>>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a statement
X such that the condition "At least one of the following statements
is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun. --------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a
statement X such that the condition "At least one of the following statements is true" is false?
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>> people who don't
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>>> where eachstatement either is a premis or follows from >>>>>>>>>>>>>>>> one or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid. >>>>>>>>>>
Through a series of truth preserving operations, when a
contradiction is given as true, any statement can be proven as >>>>>>>>>> true.
The principle of explosion is a demonstration of *why* a
formal system whose axioms lead to a contradiction is useless. >>>>>>>>>>
The only reason someone would want to get rid of the principle >>>>>>>>>> of explosion is to be able to use a system that has a
contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non- >>>>>>>> contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction
introduction.
Which you can't do because it's a truth-preserving operation.
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a
statement X such that the condition "At least one of the following
statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a
statement X such that the condition "At least one of the following
statements is true" is false?
Where X is "What time is it?"
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI (and of the >>>>>>>>>>>>>>>>>>>> many
systems of analytic implication belonging to its >>>>>>>>>>>>>>>>>>>> ilk) is
the rejection of the classically valid principle of >>>>>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula ϕ >>>>>>>>>>>>>>>>>>>> to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>>> people who don't
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>>>> where eachstatement either is a premis or follows from >>>>>>>>>>>>>>>>> one or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid. >>>>>>>>>>>
Through a series of truth preserving operations, when a >>>>>>>>>>> contradiction is given as true, any statement can be proven >>>>>>>>>>> as true.
The principle of explosion is a demonstration of *why* a >>>>>>>>>>> formal system whose axioms lead to a contradiction is useless. >>>>>>>>>>>
The only reason someone would want to get rid of the
principle of explosion is to be able to use a system that has >>>>>>>>>>> a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non- >>>>>>>>> contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction
introduction.
Which you can't do because it's a truth-preserving operation.
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a
statement X such that the condition "At least one of the following
statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a
statement X such that the condition "At least one of the following
statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true?
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment LogicsHe also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>>>> people who don't
gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI (and of the >>>>>>>>>>>>>>>>>>>>> many
systems of analytic implication belonging to its >>>>>>>>>>>>>>>>>>>>> ilk) is
the rejection of the classically valid principle of >>>>>>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula ϕ >>>>>>>>>>>>>>>>>>>>> to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given that >>>>>>>>>>>>>>>>>>>>> it is
famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>>>>> where eachstatement either is a premis or follows from >>>>>>>>>>>>>>>>>> one or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid. >>>>>>>>>>>>
Through a series of truth preserving operations, when a >>>>>>>>>>>> contradiction is given as true, any statement can be proven >>>>>>>>>>>> as true.
The principle of explosion is a demonstration of *why* a >>>>>>>>>>>> formal system whose axioms lead to a contradiction is useless. >>>>>>>>>>>>
The only reason someone would want to get rid of the
principle of explosion is to be able to use a system that >>>>>>>>>>>> has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non- >>>>>>>>>> contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction
introduction.
Which you can't do because it's a truth-preserving operation.
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement: >>>>>>
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a
statement X such that the condition "At least one of the following >>>>>> statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a
statement X such that the condition "At least one of the following
statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true?
We have a type mismatch error.
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>>>>> people who don't
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI (and of >>>>>>>>>>>>>>>>>>>>>> the many
systems of analytic implication belonging to its >>>>>>>>>>>>>>>>>>>>>> ilk) is
the rejection of the classically valid principle >>>>>>>>>>>>>>>>>>>>>> of Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula >>>>>>>>>>>>>>>>>>>>>> ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an >>>>>>>>>>>>>>>>>>>>>> arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given that >>>>>>>>>>>>>>>>>>>>>> it is
famously featured in Lewis’ derivation of an >>>>>>>>>>>>>>>>>>>>>> arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>>>>>> where eachstatement either is a premis or follows >>>>>>>>>>>>>>>>>>> from one or more earlier
statements
Except with Disjunction introduction, that is its >>>>>>>>>>>>>>>>>> problem.
So you're saying that in the following natural language >>>>>>>>>>>>>>>>> statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make it >>>>>>>>>>>>> invalid.
Through a series of truth preserving operations, when a >>>>>>>>>>>>> contradiction is given as true, any statement can be proven >>>>>>>>>>>>> as true.
The principle of explosion is a demonstration of *why* a >>>>>>>>>>>>> formal system whose axioms lead to a contradiction is useless. >>>>>>>>>>>>>
The only reason someone would want to get rid of the >>>>>>>>>>>>> principle of explosion is to be able to use a system that >>>>>>>>>>>>> has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents >>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non- >>>>>>>>>>> contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction
introduction.
Which you can't do because it's a truth-preserving operation. >>>>>>>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement: >>>>>>>
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a
statement X such that the condition "At least one of the
following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a
statement X such that the condition "At least one of the following
statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so it can't be
used in logic. I didn't think I had to make that explicit.
However, let's go with it anyway because it still illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true?
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>>>>>> people who don't
The main and distinctive feature of PAI (and of >>>>>>>>>>>>>>>>>>>>>>> the many
systems of analytic implication belonging to its >>>>>>>>>>>>>>>>>>>>>>> ilk) is
the rejection of the classically valid principle >>>>>>>>>>>>>>>>>>>>>>> of Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula >>>>>>>>>>>>>>>>>>>>>>> ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an >>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given that >>>>>>>>>>>>>>>>>>>>>>> it is
famously featured in Lewis’ derivation of an >>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a premis or >>>>>>>>>>>>>>>>>>>> follows from one or more earlier
statements
Except with Disjunction introduction, that is its >>>>>>>>>>>>>>>>>>> problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make it >>>>>>>>>>>>>> invalid.
Through a series of truth preserving operations, when a >>>>>>>>>>>>>> contradiction is given as true, any statement can be >>>>>>>>>>>>>> proven as true.
The principle of explosion is a demonstration of *why* a >>>>>>>>>>>>>> formal system whose axioms lead to a contradiction is >>>>>>>>>>>>>> useless.
The only reason someone would want to get rid of the >>>>>>>>>>>>>> principle of explosion is to be able to use a system that >>>>>>>>>>>>>> has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents >>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law of >>>>>>>>>>>> non- contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction >>>>>>>>>>> introduction.
Which you can't do because it's a truth-preserving operation. >>>>>>>>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement: >>>>>>>>
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a
statement X such that the condition "At least one of the
following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a
statement X such that the condition "At least one of the following >>>>>> statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so it can't be
used in logic. I didn't think I had to make that explicit.
However, let's go with it anyway because it still illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true?
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language statement, does
there exist a statement X such that the condition "At least one of the following statements is true" is false?
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>>>>>>> people who don't
The main and distinctive feature of PAI (and of >>>>>>>>>>>>>>>>>>>>>>>> the many
systems of analytic implication belonging to its >>>>>>>>>>>>>>>>>>>>>>>> ilk) is
the rejection of the classically valid principle >>>>>>>>>>>>>>>>>>>>>>>> of Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an >>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given >>>>>>>>>>>>>>>>>>>>>>>> that it is
famously featured in Lewis’ derivation of an >>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a premis or >>>>>>>>>>>>>>>>>>>>> follows from one or more earlier
statements
Except with Disjunction introduction, that is its >>>>>>>>>>>>>>>>>>>> problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make it >>>>>>>>>>>>>>> invalid.
Through a series of truth preserving operations, when a >>>>>>>>>>>>>>> contradiction is given as true, any statement can be >>>>>>>>>>>>>>> proven as true.
The principle of explosion is a demonstration of *why* a >>>>>>>>>>>>>>> formal system whose axioms lead to a contradiction is >>>>>>>>>>>>>>> useless.
The only reason someone would want to get rid of the >>>>>>>>>>>>>>> principle of explosion is to be able to use a system that >>>>>>>>>>>>>>> has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law of >>>>>>>>>>>>> non- contradiction goes away as it looses its basis. >>>>>>>>>>>>>
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction >>>>>>>>>>>> introduction.
Which you can't do because it's a truth-preserving operation. >>>>>>>>>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement: >>>>>>>>>
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a >>>>>>>>> statement X such that the condition "At least one of the
following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a >>>>>>> statement X such that the condition "At least one of the
following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so it can't
be used in logic. I didn't think I had to make that explicit.
However, let's go with it anyway because it still illustrates the point. >>>
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true?
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language statement, does
there exist a statement X such that the condition "At least one of the
following statements is true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier
statements
Except with Disjunction introduction, that is its problem.
by a truth-preserving transformation. Or-intrduction
discussed above is a truth-preserving transformation.
We know that "Not all lemons are yellow", as it has been assumed to be
true.
We know that "All lemons are yellow", as it has been assumed to be true.
Therefore, the two-part statement "All lemons are yellow or unicorns exist"
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more
earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a contradiction
is given as true, any statement can be proven as true.
The principle of explosion is a demonstration of *why* a formal system
whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of
explosion is to be able to use a system that has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>
statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't make it invalid.
Through a series of truth preserving operations, when a
contradiction is given as true, any statement can be proven as true. >>>>>>
The principle of explosion is a demonstration of *why* a formal
system whose axioms lead to a contradiction is useless.
The only reason someone would want to get rid of the principle of >>>>>> explosion is to be able to use a system that has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non-
contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction introduction.
Which you can't do because it's a truth-preserving operation.
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>>>>> people who don't
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI (and of >>>>>>>>>>>>>>>>>>>>>> the many
systems of analytic implication belonging to its >>>>>>>>>>>>>>>>>>>>>> ilk) is
the rejection of the classically valid principle >>>>>>>>>>>>>>>>>>>>>> of Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula >>>>>>>>>>>>>>>>>>>>>> ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an >>>>>>>>>>>>>>>>>>>>>> arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given that >>>>>>>>>>>>>>>>>>>>>> it is
famously featured in Lewis’ derivation of an >>>>>>>>>>>>>>>>>>>>>> arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>>>>>> where eachstatement either is a premis or follows >>>>>>>>>>>>>>>>>>> from one or more earlier
statements
Except with Disjunction introduction, that is its >>>>>>>>>>>>>>>>>> problem.
So you're saying that in the following natural language >>>>>>>>>>>>>>>>> statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make it >>>>>>>>>>>>> invalid.
Through a series of truth preserving operations, when a >>>>>>>>>>>>> contradiction is given as true, any statement can be proven >>>>>>>>>>>>> as true.
The principle of explosion is a demonstration of *why* a >>>>>>>>>>>>> formal system whose axioms lead to a contradiction is useless. >>>>>>>>>>>>>
The only reason someone would want to get rid of the >>>>>>>>>>>>> principle of explosion is to be able to use a system that >>>>>>>>>>>>> has a contradiction.
