• Re: The simple essence of Proof Theoretic Semantics

    From Mikko@mikko.levanto@iki.fi to sci.logic,comp.theory,sci.math,comp.ai.philosophy,comp.lang.c on Fri Jul 3 12:22:47 2026
    From Newsgroup: comp.lang.c

    On 02/07/2026 17:51, olcott wrote:
    On 7/2/2026 1:57 AM, Mikko wrote:
    On 02/07/2026 07:03, olcott wrote:
    On 7/1/2026 11:01 PM, dbush wrote:
    On 7/1/2026 11:59 PM, olcott wrote:
    On 7/1/2026 10:43 PM, dbush wrote:
    On 7/1/2026 11:37 PM, olcott wrote:
    On 7/1/2026 10:18 PM, dbush wrote:
    On 7/1/2026 11:17 PM, olcott wrote:
    On 7/1/2026 10:00 PM, dbush wrote:
    On 7/1/2026 10:53 PM, olcott wrote:
    On 7/1/2026 9:36 PM, dbush wrote:
    On 7/1/2026 7:37 PM, olcott wrote:
    On 7/1/2026 4:15 PM, dbush wrote:
    On 7/1/2026 5:04 PM, olcott wrote:
    On 7/1/2026 3:57 PM, dbush wrote:
    On 7/1/2026 4:50 PM, olcott wrote:
    On 7/1/2026 3:37 PM, dbush wrote:
    On 7/1/2026 4:29 PM, olcott wrote:
    On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote:
    On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>
    The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>> expressed in
    English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>
    I didn't ask for an example.  I asked for a >>>>>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value >>>>>>>>>>>>>>>>>>>>>>>>> of a statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>
    I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>>>>>>>> doesn't get that examples don't take the place >>>>>>>>>>>>>>>>>>>>>>>> of definitions. Examples can be useful for >>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>
    André


    You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>
    Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>
    André


    True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright
    Olcott 2018
    has been updated to this

    True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>
    That claims what it means to have the truth value >>>>>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined >>>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It doesn't in any >>>>>>>>>>>>>>>>>>>> way clarify what you think it means for something to >>>>>>>>>>>>>>>>>>>> not have a truth value.

    André


    When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>> and your fault.


    You gave no such definition of what it means for the >>>>>>>>>>>>>>>>>> truth value of a statement to not exist in a formal >>>>>>>>>>>>>>>>>> system.

    A valid answer would look something like this: >>>>>>>>>>>>>>>>>>
    "The truth value of a statement does not exist in a >>>>>>>>>>>>>>>>>> formal system when ..."

    Now complete the sentence.

    It is neither provable nor refutable in F.

    Good.  So when you say "The truth value of (∀ x, S(x) ≠ >>>>>>>>>>>>>>>> x) does not exist in Q", you mean "(∀ x, S(x) ≠ x) is >>>>>>>>>>>>>>>> unprovable in Q", which is commonly known.

    So once again, you're saying the same thing as everyone >>>>>>>>>>>>>>>> else but using different words.


    Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>>>>>
    False.  It means that there are statements in the language >>>>>>>>>>>>>> of Q that have *only* an infinite connection to the axioms >>>>>>>>>>>>>> of the system.


    OK, I verified that.


    The Halting Problem counter-example input

    Which starts with the assumption that an algorithm H >>>>>>>>>>>>>> exists that meets the following requirements:

    Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>>>>>>>> instructions) X described as <X> with input Y:

    A solution to the halting problem is an algorithm H that >>>>>>>>>>>>>> computes the following mapping:

    (<X>,Y) maps to 1 if and only if X(Y) halts when executed >>>>>>>>>>>>>> directly
    (<X>,Y) maps to 0 if and only if X(Y) does not halt when >>>>>>>>>>>>>> executed directly


    Sure and we could equally start with the requirement >>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>>
    I really don't see how everyone did not immediately see >>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>> first five minutes that this requirement was made.

    In other words, you don't understand that if this was >>>>>>>>>>>> algorithm H:


    I spent 10,000 hours on it over 22 years.

    And still don't understand that this algorithm:


    void D(ptr *I)
    {
         ptr *X = D;
         ptr *Y = I;
         int result;
         {
             result = 0;
         }
         if (result == 1) {
             while (1);
         }
    }

    Is the counter example input to this algorithm:

    int H(ptr *X, ptr *Y)
    {
         int result;
         {
             result = 0;
         }
         return result;
    }


    That is just nonsense.


    Thereby proving that you've misunderstood the halting problem >>>>>>>> for the last 22 years.

    D(D);   // merely halts
    H(D,D); // merely returns 0 and never looks at D(D)

    And algorithm H is wrong about algorithm D because algorithm D
    contains a copy of algorithm H and does the opposite.

    You just don't know jack shit dufus.
    I have been a professional C programmer since 1986.


    Says the person that just demonstrated that they don't know the
    difference between an algorithm and a C function.


    Back to being ignored for trolling again.

    Maybe by someone but you are still far from being ignored by everone.

    Do you know enough about C to understand that
    dbush example was foolish nonsense when proposed
    to show the halting problem counter-example?

    It is a valid example of a C program. It was present as a part of a
    claim about you, and your response was the false claim that "That
    is just nonsense". Later in the discussion you offer more evidence
    to support his claim.
    --
    Mikko

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