My reason to get rid of the principle of explosion
it to get rid of anything and everything that prevents >>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law of non- >>>>>>>>>>> contradiction goes away as it looses its basis.
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction
introduction.
Which you can't do because it's a truth-preserving operation. >>>>>>>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language statement: >>>>>>>
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a
statement X such that the condition "At least one of the
following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a
statement X such that the condition "At least one of the following
statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true?
We have a type mismatch error.
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>>>>>>>> people who don't
The main and distinctive feature of PAI (and of >>>>>>>>>>>>>>>>>>>>>>>>> the many
systems of analytic implication belonging to >>>>>>>>>>>>>>>>>>>>>>>>> its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an >>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given >>>>>>>>>>>>>>>>>>>>>>>>> that it is
famously featured in Lewis’ derivation of an >>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a premis >>>>>>>>>>>>>>>>>>>>>> or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is its >>>>>>>>>>>>>>>>>>>>> problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make it >>>>>>>>>>>>>>>> invalid.
Through a series of truth preserving operations, when a >>>>>>>>>>>>>>>> contradiction is given as true, any statement can be >>>>>>>>>>>>>>>> proven as true.
The principle of explosion is a demonstration of *why* a >>>>>>>>>>>>>>>> formal system whose axioms lead to a contradiction is >>>>>>>>>>>>>>>> useless.
The only reason someone would want to get rid of the >>>>>>>>>>>>>>>> principle of explosion is to be able to use a system >>>>>>>>>>>>>>>> that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law of >>>>>>>>>>>>>> non- contradiction goes away as it looses its basis. >>>>>>>>>>>>>>
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction >>>>>>>>>>>>> introduction.
Which you can't do because it's a truth-preserving operation. >>>>>>>>>>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language
statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a >>>>>>>>>> statement X such that the condition "At least one of the
following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a >>>>>>>> statement X such that the condition "At least one of the
following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so it can't
be used in logic. I didn't think I had to make that explicit.
However, let's go with it anyway because it still illustrates the
point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true?
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>> sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier >>>>>> statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is off-
topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>> other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>> formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier >>>>>>> statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is off-
topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>>>>>>>> people who don't
The main and distinctive feature of PAI (and of >>>>>>>>>>>>>>>>>>>>>>>>> the many
systems of analytic implication belonging to >>>>>>>>>>>>>>>>>>>>>>>>> its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an >>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given >>>>>>>>>>>>>>>>>>>>>>>>> that it is
famously featured in Lewis’ derivation of an >>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a premis >>>>>>>>>>>>>>>>>>>>>> or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is its >>>>>>>>>>>>>>>>>>>>> problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make it >>>>>>>>>>>>>>>> invalid.
Through a series of truth preserving operations, when a >>>>>>>>>>>>>>>> contradiction is given as true, any statement can be >>>>>>>>>>>>>>>> proven as true.
The principle of explosion is a demonstration of *why* a >>>>>>>>>>>>>>>> formal system whose axioms lead to a contradiction is >>>>>>>>>>>>>>>> useless.
The only reason someone would want to get rid of the >>>>>>>>>>>>>>>> principle of explosion is to be able to use a system >>>>>>>>>>>>>>>> that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law of >>>>>>>>>>>>>> non- contradiction goes away as it looses its basis. >>>>>>>>>>>>>>
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction >>>>>>>>>>>>> introduction.
Which you can't do because it's a truth-preserving operation. >>>>>>>>>>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language
statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a >>>>>>>>>> statement X such that the condition "At least one of the
following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a >>>>>>>> statement X such that the condition "At least one of the
following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so it can't
be used in logic. I didn't think I had to make that explicit.
However, let's go with it anyway because it still illustrates the
point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true?
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a head
game in your next reply or within one hour of you next post in this newsgroup will be taken as your official, on-the-record admission that Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't
The main and distinctive feature of PAI (and >>>>>>>>>>>>>>>>>>>>>>>>>> of the many
systems of analytic implication belonging to >>>>>>>>>>>>>>>>>>>>>>>>>> its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an >>>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given >>>>>>>>>>>>>>>>>>>>>>>>>> that it is
famously featured in Lewis’ derivation of an >>>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula ψ from a contradiction of the form ϕ ∧ >>>>>>>>>>>>>>>>>>>>>>>>>> ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a premis >>>>>>>>>>>>>>>>>>>>>>> or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is its >>>>>>>>>>>>>>>>>>>>>> problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make it >>>>>>>>>>>>>>>>> invalid.
Through a series of truth preserving operations, when a >>>>>>>>>>>>>>>>> contradiction is given as true, any statement can be >>>>>>>>>>>>>>>>> proven as true.
The principle of explosion is a demonstration of *why* >>>>>>>>>>>>>>>>> a formal system whose axioms lead to a contradiction is >>>>>>>>>>>>>>>>> useless.
The only reason someone would want to get rid of the >>>>>>>>>>>>>>>>> principle of explosion is to be able to use a system >>>>>>>>>>>>>>>>> that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law of >>>>>>>>>>>>>>> non- contradiction goes away as it looses its basis. >>>>>>>>>>>>>>>
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction >>>>>>>>>>>>>> introduction.
Which you can't do because it's a truth-preserving operation. >>>>>>>>>>>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language >>>>>>>>>>> statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a >>>>>>>>>>> statement X such that the condition "At least one of the >>>>>>>>>>> following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist a >>>>>>>>> statement X such that the condition "At least one of the
following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so it can't >>>>> be used in logic. I didn't think I had to make that explicit.
However, let's go with it anyway because it still illustrates the
point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true?
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record admission
that Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above question or explain why it is a head game. Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more
earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
That my proof to the contrary was simply erased
is dishonest.
is perfectly honest.In any sensible logic every tautology is provable.
Then the principle of explosion follows.
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:We have a type mismatch error.
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't
The main and distinctive feature of PAI (and >>>>>>>>>>>>>>>>>>>>>>>>>>> of the many
systems of analytic implication belonging to >>>>>>>>>>>>>>>>>>>>>>>>>>> its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an >>>>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given >>>>>>>>>>>>>>>>>>>>>>>>>>> that it is
famously featured in Lewis’ derivation of an >>>>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula ψ from a contradiction of the form ϕ >>>>>>>>>>>>>>>>>>>>>>>>>>> ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a premis >>>>>>>>>>>>>>>>>>>>>>>> or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is its >>>>>>>>>>>>>>>>>>>>>>> problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make it >>>>>>>>>>>>>>>>>> invalid.
Through a series of truth preserving operations, when >>>>>>>>>>>>>>>>>> a contradiction is given as true, any statement can be >>>>>>>>>>>>>>>>>> proven as true.
The principle of explosion is a demonstration of *why* >>>>>>>>>>>>>>>>>> a formal system whose axioms lead to a contradiction >>>>>>>>>>>>>>>>>> is useless.
The only reason someone would want to get rid of the >>>>>>>>>>>>>>>>>> principle of explosion is to be able to use a system >>>>>>>>>>>>>>>>>> that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law of >>>>>>>>>>>>>>>> non- contradiction goes away as it looses its basis. >>>>>>>>>>>>>>>>
You keep failing to pay close enough attention.
I only get rid of the POE by getting rid of Disjunction >>>>>>>>>>>>>>> introduction.
Which you can't do because it's a truth-preserving operation. >>>>>>>>>>>>>>
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING.
So you're saying that in the following natural language >>>>>>>>>>>> statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a >>>>>>>>>>>> statement X such that the condition "At least one of the >>>>>>>>>>>> following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist >>>>>>>>>> a statement X such that the condition "At least one of the >>>>>>>>>> following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true? >>>>>>>
The statement you gave isn't a truth-bearing statement, so it
can't be used in logic. I didn't think I had to make that explicit. >>>>>>
However, let's go with it anyway because it still illustrates the >>>>>> point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true?
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least
one of the following statements is true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record
admission that Disjunction introduction is in fact truth preserving
and valid, and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this
newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above
question or explain why it is a head game. Therefore, as per the
above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:We have a type mismatch error.
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>>>>>>>>>>A simple logical matrix and sequent calculus >>>>>>>>>>>>>>>>>>>>>>>>>>>> forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI (and >>>>>>>>>>>>>>>>>>>>>>>>>>>> of the many
systems of analytic implication belonging to >>>>>>>>>>>>>>>>>>>>>>>>>>>> its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an >>>>>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication—given >>>>>>>>>>>>>>>>>>>>>>>>>>>> that it is
famously featured in Lewis’ derivation of an >>>>>>>>>>>>>>>>>>>>>>>>>>>> arbitrary
formula ψ from a contradiction of the form ϕ >>>>>>>>>>>>>>>>>>>>>>>>>>>> ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is >>>>>>>>>>>>>>>>>>>>>>>> its problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic.
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make >>>>>>>>>>>>>>>>>>> it invalid.
Through a series of truth preserving operations, when >>>>>>>>>>>>>>>>>>> a contradiction is given as true, any statement can >>>>>>>>>>>>>>>>>>> be proven as true.
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of the >>>>>>>>>>>>>>>>>>> principle of explosion is to be able to use a system >>>>>>>>>>>>>>>>>>> that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law >>>>>>>>>>>>>>>>> of non- contradiction goes away as it looses its basis. >>>>>>>>>>>>>>>>>
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of Disjunction >>>>>>>>>>>>>>>> introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists a >>>>>>>>>>>>> statement X such that the condition "At least one of the >>>>>>>>>>>>> following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there exist >>>>>>>>>>> a statement X such that the condition "At least one of the >>>>>>>>>>> following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>
The statement you gave isn't a truth-bearing statement, so it
can't be used in logic. I didn't think I had to make that explicit. >>>>>>>
However, let's go with it anyway because it still illustrates the >>>>>>> point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true?
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language statement, >>>>>> does there exist a statement X such that the condition "At least
one of the following statements is true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record
admission that Disjunction introduction is in fact truth preserving
and valid, and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this
newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above
question or explain why it is a head game. Therefore, as per the
above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different rules.
That has no bearing on existing systems.
If you want to make up your own system, you need to throw out every that depends on any definition or rule that you changed and prove everything *from scratch*.
As you've demonstrated on countless occasions, you don't even have a
high school understanding of logic, so this is far beyond your abilities.
In the system everyone works in, Disjunction introduction is truth preserving and valid, and therefore so is the Principle of Explosion, as
you have just admitted on the record above.
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:We have a type mismatch error.
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.A simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many
systems of analytic implication belonging >>>>>>>>>>>>>>>>>>>>>>>>>>>>> to its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula. Parry blamed on this principle the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> derivability
of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is
famously featured in Lewis’ derivation of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula ψ from a contradiction of the form >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is >>>>>>>>>>>>>>>>>>>>>>>>> its problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make >>>>>>>>>>>>>>>>>>>> it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any statement >>>>>>>>>>>>>>>>>>>> can be proven as true.
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of the >>>>>>>>>>>>>>>>>>>> principle of explosion is to be able to use a system >>>>>>>>>>>>>>>>>>>> that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law >>>>>>>>>>>>>>>>>> of non- contradiction goes away as it looses its basis. >>>>>>>>>>>>>>>>>>
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of Disjunction >>>>>>>>>>>>>>>>> introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists >>>>>>>>>>>>>> a statement X such that the condition "At least one of the >>>>>>>>>>>>>> following statements is true" is false.
Name it.
That is not Disjunction introduction combined with
Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>> exist a statement X such that the condition "At least one of >>>>>>>>>>>> the following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>
The statement you gave isn't a truth-bearing statement, so it >>>>>>>> can't be used in logic. I didn't think I had to make that
explicit.
However, let's go with it anyway because it still illustrates >>>>>>>> the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language statement, >>>>>>> does there exist a statement X such that the condition "At least >>>>>>> one of the following statements is true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in >>>>> this newsgroup will be taken as your official, on-the-record
admission that Disjunction introduction is in fact truth preserving >>>>> and valid, and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in
this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the
above question or explain why it is a head game. Therefore, as per
the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different rules.
That has no bearing on existing systems.
The bearing that it has on existing systems is
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
https://en.wikipedia.org/wiki/Relevance_logic
Does this same sort of thing in that they limit logic
in a different way. If the conclusion is semantically
irrelevant to its premises then the conclusion is not
derived.
If you want to make up your own system, you need to throw out every
that depends on any definition or rule that you changed and prove
everything *from scratch*.
In my system we toss out and reject any and all
logical inference that is not semantic entailment.
Good: Bobby cut his hair therefore Bobby has less hair.
Bad: Bobby cut his hair therefore Bobby filled his gas tank.
The Prolog way to look at this is that in any system
when the expression x cannot reach Facts though its
Rules counts as untrue.
Prolog goes a step further with its "closed world"
"negation as failure" assumption that unprovable means false.
I only say that unprovable means untrue it does not
mean false.
As you've demonstrated on countless occasions, you don't even have a
high school understanding of logic, so this is far beyond your abilities.
In the system everyone works in, Disjunction introduction is truth
preserving and valid, and therefore so is the Principle of Explosion,
as you have just admitted on the record above.
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>> other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>> formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more earlier >>>>>>> statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is off-
topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more
earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic. The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record admission
that Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above question or explain why it is a head game. Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:We have a type mismatch error.
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that >>>>>>>>>>>>>>>>>>>>>>>>>>>> whenA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many
systems of analytic implication belonging >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability
of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is
famously featured in Lewis’ derivation of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula ψ from a contradiction of the form >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is >>>>>>>>>>>>>>>>>>>>>>>>>> its problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make >>>>>>>>>>>>>>>>>>>>> it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>> statement can be proven as true.
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use a >>>>>>>>>>>>>>>>>>>>> system that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law >>>>>>>>>>>>>>>>>>> of non- contradiction goes away as it looses its basis. >>>>>>>>>>>>>>>>>>>
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists >>>>>>>>>>>>>>> a statement X such that the condition "At least one of >>>>>>>>>>>>>>> the following statements is true" is false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>> exist a statement X such that the condition "At least one >>>>>>>>>>>>> of the following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>
The statement you gave isn't a truth-bearing statement, so it >>>>>>>>> can't be used in logic. I didn't think I had to make that >>>>>>>>> explicit.
However, let's go with it anyway because it still illustrates >>>>>>>>> the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language
statement, does there exist a statement X such that the
condition "At least one of the following statements is true" is >>>>>>>> false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a >>>>>> head game in your next reply or within one hour of you next post
in this newsgroup will be taken as your official, on-the-record
admission that Disjunction introduction is in fact truth
preserving and valid, and therefore so is the Principle of Explosion. >>>>>>
Let the record show that Peter Olcott made the following post in
this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the
above question or explain why it is a head game. Therefore, as per >>>>> the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and
valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different rules.
That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting with
the precondition that a contradiction has been proven, as you have
admitted above on the record.
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:We have a type mismatch error.
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication belonging >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even know >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
anyone else ever did this. I just knew that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is >>>>>>>>>>>>>>>>>>>>>>>>>>> its problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction enables >>>>>>>>>>>>>>>>>>>>>>> the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>>> statement can be proven as true.
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use a >>>>>>>>>>>>>>>>>>>>>> system that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses its >>>>>>>>>>>>>>>>>>>> basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>> exists a statement X such that the condition "At least >>>>>>>>>>>>>>>> one of the following statements is true" is false. >>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>> exist a statement X such that the condition "At least one >>>>>>>>>>>>>> of the following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>>
The statement you gave isn't a truth-bearing statement, so it >>>>>>>>>> can't be used in logic. I didn't think I had to make that >>>>>>>>>> explicit.
However, let's go with it anyway because it still illustrates >>>>>>>>>> the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language
statement, does there exist a statement X such that the
condition "At least one of the following statements is true" is >>>>>>>>> false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is >>>>>>> a head game in your next reply or within one hour of you next
post in this newsgroup will be taken as your official, on-the-
record admission that Disjunction introduction is in fact truth >>>>>>> preserving and valid, and therefore so is the Principle of
Explosion.
Let the record show that Peter Olcott made the following post in
this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the
above question or explain why it is a head game. Therefore, as
per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and
valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different rules.
That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting with
the precondition that a contradiction has been proven, as you have
admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:We have a type mismatch error.
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I figured >>>>>>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that >>>>>>>>>>>>>>>>>>>>>>>>>>>> whenA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many
systems of analytic implication belonging >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability
of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is
famously featured in Lewis’ derivation of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula ψ from a contradiction of the form >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is >>>>>>>>>>>>>>>>>>>>>>>>>> its problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction enables the >>>>>>>>>>>>>>>>>>>>>> Principle of Explosion.
Rejected, as you not liking the result doesn't make >>>>>>>>>>>>>>>>>>>>> it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>> statement can be proven as true.
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use a >>>>>>>>>>>>>>>>>>>>> system that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the law >>>>>>>>>>>>>>>>>>> of non- contradiction goes away as it looses its basis. >>>>>>>>>>>>>>>>>>>
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there exists >>>>>>>>>>>>>>> a statement X such that the condition "At least one of >>>>>>>>>>>>>>> the following statements is true" is false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>> exist a statement X such that the condition "At least one >>>>>>>>>>>>> of the following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>
The statement you gave isn't a truth-bearing statement, so it >>>>>>>>> can't be used in logic. I didn't think I had to make that >>>>>>>>> explicit.
However, let's go with it anyway because it still illustrates >>>>>>>>> the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language
statement, does there exist a statement X such that the
condition "At least one of the following statements is true" is >>>>>>>> false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a >>>>>> head game in your next reply or within one hour of you next post
in this newsgroup will be taken as your official, on-the-record
admission that Disjunction introduction is in fact truth
preserving and valid, and therefore so is the Principle of Explosion. >>>>>>
Let the record show that Peter Olcott made the following post in
this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the
above question or explain why it is a head game. Therefore, as per >>>>> the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and
valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different rules.
That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who don't >>>>>>>>>> understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where
eachstatement either is a premis or follows from one or more
earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
Model theory was created only because keeping semantics
directly within logic at the time was too complicated.
It did make logic easier to work with and it also made
logic diverge from correct reasoning.
Only people having actual psychosis would conclude
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:We have a type mismatch error.
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication belonging >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even know >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
anyone else ever did this. I just knew that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is >>>>>>>>>>>>>>>>>>>>>>>>>>> its problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction enables >>>>>>>>>>>>>>>>>>>>>>> the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>>> statement can be proven as true.
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use a >>>>>>>>>>>>>>>>>>>>>> system that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses its >>>>>>>>>>>>>>>>>>>> basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>> exists a statement X such that the condition "At least >>>>>>>>>>>>>>>> one of the following statements is true" is false. >>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>> exist a statement X such that the condition "At least one >>>>>>>>>>>>>> of the following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>>
The statement you gave isn't a truth-bearing statement, so it >>>>>>>>>> can't be used in logic. I didn't think I had to make that >>>>>>>>>> explicit.
However, let's go with it anyway because it still illustrates >>>>>>>>>> the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language
statement, does there exist a statement X such that the
condition "At least one of the following statements is true" is >>>>>>>>> false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is >>>>>>> a head game in your next reply or within one hour of you next
post in this newsgroup will be taken as your official, on-the-
record admission that Disjunction introduction is in fact truth >>>>>>> preserving and valid, and therefore so is the Principle of
Explosion.
Let the record show that Peter Olcott made the following post in
this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the
above question or explain why it is a head game. Therefore, as
per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and
valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different rules.
That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting with
the precondition that a contradiction has been proven, as you have
admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
On 29/06/2026 16:23, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:We have a type mismatch error.
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote:
On 6/27/2026 1:34 PM, dbush wrote:
On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication belonging >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to its ilk) is
the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an arbitrary
formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even know >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
anyone else ever did this. I just knew that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that is >>>>>>>>>>>>>>>>>>>>>>>>>>> its problem.
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>>>>>> language statement:
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all.
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction enables >>>>>>>>>>>>>>>>>>>>>>> the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>>> statement can be proven as true.
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use a >>>>>>>>>>>>>>>>>>>>>> system that has a contradiction.
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that prevents >>>>>>>>>>>>>>>>>>>>> infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses its >>>>>>>>>>>>>>>>>>>> basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion#Proof >>>>>>>>>>>>>>>>>
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>> exists a statement X such that the condition "At least >>>>>>>>>>>>>>>> one of the following statements is true" is false. >>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction.
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>> exist a statement X such that the condition "At least one >>>>>>>>>>>>>> of the following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>>
The statement you gave isn't a truth-bearing statement, so it >>>>>>>>>> can't be used in logic. I didn't think I had to make that >>>>>>>>>> explicit.
However, let's go with it anyway because it still illustrates >>>>>>>>>> the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>
On second though, let's back up as that might confuse you.
Given that <X> is any *truth bearing* natural language
statement, does there exist a statement X such that the
condition "At least one of the following statements is true" is >>>>>>>>> false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is >>>>>>> a head game in your next reply or within one hour of you next
post in this newsgroup will be taken as your official, on-the-
record admission that Disjunction introduction is in fact truth >>>>>>> preserving and valid, and therefore so is the Principle of
Explosion.
Let the record show that Peter Olcott made the following post in
this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the
above question or explain why it is a head game. Therefore, as
per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and
valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different rules.
That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
One can construct a system where a truth-preserving operation is not
valid, and must if one wants to construct a paraconsistent system,
where some but not every sentence can be both PTS-true and PTS-false.
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who >>>>>>>>>>> don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Model theory was created only because keeping semantics
directly within logic at the time was too complicated.
It did make logic easier to work with and it also made
logic diverge from correct reasoning.
In a formal context the formal system specifies what reasoning is
correct. In real world application the sules of ordinary logic are empirically correct, i.e., no situation is observed where the rules
of logic are violated.
Only people having actual psychosis would conclude
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
A proof in a formal system is a finite string that satisfies certain syntactic rules specifiec for the system. There is no reference to
any semantics.
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who >>>>>>>>>>>> don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
There is nothing semantically meaningful about a
contradiction that derives anything at all besides FALSE.
There is nothing semantically meaningful about FALSE
that derives anything at all besides FALSE.
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record admission
that Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above question or explain why it is a head game. Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even know >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>>>> statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use a >>>>>>>>>>>>>>>>>>>>>>> system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>> exists a statement X such that the condition "At least >>>>>>>>>>>>>>>>> one of the following statements is true" is false. >>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>> exist a statement X such that the condition "At least one >>>>>>>>>>>>>>> of the following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so it >>>>>>>>>>> can't be used in logic. I didn't think I had to make that >>>>>>>>>>> explicit.
However, let's go with it anyway because it still illustrates >>>>>>>>>>> the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>>
On second though, let's back up as that might confuse you. >>>>>>>>>>
Given that <X> is any *truth bearing* natural language
statement, does there exist a statement X such that the
condition "At least one of the following statements is true" >>>>>>>>>> is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is >>>>>>>> a head game in your next reply or within one hour of you next >>>>>>>> post in this newsgroup will be taken as your official, on-the- >>>>>>>> record admission that Disjunction introduction is in fact truth >>>>>>>> preserving and valid, and therefore so is the Principle of
Explosion.
Let the record show that Peter Olcott made the following post in >>>>>>> this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the >>>>>>> above question or explain why it is a head game. Therefore, as >>>>>>> per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and
valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting with
the precondition that a contradiction has been proven, as you have
admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and
the Moon is not made from green cheese and Donald Trump is not the one
and only Lord and Savior Jesus Christ?
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural >>>>>>>>>>>>>>>>>> language statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of statement where eachstatement either is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>>>>> statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use >>>>>>>>>>>>>>>>>>>>>>>> a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At least >>>>>>>>>>>>>>>>>> one of the following statements is true" is false. >>>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
Given that the following natural language statement is >>>>>>>>>>>>>>>> true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>>> exist a statement X such that the condition "At least >>>>>>>>>>>>>>>> one of the following statements is true" is false? >>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so >>>>>>>>>>>> it can't be used in logic. I didn't think I had to make >>>>>>>>>>>> that explicit.
However, let's go with it anyway because it still
illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>>>
On second though, let's back up as that might confuse you. >>>>>>>>>>>
Given that <X> is any *truth bearing* natural language
statement, does there exist a statement X such that the >>>>>>>>>>> condition "At least one of the following statements is true" >>>>>>>>>>> is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it >>>>>>>>> is a head game in your next reply or within one hour of you >>>>>>>>> next post in this newsgroup will be taken as your official, on- >>>>>>>>> the- record admission that Disjunction introduction is in fact >>>>>>>>> truth preserving and valid, and therefore so is the Principle >>>>>>>>> of Explosion.
Let the record show that Peter Olcott made the following post in >>>>>>>> this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the >>>>>>>> above question or explain why it is a head game. Therefore, as >>>>>>>> per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and >>>>>>>> valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting
with the precondition that a contradiction has been proven, as you
have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and
the Moon is not made from green cheese and Donald Trump is not the one
and only Lord and Savior Jesus Christ?
Counter-factual
On 6/30/2026 2:55 AM, Mikko wrote:
On 29/06/2026 16:23, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even know >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>>>> statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use a >>>>>>>>>>>>>>>>>>>>>>> system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>> exists a statement X such that the condition "At least >>>>>>>>>>>>>>>>> one of the following statements is true" is false. >>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
Given that the following natural language statement is true: >>>>>>>>>>>>>>>
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>> exist a statement X such that the condition "At least one >>>>>>>>>>>>>>> of the following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so it >>>>>>>>>>> can't be used in logic. I didn't think I had to make that >>>>>>>>>>> explicit.
However, let's go with it anyway because it still illustrates >>>>>>>>>>> the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>>
On second though, let's back up as that might confuse you. >>>>>>>>>>
Given that <X> is any *truth bearing* natural language
statement, does there exist a statement X such that the
condition "At least one of the following statements is true" >>>>>>>>>> is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is >>>>>>>> a head game in your next reply or within one hour of you next >>>>>>>> post in this newsgroup will be taken as your official, on-the- >>>>>>>> record admission that Disjunction introduction is in fact truth >>>>>>>> preserving and valid, and therefore so is the Principle of
Explosion.
Let the record show that Peter Olcott made the following post in >>>>>>> this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the >>>>>>> above question or explain why it is a head game. Therefore, as >>>>>>> per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and
valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
One can construct a system where a truth-preserving operation is not
valid, and must if one wants to construct a paraconsistent system,
where some but not every sentence can be both PTS-true and PTS-false.
Current semantic entailment is the only inference step allowed.
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who >>>>>>>>>>>> don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who >>>>>>>>>>>> don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is
off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
On 30/06/2026 17:37, olcott wrote:
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural >>>>>>>>>>>>>>>>>>> language statement:
On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>1) P ∧ ¬P // Premise
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of statement where eachstatement either >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is a premis or follows from one or more >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration >>>>>>>>>>>>>>>>>>>>>>>>> of *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid >>>>>>>>>>>>>>>>>>>>>>>>> of the principle of explosion is to be able to >>>>>>>>>>>>>>>>>>>>>>>>> use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>> - <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>> least one of the following statements is true" is false. >>>>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
Given that the following natural language statement is >>>>>>>>>>>>>>>>> true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement: >>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>>>> exist a statement X such that the condition "At least >>>>>>>>>>>>>>>>> one of the following statements is true" is false? >>>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so >>>>>>>>>>>>> it can't be used in logic. I didn't think I had to make >>>>>>>>>>>>> that explicit.
However, let's go with it anyway because it still
illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>> true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>
Given that <X> is any *truth bearing* natural language >>>>>>>>>>>> statement, does there exist a statement X such that the >>>>>>>>>>>> condition "At least one of the following statements is true" >>>>>>>>>>>> is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it >>>>>>>>>> is a head game in your next reply or within one hour of you >>>>>>>>>> next post in this newsgroup will be taken as your official, >>>>>>>>>> on- the- record admission that Disjunction introduction is in >>>>>>>>>> fact truth preserving and valid, and therefore so is the
Principle of Explosion.
Let the record show that Peter Olcott made the following post >>>>>>>>> in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the >>>>>>>>> above question or explain why it is a head game. Therefore, as >>>>>>>>> per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and >>>>>>>>> valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting
with the precondition that a contradiction has been proven, as you
have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and
the Moon is not made from green cheese and Donald Trump is not the one
and only Lord and Savior Jesus Christ?
Counter-factual
For logic the distinction between factual and counter-factual is not
as imortant as the distinction between consistent and contradictory.
As long as the premises are consistent they may be true about
some situation even if they are false in the intended interpretation. Contradictory premises cannot be all true in any interpretation.
From contradictory or otherwise false premises it is possible to
infer both true and false conclusions.
On 30/06/2026 16:45, olcott wrote:
On 6/30/2026 2:55 AM, Mikko wrote:
On 29/06/2026 16:23, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural >>>>>>>>>>>>>>>>>> language statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of statement where eachstatement either is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>>>>> statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use >>>>>>>>>>>>>>>>>>>>>>>> a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At least >>>>>>>>>>>>>>>>>> one of the following statements is true" is false. >>>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
Given that the following natural language statement is >>>>>>>>>>>>>>>> true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>>> exist a statement X such that the condition "At least >>>>>>>>>>>>>>>> one of the following statements is true" is false? >>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so >>>>>>>>>>>> it can't be used in logic. I didn't think I had to make >>>>>>>>>>>> that explicit.
However, let's go with it anyway because it still
illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>>>
On second though, let's back up as that might confuse you. >>>>>>>>>>>
Given that <X> is any *truth bearing* natural language
statement, does there exist a statement X such that the >>>>>>>>>>> condition "At least one of the following statements is true" >>>>>>>>>>> is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it >>>>>>>>> is a head game in your next reply or within one hour of you >>>>>>>>> next post in this newsgroup will be taken as your official, on- >>>>>>>>> the- record admission that Disjunction introduction is in fact >>>>>>>>> truth preserving and valid, and therefore so is the Principle >>>>>>>>> of Explosion.
Let the record show that Peter Olcott made the following post in >>>>>>>> this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the >>>>>>>> above question or explain why it is a head game. Therefore, as >>>>>>>> per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and >>>>>>>> valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
One can construct a system where a truth-preserving operation is not
valid, and must if one wants to construct a paraconsistent system,
where some but not every sentence can be both PTS-true and PTS-false.
Current semantic entailment is the only inference step allowed.
Every truth-prserving transformation is a correct semantic entailment.
In particular, disjunction introduction is.
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who >>>>>>>>>>>>> don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>> the rejection of the classically valid principle of Addition, >>>>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people who >>>>>>>>>>>>> don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem.
So you're saying that in the following natural language statement: >>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
On 7/1/2026 1:50 AM, Mikko wrote:
On 30/06/2026 16:45, olcott wrote:
On 6/30/2026 2:55 AM, Mikko wrote:
On 29/06/2026 16:23, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural >>>>>>>>>>>>>>>>>>> language statement:
On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>1) P ∧ ¬P // Premise
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of statement where eachstatement either >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is a premis or follows from one or more >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration >>>>>>>>>>>>>>>>>>>>>>>>> of *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid >>>>>>>>>>>>>>>>>>>>>>>>> of the principle of explosion is to be able to >>>>>>>>>>>>>>>>>>>>>>>>> use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>> - <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>> least one of the following statements is true" is false. >>>>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
Given that the following natural language statement is >>>>>>>>>>>>>>>>> true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement: >>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>>>> exist a statement X such that the condition "At least >>>>>>>>>>>>>>>>> one of the following statements is true" is false? >>>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so >>>>>>>>>>>>> it can't be used in logic. I didn't think I had to make >>>>>>>>>>>>> that explicit.
However, let's go with it anyway because it still
illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>> true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>
Given that <X> is any *truth bearing* natural language >>>>>>>>>>>> statement, does there exist a statement X such that the >>>>>>>>>>>> condition "At least one of the following statements is true" >>>>>>>>>>>> is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it >>>>>>>>>> is a head game in your next reply or within one hour of you >>>>>>>>>> next post in this newsgroup will be taken as your official, >>>>>>>>>> on- the- record admission that Disjunction introduction is in >>>>>>>>>> fact truth preserving and valid, and therefore so is the
Principle of Explosion.
Let the record show that Peter Olcott made the following post >>>>>>>>> in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the >>>>>>>>> above question or explain why it is a head game. Therefore, as >>>>>>>>> per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and >>>>>>>>> valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
One can construct a system where a truth-preserving operation is not
valid, and must if one wants to construct a paraconsistent system,
where some but not every sentence can be both PTS-true and PTS-false.
Current semantic entailment is the only inference step allowed.
Every truth-prserving transformation is a correct semantic entailment.
In particular, disjunction introduction is.
That is counter-factual. POE is misconstrued as truth preserving.
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record admission
that Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above question or explain why it is a head game. Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
On 7/1/2026 2:32 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>
statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
Parry’s logic of Analytic Implication
and Relevance logic are two sensible systems
that get rid of the Principle of Explosion.
It was dead-obviously correct to anyone paying
any attention at all that every contradiction
only semantically entails FALSE.
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record admission
that Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above question or explain why it is a head game. Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
On 7/1/2026 11:25 AM, olcott wrote:
On 7/1/2026 2:32 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere >>>>>>>>>>>>>> (as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>>> eachstatement either is a premis or follows from one or >>>>>>>>>>>>> more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
Parry’s logic of Analytic Implication
and Relevance logic are two sensible systems
that get rid of the Principle of Explosion.
It was dead-obviously correct to anyone paying
any attention at all that every contradiction
only semantically entails FALSE.
False, as you have admitted on the record:
On 6/28/2026 11:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record admission
that Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
> Q also can't bake a birthday cake, this does not make
> Q in any way "incomplete" relative to what it was
> defined to do.
> ...
And more that one hour has passed with no attempt to answer the above question or explain why it is a head game. Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
On 7/1/2026 12:37 PM, dbush wrote:
On 7/1/2026 11:25 AM, olcott wrote:
On 7/1/2026 2:32 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when >>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>> where eachstatement either is a premis or follows from one >>>>>>>>>>>>>> or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable. >>>>>>>> Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
Parry’s logic of Analytic Implication
and Relevance logic are two sensible systems
that get rid of the Principle of Explosion.
It was dead-obviously correct to anyone paying
any attention at all that every contradiction
only semantically entails FALSE.
False, as you have admitted on the record:
Liar
On 6/28/2026 11:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:one
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:;
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
Given that the following natural language statement is true:
;
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
;
In the following natural language statement:
;
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least
admission;of the following statements is true" is false?;
;
Head games will be ignored.
;
Explain in detail how this is a head game.
;
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record
abovethat Disjunction introduction is in fact truth preserving and valid,;
and therefore so is the Principle of Explosion.
;
Let the record show that Peter Olcott made the following post in this
newsgroup:
;
On 6/28/2026 10:52 PM, olcott wrote:
; > Q also can't bake a birthday cake, this does not make
; > Q in any way "incomplete" relative to what it was
; > defined to do.
; > ...
;
And more that one hour has passed with no attempt to answer the above
question or explain why it is a head game. Therefore, as per the
criteria:valid, and
;
Let The Record Show
;
That Peter Olcott
;
Has *Officially* Admitted:
;
That Disjunction introduction is in fact truth preserving and
therefore so is the Principle of Explosion.
On 7/1/2026 1:46 AM, Mikko wrote:
On 30/06/2026 17:37, olcott wrote:
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>> language statement:
On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>1) P ∧ ¬P // Premise
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> valid principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ψ is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> implication — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derivation of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of statement where eachstatement either >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is a premis or follows from one or more >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is its problem. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration >>>>>>>>>>>>>>>>>>>>>>>>>> of *why* a formal system whose axioms lead to >>>>>>>>>>>>>>>>>>>>>>>>>> a contradiction is useless. >>>>>>>>>>>>>>>>>>>>>>>>>>
The only reason someone would want to get rid >>>>>>>>>>>>>>>>>>>>>>>>>> of the principle of explosion is to be able to >>>>>>>>>>>>>>>>>>>>>>>>>> use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning. >>>>>>>>>>>>>>>>>>>>>>>>>
If you get rid of the principle of explosion, >>>>>>>>>>>>>>>>>>>>>>>> the law of non- contradiction goes away as it >>>>>>>>>>>>>>>>>>>>>>>> looses its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>>> least one of the following statements is true" is >>>>>>>>>>>>>>>>>>>> false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
Given that the following natural language statement is >>>>>>>>>>>>>>>>>> true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement: >>>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does >>>>>>>>>>>>>>>>>> there exist a statement X such that the condition "At >>>>>>>>>>>>>>>>>> least one of the following statements is true" is false? >>>>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>> sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so >>>>>>>>>>>>>> it can't be used in logic. I didn't think I had to make >>>>>>>>>>>>>> that explicit.
However, let's go with it anyway because it still >>>>>>>>>>>>>> illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>> true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>>
Given that <X> is any *truth bearing* natural language >>>>>>>>>>>>> statement, does there exist a statement X such that the >>>>>>>>>>>>> condition "At least one of the following statements is >>>>>>>>>>>>> true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it >>>>>>>>>>> is a head game in your next reply or within one hour of you >>>>>>>>>>> next post in this newsgroup will be taken as your official, >>>>>>>>>>> on- the- record admission that Disjunction introduction is in >>>>>>>>>>> fact truth preserving and valid, and therefore so is the >>>>>>>>>>> Principle of Explosion.
Let the record show that Peter Olcott made the following post >>>>>>>>>> in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer >>>>>>>>>> the above question or explain why it is a head game.
Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and >>>>>>>>>> valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>> sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different >>>>>>>> rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting
with the precondition that a contradiction has been proven, as you >>>>>> have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and
the Moon is not made from green cheese and Donald Trump is not the one >>>> and only Lord and Savior Jesus Christ?
Counter-factual
For logic the distinction between factual and counter-factual is not
as imortant as the distinction between consistent and contradictory.
Counter-factual may indicate a psychotic break from reality.
On 7/1/2026 1:50 AM, Mikko wrote:
On 30/06/2026 16:45, olcott wrote:
On 6/30/2026 2:55 AM, Mikko wrote:
On 29/06/2026 16:23, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural >>>>>>>>>>>>>>>>>>> language statement:
On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>1) P ∧ ¬P // Premise
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of statement where eachstatement either >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is a premis or follows from one or more >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration >>>>>>>>>>>>>>>>>>>>>>>>> of *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid >>>>>>>>>>>>>>>>>>>>>>>>> of the principle of explosion is to be able to >>>>>>>>>>>>>>>>>>>>>>>>> use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>> - <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>> least one of the following statements is true" is false. >>>>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
Given that the following natural language statement is >>>>>>>>>>>>>>>>> true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement: >>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>>>> exist a statement X such that the condition "At least >>>>>>>>>>>>>>>>> one of the following statements is true" is false? >>>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so >>>>>>>>>>>>> it can't be used in logic. I didn't think I had to make >>>>>>>>>>>>> that explicit.
However, let's go with it anyway because it still
illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>> true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>
Given that <X> is any *truth bearing* natural language >>>>>>>>>>>> statement, does there exist a statement X such that the >>>>>>>>>>>> condition "At least one of the following statements is true" >>>>>>>>>>>> is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it >>>>>>>>>> is a head game in your next reply or within one hour of you >>>>>>>>>> next post in this newsgroup will be taken as your official, >>>>>>>>>> on- the- record admission that Disjunction introduction is in >>>>>>>>>> fact truth preserving and valid, and therefore so is the
Principle of Explosion.
Let the record show that Peter Olcott made the following post >>>>>>>>> in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the >>>>>>>>> above question or explain why it is a head game. Therefore, as >>>>>>>>> per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and >>>>>>>>> valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
One can construct a system where a truth-preserving operation is not
valid, and must if one wants to construct a paraconsistent system,
where some but not every sentence can be both PTS-true and PTS-false.
Current semantic entailment is the only inference step allowed.
Every truth-prserving transformation is a correct semantic entailment.
In particular, disjunction introduction is.
That is counter-factual. POE is misconstrued as truth preserving.
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>
statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
On 7/1/2026 2:32 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>
statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
Parry’s logic of Analytic Implication
and Relevance logic are two sensible systems
that get rid of the Principle of Explosion.
On 01/07/2026 18:01, olcott wrote:
On 7/1/2026 1:46 AM, Mikko wrote:
On 30/06/2026 17:37, olcott wrote:
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:30 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>> language statement:1) P ∧ ¬P // PremiseExplain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> valid principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ψ is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> implication — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derivation of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> another sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of nowhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sequence of statement where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eachstatement either is a premis or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is its problem. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Rejected, as you not liking the result >>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't make it invalid. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration >>>>>>>>>>>>>>>>>>>>>>>>>>> of *why* a formal system whose axioms lead to >>>>>>>>>>>>>>>>>>>>>>>>>>> a contradiction is useless. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The only reason someone would want to get rid >>>>>>>>>>>>>>>>>>>>>>>>>>> of the principle of explosion is to be able >>>>>>>>>>>>>>>>>>>>>>>>>>> to use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of >>>>>>>>>>>>>>>>>>>>>>>>>> explosion
it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning. >>>>>>>>>>>>>>>>>>>>>>>>>>
If you get rid of the principle of explosion, >>>>>>>>>>>>>>>>>>>>>>>>> the law of non- contradiction goes away as it >>>>>>>>>>>>>>>>>>>>>>>>> looses its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth- >>>>>>>>>>>>>>>>>>>>>>> preserving operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>>>> least one of the following statements is true" is >>>>>>>>>>>>>>>>>>>>> false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then. >>>>>>>>>>>>>>>>>>>
Given that the following natural language statement >>>>>>>>>>>>>>>>>>> is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement: >>>>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>> - <X>
--------------------------------------
Where <X> is any natural language statement, does >>>>>>>>>>>>>>>>>>> there exist a statement X such that the condition "At >>>>>>>>>>>>>>>>>>> least one of the following statements is true" is false? >>>>>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>>> sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, >>>>>>>>>>>>>>> so it can't be used in logic. I didn't think I had to >>>>>>>>>>>>>>> make that explicit.
However, let's go with it anyway because it still >>>>>>>>>>>>>>> illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>>> true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>>>
Given that <X> is any *truth bearing* natural language >>>>>>>>>>>>>> statement, does there exist a statement X such that the >>>>>>>>>>>>>> condition "At least one of the following statements is >>>>>>>>>>>>>> true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how >>>>>>>>>>>> it is a head game in your next reply or within one hour of >>>>>>>>>>>> you next post in this newsgroup will be taken as your >>>>>>>>>>>> official, on- the- record admission that Disjunction
introduction is in fact truth preserving and valid, and >>>>>>>>>>>> therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post >>>>>>>>>>> in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make >>>>>>>>>>> > Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer >>>>>>>>>>> the above question or explain why it is a head game.
Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and >>>>>>>>>>> valid, and therefore so is the Principle of Explosion.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>> formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different >>>>>>>>> rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting >>>>>>> with the precondition that a contradiction has been proven, as
you have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and >>>>> the Moon is not made from green cheese and Donald Trump is not the one >>>>> and only Lord and Savior Jesus Christ?
Counter-factual
For logic the distinction between factual and counter-factual is not
as imortant as the distinction between consistent and contradictory.
Counter-factual may indicate a psychotic break from reality.
No, it does not. It is much more common than anything psychotic.
Besudes, any mention of anything psychotic is off-topic in these
groups.
On 01/07/2026 18:06, olcott wrote:
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere >>>>>>>>>>>>>> (as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>>> eachstatement either is a premis or follows from one or >>>>>>>>>>>>> more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
So is any semantics other than real world semantics.
On 01/07/2026 18:25, olcott wrote:
On 7/1/2026 2:32 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere >>>>>>>>>>>>>> (as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>>> eachstatement either is a premis or follows from one or >>>>>>>>>>>>> more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
Parry’s logic of Analytic Implication
and Relevance logic are two sensible systems
that get rid of the Principle of Explosion.
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
On 7/2/2026 1:21 AM, Mikko wrote:
On 01/07/2026 18:01, olcott wrote:
On 7/1/2026 1:46 AM, Mikko wrote:
On 30/06/2026 17:37, olcott wrote:
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:30 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>> language statement:1) P ∧ ¬P // PremiseExplain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Except with Disjunction introduction, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is its problem. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I figured >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knew that when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> another sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>A simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> valid principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> where ψ is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> implication — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derivation of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of nowhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sequence of statement where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eachstatement either is a premis or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Rejected, as you not liking the result >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't make it invalid. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a >>>>>>>>>>>>>>>>>>>>>>>>>>>> demonstration of *why* a formal system whose >>>>>>>>>>>>>>>>>>>>>>>>>>>> axioms lead to a contradiction is useless. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The only reason someone would want to get >>>>>>>>>>>>>>>>>>>>>>>>>>>> rid of the principle of explosion is to be >>>>>>>>>>>>>>>>>>>>>>>>>>>> able to use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>> explosion
it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning. >>>>>>>>>>>>>>>>>>>>>>>>>>>
If you get rid of the principle of explosion, >>>>>>>>>>>>>>>>>>>>>>>>>> the law of non- contradiction goes away as it >>>>>>>>>>>>>>>>>>>>>>>>>> looses its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth- >>>>>>>>>>>>>>>>>>>>>>>> preserving operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>>>>> least one of the following statements is true" is >>>>>>>>>>>>>>>>>>>>>> false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then. >>>>>>>>>>>>>>>>>>>>
Given that the following natural language statement >>>>>>>>>>>>>>>>>>>> is true:
-------------------------------------- >>>>>>>>>>>>>>>>>>>> Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>> -------------------------------------- >>>>>>>>>>>>>>>>>>>>
In the following natural language statement: >>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, does >>>>>>>>>>>>>>>>>>>> there exist a statement X such that the condition >>>>>>>>>>>>>>>>>>>> "At least one of the following statements is true" >>>>>>>>>>>>>>>>>>>> is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>>>> sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, >>>>>>>>>>>>>>>> so it can't be used in logic. I didn't think I had to >>>>>>>>>>>>>>>> make that explicit.
However, let's go with it anyway because it still >>>>>>>>>>>>>>>> illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>> sun" true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>>>>
Given that <X> is any *truth bearing* natural language >>>>>>>>>>>>>>> statement, does there exist a statement X such that the >>>>>>>>>>>>>>> condition "At least one of the following statements is >>>>>>>>>>>>>>> true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how >>>>>>>>>>>>> it is a head game in your next reply or within one hour of >>>>>>>>>>>>> you next post in this newsgroup will be taken as your >>>>>>>>>>>>> official, on- the- record admission that Disjunction >>>>>>>>>>>>> introduction is in fact truth preserving and valid, and >>>>>>>>>>>>> therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following >>>>>>>>>>>> post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make >>>>>>>>>>>> > Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer >>>>>>>>>>>> the above question or explain why it is a head game.
Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving >>>>>>>>>>>> and valid, and therefore so is the Principle of Explosion. >>>>>>>>>>>>
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>
the rejection of the classically valid principle of Addition, >>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>
other words, the principle leading from a formula ϕ to a >>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different >>>>>>>>>> rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting >>>>>>>> with the precondition that a contradiction has been proven, as >>>>>>>> you have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and >>>>>> the Moon is not made from green cheese and Donald Trump is not the >>>>>> one
and only Lord and Savior Jesus Christ?
Counter-factual
For logic the distinction between factual and counter-factual is not
as imortant as the distinction between consistent and contradictory.
Counter-factual may indicate a psychotic break from reality.
No, it does not. It is much more common than anything psychotic.
Besudes, any mention of anything psychotic is off-topic in these
groups.
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction" https://en.wikipedia.org/wiki/Principle_of_explosion
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record admission
that Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above question or explain why it is a head game. Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
On 7/2/2026 1:21 AM, Mikko wrote:
On 01/07/2026 18:01, olcott wrote:
On 7/1/2026 1:46 AM, Mikko wrote:
On 30/06/2026 17:37, olcott wrote:
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:30 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>> language statement:1) P ∧ ¬P // PremiseExplain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Except with Disjunction introduction, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is its problem. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I figured >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knew that when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> another sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>A simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> valid principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> where ψ is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> implication — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derivation of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of nowhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sequence of statement where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eachstatement either is a premis or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Rejected, as you not liking the result >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't make it invalid. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a >>>>>>>>>>>>>>>>>>>>>>>>>>>> demonstration of *why* a formal system whose >>>>>>>>>>>>>>>>>>>>>>>>>>>> axioms lead to a contradiction is useless. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The only reason someone would want to get >>>>>>>>>>>>>>>>>>>>>>>>>>>> rid of the principle of explosion is to be >>>>>>>>>>>>>>>>>>>>>>>>>>>> able to use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>> explosion
it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning. >>>>>>>>>>>>>>>>>>>>>>>>>>>
If you get rid of the principle of explosion, >>>>>>>>>>>>>>>>>>>>>>>>>> the law of non- contradiction goes away as it >>>>>>>>>>>>>>>>>>>>>>>>>> looses its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth- >>>>>>>>>>>>>>>>>>>>>>>> preserving operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>>>>> least one of the following statements is true" is >>>>>>>>>>>>>>>>>>>>>> false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then. >>>>>>>>>>>>>>>>>>>>
Given that the following natural language statement >>>>>>>>>>>>>>>>>>>> is true:
-------------------------------------- >>>>>>>>>>>>>>>>>>>> Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>> -------------------------------------- >>>>>>>>>>>>>>>>>>>>
In the following natural language statement: >>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, does >>>>>>>>>>>>>>>>>>>> there exist a statement X such that the condition >>>>>>>>>>>>>>>>>>>> "At least one of the following statements is true" >>>>>>>>>>>>>>>>>>>> is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>>>> sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, >>>>>>>>>>>>>>>> so it can't be used in logic. I didn't think I had to >>>>>>>>>>>>>>>> make that explicit.
However, let's go with it anyway because it still >>>>>>>>>>>>>>>> illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>> sun" true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>>>>
Given that <X> is any *truth bearing* natural language >>>>>>>>>>>>>>> statement, does there exist a statement X such that the >>>>>>>>>>>>>>> condition "At least one of the following statements is >>>>>>>>>>>>>>> true" is false?
Head games will be ignored.
That you did so well on the other things
so I will not block you.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how >>>>>>>>>>>>> it is a head game in your next reply or within one hour of >>>>>>>>>>>>> you next post in this newsgroup will be taken as your >>>>>>>>>>>>> official, on- the- record admission that Disjunction >>>>>>>>>>>>> introduction is in fact truth preserving and valid, and >>>>>>>>>>>>> therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following >>>>>>>>>>>> post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make >>>>>>>>>>>> > Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer >>>>>>>>>>>> the above question or explain why it is a head game.
Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving >>>>>>>>>>>> and valid, and therefore so is the Principle of Explosion. >>>>>>>>>>>>
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>
the rejection of the classically valid principle of Addition, >>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>
other words, the principle leading from a formula ϕ to a >>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different >>>>>>>>>> rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting >>>>>>>> with the precondition that a contradiction has been proven, as >>>>>>>> you have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and >>>>>> the Moon is not made from green cheese and Donald Trump is not the >>>>>> one
and only Lord and Savior Jesus Christ?
Counter-factual
For logic the distinction between factual and counter-factual is not
as imortant as the distinction between consistent and contradictory.
Counter-factual may indicate a psychotic break from reality.
No, it does not. It is much more common than anything psychotic.
Besudes, any mention of anything psychotic is off-topic in these
groups.
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction" https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
On 7/2/2026 1:29 AM, Mikko wrote:
On 01/07/2026 18:06, olcott wrote:
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when >>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>> where eachstatement either is a premis or follows from one >>>>>>>>>>>>>> or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable. >>>>>>>> Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
So is any semantics other than real world semantics.
Hypotheticals are useful for making decisions.
On 7/2/2026 1:31 AM, Mikko wrote:
On 01/07/2026 18:25, olcott wrote:
On 7/1/2026 2:32 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when >>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>> where eachstatement either is a premis or follows from one >>>>>>>>>>>>>> or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable. >>>>>>>> Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
Parry’s logic of Analytic Implication
and Relevance logic are two sensible systems
that get rid of the Principle of Explosion.
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
But false is false even if the proof is
something less obvious.
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:29 AM, Mikko wrote:
On 01/07/2026 18:06, olcott wrote:
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>> where eachstatement either is a premis or follows from >>>>>>>>>>>>>>> one or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable. >>>>>>>>> Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies >>>>>>> of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
So is any semantics other than real world semantics.
Hypotheticals are useful for making decisions.
Which is an example of the usefulness of a break from reality. It
als shows that calling a break from reality "psychotic" without
further consideration.
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
but I think that most of people would consder
getting rid of fires is more rational that getting rid of fire
alarms.
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth. My correction to the Principle of Explosion:
(P ∧ ~P) ⊢ FALSE
FALSE ⊢ FALSE
but I think that most of people would consder
getting rid of fires is more rational that getting rid of fire
alarms.
It is not a fire alarm it is getting rid of semantics
within inference. My correct reasoning correction to
logic gets rid of every type of inference besides
semantic entailment.
Validity and Soundness
A deductive argument is said to be valid if
and only if it takes a form that makes it
impossible for the premises to be true and
the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to
be invalid. https://iep.utm.edu/val-snd/
*That big mistake is corrected thusly*
A deductive argument is said to be valid if
and only if its conclusion is a necessary
consequence of all of its premises Otherwise,
a deductive argument is said to be invalid.
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
On 7/3/2026 3:22 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:29 AM, Mikko wrote:
On 01/07/2026 18:06, olcott wrote:
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>> people who don't
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>>> where eachstatement either is a premis or follows from >>>>>>>>>>>>>>>> one or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable. >>>>>>>>>> Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies >>>>>>>> of a false premise, which already is a break from reality even >>>>>>>> when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
So is any semantics other than real world semantics.
Hypotheticals are useful for making decisions.
Which is an example of the usefulness of a break from reality. It
als shows that calling a break from reality "psychotic" without
further consideration.
That Donald Trump might start WW III is a hypothetical
that can possibly be is useful.
That Donald Trump is the one and only Lord and Savior Jesus Christ
is a hypothetical that cannot possible be making it useless.
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth.
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
(P ∧ ~P) ⊢ FALSE // is what can really be proved semantically
On 6/27/2026 11:34 PM, dbush wrote:--- Synchronet 3.22a-Linux NewsLink 1.2
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record admission
that Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above question or explain why it is a head game. Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
On 03/07/2026 18:04, olcott wrote:
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth. My correction to the Principle of Explosion:
(P ∧ ~P) ⊢ FALSE
FALSE ⊢ FALSE
but I think that most of people would consder
getting rid of fires is more rational that getting rid of fire
alarms.
It is not a fire alarm it is getting rid of semantics
within inference. My correct reasoning correction to
logic gets rid of every type of inference besides
semantic entailment.
Getting rid of any type of inference does not make much difference
as long as you get the same conclusions through other inferences.
Only getting rid of some conscusions it makes a significant
difference. But you have never shown an example of getting rid of
a conclusion without losing a semantic entailment.
Validity and Soundness
A deductive argument is said to be valid if
and only if it takes a form that makes it
impossible for the premises to be true and
the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to
be invalid. https://iep.utm.edu/val-snd/
*That big mistake is corrected thusly*
A deductive argument is said to be valid if
and only if its conclusion is a necessary
consequence of all of its premises Otherwise,
a deductive argument is said to be invalid.
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
You don't need any of above if you have ¬, ∨, and ∧.
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
□ is a unary operator and
an expression like P □ Q makes absolutely no sense.
If you want to use this as a binary operator you'd actually need to
*define* it. You don't seem to grasp this. You can't just introduce a
new operator and expect people to know what it means.
Also, moving into the domain of modal logic would be an incredibly
strange thing for you to do given that in previous posts you claimed to
reject the idea of models. But modal logic is *replete* with models.
Modal logic operates over a set of many models. □P means that P is true
in all accessible models of the system.
André
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
□ is a unary operator and an expression like P □ Q makes absolutely no >> sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
If you want to use this as a binary operator you'd actually need to
*define* it. You don't seem to grasp this. You can't just introduce a
new operator and expect people to know what it means.
□ Already means necessity, it is not that hard unless
one makes great effort to pretend to not understand
what is already unequivocally clear. >
Also, moving into the domain of modal logic would be an incredibly
strange thing for you to do given that in previous posts you claimed to
The only thing that I am using is logical necessity.
reject the idea of models. But modal logic is *replete* with models.
Modal logic operates over a set of many models. □P means that P is
true in all accessible models of the system.
André
On 03/07/2026 17:50, olcott wrote:
On 7/3/2026 3:22 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
Hypotheticals are useful for making decisions.
Which is an example of the usefulness of a break from reality. It
als shows that calling a break from reality "psychotic" without
further consideration.
That Donald Trump might start WW III is a hypothetical
that can possibly be is useful.
Whether Donald Trump will start WW III is not yet known, so that
cannot be called an example of counter-factual.
That Donald Trump is the one and only Lord and Savior Jesus Christ
is a hypothetical that cannot possible be making it useless.
Maybe, but irrelevent as you did not claim it be useful when you
presented it.
On 03/07/2026 18:04, olcott wrote:
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth.
You did not compute correctely, let aloone coherently, whether
I an irrational. You onlu presented your opinion about it.
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes absolutely >>> no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
not as the nonsensical P □
Q. But you claim to have gotten rid of →, so how this is to be
interpreted remains a mystery (and getting rid of → makes no sense since → represents a specific truth table which still exists regardless of whether you've assigned a symbol to it or not)
If you want to use this as a binary operator you'd actually need to
*define* it. You don't seem to grasp this. You can't just introduce a
new operator and expect people to know what it means.
□ Already means necessity, it is not that hard unless
one makes great effort to pretend to not understand
what is already unequivocally clear. >
Also, moving into the domain of modal logic would be an incredibly
strange thing for you to do given that in previous posts you claimed to
The only thing that I am using is logical necessity.
So how would you interpret 'necessity' without models?
André
reject the idea of models. But modal logic is *replete* with models.
Modal logic operates over a set of many models. □P means that P is
true in all accessible models of the system.
André
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes absolutely >>>> no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So how would you interpret 'necessity' without models?
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes absolutely >>>>> no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity between
P and Q". Necessity applies to propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean something other than that you're really going to have to clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If a
truth table contains any symbol other than T or F, you're dealing with a three or more valued logic which means you have to completely redefine
every single logical operator before you can proceed.
And there's nothing about the above table which in any way captures the meaning of 'necessity' so it's entirely unclear why you want to use the
□ symbol here. Your '□' doesn't have any relation to necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it for
some ill-defined binary operation as well. You need a new symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use of
models?
André
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes
absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't hold
*between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean
something other than that you're really going to have to clarify what
you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If a
truth table contains any symbol other than T or F, you're dealing with
a three or more valued logic which means you have to completely
redefine every single logical operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
And there's nothing about the above table which in any way captures
the meaning of 'necessity' so it's entirely unclear why you want to
use the □ symbol here. Your '□' doesn't have any relation to necessity >> any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it
for some ill-defined binary operation as well. You need a new symbol
since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal logic
is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use of
models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes
absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't hold
*between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean
something other than that you're really going to have to clarify what
you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If a
truth table contains any symbol other than T or F, you're dealing
with a three or more valued logic which means you have to completely
redefine every single logical operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt to explain what is meant by this (by you).
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you can't do that, then your use of 'necessary' is completely meaningless verbiage.
And there's nothing about the above table which in any way captures
the meaning of 'necessity' so it's entirely unclear why you want to
use the □ symbol here. Your '□' doesn't have any relation to
necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it
for some ill-defined binary operation as well. You need a new symbol
since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal logic
is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use of
models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes
absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't hold
*between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean
something other than that you're really going to have to clarify
what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If a
truth table contains any symbol other than T or F, you're dealing
with a three or more valued logic which means you have to completely
redefine every single logical operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt to
explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you can't
do that, then your use of 'necessary' is completely meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
And there's nothing about the above table which in any way captures
the meaning of 'necessity' so it's entirely unclear why you want to
use the □ symbol here. Your '□' doesn't have any relation to
necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it
for some ill-defined binary operation as well. You need a new symbol
since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal
logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use of
models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't
hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean
something other than that you're really going to have to clarify
what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If
a truth table contains any symbol other than T or F, you're dealing >>>>> with a three or more valued logic which means you have to
completely redefine every single logical operator before you can
proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt to
explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you can't
do that, then your use of 'necessary' is completely meaningless
verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between 'necessary consequence' and mere 'consequence'. The two examples above don't even mention the word 'necessary'.
And there's nothing about the above table which in any way captures >>>>> the meaning of 'necessity' so it's entirely unclear why you want to >>>>> use the □ symbol here. Your '□' doesn't have any relation to
necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it >>>>> for some ill-defined binary operation as well. You need a new
symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal
logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use
of models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
No.
André
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't
hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>> something other than that you're really going to have to clarify
what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If >>>>>> a truth table contains any symbol other than T or F, you're
dealing with a three or more valued logic which means you have to >>>>>> completely redefine every single logical operator before you can
proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt
to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you
can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between 'necessary
consequence' and mere 'consequence'. The two examples above don't even
mention the word 'necessary'.
And there's nothing about the above table which in any way
captures the meaning of 'necessity' so it's entirely unclear why
you want to use the □ symbol here. Your '□' doesn't have any
relation to necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as >>>>>> operator overloading, so you can't take a unary operator and use
it for some ill-defined binary operation as well. You need a new
symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal
logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use >>>>>> of models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
No.
André
Truth Tables ARE Propositional Model Theory
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity >>>>>>> between P and Q". Necessity applies to propositions. It doesn't >>>>>>> hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>>> something other than that you're really going to have to clarify >>>>>>> what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. >>>>>>> If a truth table contains any symbol other than T or F, you're
dealing with a three or more valued logic which means you have to >>>>>>> completely redefine every single logical operator before you can >>>>>>> proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt
to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither 'impossibly
false' nor 'impossibly true' are English.
In English, 'impossibly x'
does not mean 'not possible to be x'. 'Impossibly' is an *itensifier*
with a meaning of extremely. So 'impossibly true' would mean 'extremely true', which makes no sense since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you
can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between 'necessary
consequence' and mere 'consequence'. The two examples above don't
even mention the word 'necessary'.
This question was the central point of my post and you have ignored it.
I maintain that when you use the term 'necessary' your just tossing in a meaningless word for no reason. If you can answer the above question you will show me wrong.
And there's nothing about the above table which in any way
captures the meaning of 'necessity' so it's entirely unclear why >>>>>>> you want to use the □ symbol here. Your '□' doesn't have any >>>>>>> relation to necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing >>>>>>> as operator overloading, so you can't take a unary operator and >>>>>>> use it for some ill-defined binary operation as well. You need a >>>>>>> new symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal >>>>>>> logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use >>>>>>> of models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
No.
André
Truth Tables ARE Propositional Model Theory
No they're not. Truth tables are used to define the basic operators in a truth-functional logic.
Please evaluate the propositional calculus expression P → Q. Without knowing what P or Q stand for you cannot do this. The model tells you
what P and Q actually mean making it possible to assign a truth value to
P → Q.
André
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity >>>>>>>> between P and Q". Necessity applies to propositions. It doesn't >>>>>>>> hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>>>> something other than that you're really going to have to clarify >>>>>>>> what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. >>>>>>>> If a truth table contains any symbol other than T or F, you're >>>>>>>> dealing with a three or more valued logic which means you have >>>>>>>> to completely redefine every single logical operator before you >>>>>>>> can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt >>>>>> to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither 'impossibly
false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense
since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you
can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between 'necessary
consequence' and mere 'consequence'. The two examples above don't
even mention the word 'necessary'.
This question was the central point of my post and you have ignored
it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
If Q is a necessary consequence of P then
we are not allowed to infer anything from ~P
And there's nothing about the above table which in any way
captures the meaning of 'necessity' so it's entirely unclear why >>>>>>>> you want to use the □ symbol here. Your '□' doesn't have any >>>>>>>> relation to necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing >>>>>>>> as operator overloading, so you can't take a unary operator and >>>>>>>> use it for some ill-defined binary operation as well. You need a >>>>>>>> new symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal >>>>>>>> logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making >>>>>>>> use of models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
No.
André
Truth Tables ARE Propositional Model Theory
No they're not. Truth tables are used to define the basic operators in
a truth-functional logic.
Please evaluate the propositional calculus expression P → Q. Without
knowing what P or Q stand for you cannot do this. The model tells you
what P and Q actually mean making it possible to assign a truth value
to P → Q.
André
In propositional logic they are only Boolean variables
with zero additional meaning besides true and false.
If you think otherwise then cite a source.
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete
necessity between P and Q". Necessity applies to propositions. >>>>>>>>> It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>>>>> something other than that you're really going to have to
clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. >>>>>>>>> If a truth table contains any symbol other than T or F, you're >>>>>>>>> dealing with a three or more valued logic which means you have >>>>>>>>> to completely redefine every single logical operator before you >>>>>>>>> can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any
attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither 'impossibly
false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both perfectly well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense
since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you >>>>>>> can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples
above don't even mention the word 'necessary'.
This question was the central point of my post and you have ignored
it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete
necessity between P and Q". Necessity applies to propositions. >>>>>>>>>> It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>>>>>> something other than that you're really going to have to
clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued
logic. If a truth table contains any symbol other than T or F, >>>>>>>>>> you're dealing with a three or more valued logic which means >>>>>>>>>> you have to completely redefine every single logical operator >>>>>>>>>> before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any
attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both perfectly
well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense
since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you >>>>>>>> can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples
above don't even mention the word 'necessary'.
This question was the central point of my post and you have ignored
it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 1
1 0 0
1 1 1
On 2026-07-04 19:18, olcott wrote:
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete
necessity between P and Q". Necessity applies to
propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you >>>>>>>>>>> mean something other than that you're really going to have to >>>>>>>>>>> clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued >>>>>>>>>>> logic. If a truth table contains any symbol other than T or >>>>>>>>>>> F, you're dealing with a three or more valued logic which >>>>>>>>>>> means you have to completely redefine every single logical >>>>>>>>>>> operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any
attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English. >>>>>>>
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both perfectly
well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense >>>>> since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you >>>>>>>>> can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples >>>>>>> above don't even mention the word 'necessary'.
This question was the central point of my post and you have ignored >>>>> it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Your definitions are not coherent.
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 1
1 0 0
1 1 1
That's simply the truth table for 'and'. It sheds no light on what it is your trying to convey by your use of 'necessity'. And the operator □ is already taken and is not a truth-functional operator so reusing it for something else is just plain stupid.
On 7/4/2026 8:28 PM, André G. Isaak wrote:
On 2026-07-04 19:18, olcott wrote:
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete >>>>>>>>>>>> necessity between P and Q". Necessity applies to
propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you >>>>>>>>>>>> mean something other than that you're really going to have >>>>>>>>>>>> to clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued >>>>>>>>>>>> logic. If a truth table contains any symbol other than T or >>>>>>>>>>>> F, you're dealing with a three or more valued logic which >>>>>>>>>>>> means you have to completely redefine every single logical >>>>>>>>>>>> operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any >>>>>>>>>> attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English. >>>>>>>>
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both
perfectly well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no
sense since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If >>>>>>>>>> you can't do that, then your use of 'necessary' is completely >>>>>>>>>> meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples >>>>>>>> above don't even mention the word 'necessary'.
This question was the central point of my post and you have
ignored it. I maintain that when you use the term 'necessary' your >>>>>> just tossing in a meaningless word for no reason. If you can
answer the above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Your definitions are not coherent.
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 1
1 0 0
1 1 1
That's simply the truth table for 'and'. It sheds no light on what it
is your trying to convey by your use of 'necessity'. And the operator
□ is already taken and is not a truth-functional operator so reusing
it for something else is just plain stupid.
Dogs are cats → Monkeys have wings
¬(Dogs are cats □ Monkeys have wings)
On 2026-07-04 19:18, olcott wrote:
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete
necessity between P and Q". Necessity applies to
propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you >>>>>>>>>>> mean something other than that you're really going to have to >>>>>>>>>>> clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued >>>>>>>>>>> logic. If a truth table contains any symbol other than T or >>>>>>>>>>> F, you're dealing with a three or more valued logic which >>>>>>>>>>> means you have to completely redefine every single logical >>>>>>>>>>> operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any
attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English. >>>>>>>
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both perfectly
well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense >>>>> since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you >>>>>>>>> can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples >>>>>>> above don't even mention the word 'necessary'.
This question was the central point of my post and you have ignored >>>>> it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Your definitions are not coherent.
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
That's simply the truth table for 'and'.
It sheds no light on what it is
your trying to convey by your use of 'necessity'. And the operator □ is already taken and is not a truth-functional operator so reusing it for something else is just plain stupid.
And snipping my question doesn't make it go away:
Can you give an example where (a) hold true but where (b) does not. An example from ordinary English is fine.
a) Q is a consequence of P
b) Q is a necessary consequence of P.
If you can't, your use of the term 'necessary' serves absolutely no
purpose.
André
On 7/4/2026 8:28 PM, André G. Isaak wrote:
On 2026-07-04 19:18, olcott wrote:
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete >>>>>>>>>>>> necessity between P and Q". Necessity applies to
propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you >>>>>>>>>>>> mean something other than that you're really going to have >>>>>>>>>>>> to clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued >>>>>>>>>>>> logic. If a truth table contains any symbol other than T or >>>>>>>>>>>> F, you're dealing with a three or more valued logic which >>>>>>>>>>>> means you have to completely redefine every single logical >>>>>>>>>>>> operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any >>>>>>>>>> attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English. >>>>>>>>
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both
perfectly well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no
sense since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If >>>>>>>>>> you can't do that, then your use of 'necessary' is completely >>>>>>>>>> meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples >>>>>>>> above don't even mention the word 'necessary'.
This question was the central point of my post and you have
ignored it. I maintain that when you use the term 'necessary' your >>>>>> just tossing in a meaningless word for no reason. If you can
answer the above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Your definitions are not coherent.
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
That's simply the truth table for 'and'.
It had a typo
It sheds no light on what it is your trying to convey by your use of
'necessity'. And the operator □ is already taken and is not a
truth-functional operator so reusing it for something else is just
plain stupid.
And snipping my question doesn't make it go away:
Can you give an example where (a) hold true but where (b) does not. An
example from ordinary English is fine.
a) Q is a consequence of P
b) Q is a necessary consequence of P.
If you can't, your use of the term 'necessary' serves absolutely no
purpose.
Q is a necessary consequence of P
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
On 2026-07-04 21:17, olcott wrote:
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P Q □
0 0 0
0 1 0
1 0 0
1 1 1
That's *not* a valid truth table. It has no entry for P = 0 and Q = 1.
And Parry is working in relevance logic. He doesn't deal with modal expressions like 'necessary'.
André
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
Changes the notion of valid inference too much.
I myself simply leap all the way to the end and
say that the full natural language semantic meaning
must be encoded for both P and Q such that P ⊢ Q
by semantic entailment specified syntactically.
This is accomplished in a language such as CycL. https://en.wikipedia.org/wiki/CycL
On 2026-07-04 21:17, olcott wrote:
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
Changes the notion of valid inference too much.
It doesn't change anything. It's simply invalid since its not a well-
formed truth table.
I myself simply leap all the way to the end and
say that the full natural language semantic meaning
must be encoded for both P and Q such that P ⊢ Q
by semantic entailment specified syntactically.
This is accomplished in a language such as CycL.
https://en.wikipedia.org/wiki/CycL
The above sheds no light on anything. In particular it doesn't clarify
what you think the difference between entailment and necessary
entailment is which is the question I have been trying to get you to address.
On 7/4/2026 10:52 PM, André G. Isaak wrote:
On 2026-07-04 21:17, olcott wrote:
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
Changes the notion of valid inference too much.
It doesn't change anything. It's simply invalid since its not a well-
formed truth table.
I myself simply leap all the way to the end and
say that the full natural language semantic meaning
must be encoded for both P and Q such that P ⊢ Q
by semantic entailment specified syntactically.
This is accomplished in a language such as CycL.
https://en.wikipedia.org/wiki/CycL
The above sheds no light on anything. In particular it doesn't clarify
what you think the difference between entailment and necessary
entailment is which is the question I have been trying to get you to
address.
*This says the whole thing better*
P ⊢ Q means: syntactic derivation implements semantic entailment encoded in the language. The inference rules are syntactic rules that realize semantic entailment. These are the only allowed inference steps. The entailment rules depend on the represented domain.
Dogs are cats ⊢ Monkeys have wings // rejected
On 2026-07-04 22:05, olcott wrote:
On 7/4/2026 10:52 PM, André G. Isaak wrote:
On 2026-07-04 21:17, olcott wrote:
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
Changes the notion of valid inference too much.
It doesn't change anything. It's simply invalid since its not a well-
formed truth table.
I myself simply leap all the way to the end and
say that the full natural language semantic meaning
must be encoded for both P and Q such that P ⊢ Q
by semantic entailment specified syntactically.
This is accomplished in a language such as CycL.
https://en.wikipedia.org/wiki/CycL
The above sheds no light on anything. In particular it doesn't
clarify what you think the difference between entailment and
necessary entailment is which is the question I have been trying to
get you to address.
*This says the whole thing better*
P ⊢ Q means: syntactic derivation implements semantic entailment
encoded in the language. The inference rules are syntactic rules that
realize semantic entailment. These are the only allowed inference
steps. The entailment rules depend on the represented domain.
Dogs are cats ⊢ Monkeys have wings // rejected
The topic under discussion was Q, which contains neither dogs, cats, monkeys, or wings.
Why don't you illustrate your claim with an actual example from
arithmetic. Say, for example 9 × 5 = 45. What exactly would be the "semantic entailments encoded in the language" involved here?
André
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