From Newsgroup: comp.theory

At the most fundamental level:
All Turing machines only compute the mapping
from input finite strings to some value.

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

A further elaboration of this comes from the
notion of computable functions and Rice's
Theorem:

Turing machine deciders compute functions from
*finite string inputs* to {accept, reject} values
according to whether the input has a syntactic
property or specifies a semantic property.

Turing machine deciders only report on the behavior
of Turing machines indirectly through the proxy of
finite string inputs. *This key detail has been ignored*
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/13/25 11:44 AM, olcott wrote:

At the most fundamental level:
All Turing machines only compute the mapping
from input finite strings to some value.

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

A further elaboration of this comes from the
notion of computable functions and Rice's
Theorem:

Turing machine deciders compute functions from
*finite string inputs* to {accept, reject} values
according to whether the input has a syntactic
property or specifies a semantic property.

Turing machine deciders only report on the behavior
of Turing machines indirectly through the proxy of
finite string inputs. *This key detail has been ignored*

So, if the function isn't "Computable", it is still a Function, but no
Turing Machine (or equivalent) can compute it.

Nothing says that the Halting Function is computable, and in fact, the
Halting Problem proof says it is not.

This doesn't make it "invalid", just not computable.

Thus, there can not exist an actual Halt Decider, as Halting as defined
just isn't a computable function.

This also doesn't mean that the string can't have the semantic meaning
of the behavior of the Machine it describes, we just find that Semantic Properties tend not to be Computable, as Turing Machines are powerful
enough to break any Decider trying to decide on an actual Semantic Property.

This is just like an any logic system with sufficient power (roughly
able to express the poperties of the Natural Numbers) will have
statements that are true in them, but are not provable.

There is a isomophism between Computability and Provability.
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From Newsgroup: comp.theory

On 13/12/2025 16:44, olcott wrote:

At the most fundamental level:
All Turing machines only compute the mapping
from input finite strings to some value.

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

I continue to reject the use of "accept" and "reject" here. And I also
reject the use of "indicates" wrt to them.

There's no good reason to suppose this is about grammars and strings
rather than propositions about programs. To the extent that they might
be isomorphic you need to introduce the notion of grammars and string acceptance by them to give "accept" and "reject" and "indicates" the
correct meaning.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/13/2025 1:33 PM, Tristan Wibberley wrote:

On 13/12/2025 16:44, olcott wrote:

At the most fundamental level:
All Turing machines only compute the mapping
from input finite strings to some value.

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

I continue to reject the use of "accept" and "reject" here. And I also
reject the use of "indicates" wrt to them.

My goal is to have accepted definitions as my only basis.

There's no good reason to suppose this is about grammars and strings
rather than propositions about programs. To the extent that they might
be isomorphic you need to introduce the notion of grammars and string acceptance by them to give "accept" and "reject" and "indicates" the
correct meaning.

This is a grammatically correct English sentence:
"flpm erf09-25k (*&j^*&NJ*&jkNef", reject.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/13/2025 1:14 PM, Richard Damon wrote:

On 12/13/25 11:44 AM, olcott wrote:

At the most fundamental level:
All Turing machines only compute the mapping
from input finite strings to some value.

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

A further elaboration of this comes from the
notion of computable functions and Rice's
Theorem:

Turing machine deciders compute functions from
*finite string inputs* to {accept, reject} values
according to whether the input has a syntactic
property or specifies a semantic property.

Turing machine deciders only report on the behavior
of Turing machines indirectly through the proxy of
finite string inputs. *This key detail has been ignored*

So, if the function isn't "Computable", it is still a Function, but no Turing Machine (or equivalent) can compute it.

There seems to be no such thing as uncomputable
functions when Turing machines are construed
entirely in terms of finite string rewrite rules.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/13/25 3:13 PM, olcott wrote:

On 12/13/2025 1:14 PM, Richard Damon wrote:

On 12/13/25 11:44 AM, olcott wrote:

At the most fundamental level:
All Turing machines only compute the mapping
from input finite strings to some value.

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

A further elaboration of this comes from the
notion of computable functions and Rice's
Theorem:

Turing machine deciders compute functions from
*finite string inputs* to {accept, reject} values
according to whether the input has a syntactic
property or specifies a semantic property.

Turing machine deciders only report on the behavior
of Turing machines indirectly through the proxy of
finite string inputs. *This key detail has been ignored*

So, if the function isn't "Computable", it is still a Function, but no
Turing Machine (or equivalent) can compute it.

There seems to be no such thing as uncomputable
functions when Turing machines are construed
entirely in terms of finite string rewrite rules.

Sure there are, Your problem is you have the ideas reversed.

Not all functions need to be generatable by Turing Machine.

Those that can not be, are uncomputable.

Since not all Functions, that is generic mappings of the complete set of
one domain, to anther, can be implemented in Turing Machines, not all
are computable.

If you think there doesn't exist an uncomputable Function, show me how
you compute the Halting Function, being the mapping of a Turing Machine
(with its input) to whether it halts or not.

Since you have tried to claim that it is impossible to even ask this
question of a Decider, it must be non-computable.

But of course, you get a lot of things backwards since you chose to work
with zero-principle knowledge.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 13/12/2025 18:44, olcott wrote:

At the most fundamental level:
All Turing machines only compute the mapping
from input finite strings to some value.

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

A further elaboration of this comes from the
notion of computable functions and Rice's
Theorem:

Turing machine deciders compute functions from
*finite string inputs* to {accept, reject} values
according to whether the input has a syntactic
property or specifies a semantic property.

Every property a Turing machine can compute is a syntactic property.
A Turing machine sees only its input. It does not see any neaning of
the input. Therefore it has no access to semantic properties. A
semantic property can be computed only if it is equivalent to a
syntactic property.
--
Mikko
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 13/12/2025 19:50, olcott wrote:

On 12/13/2025 1:33 PM, Tristan Wibberley wrote:

On 13/12/2025 16:44, olcott wrote:

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

I continue to reject the use of "accept" and "reject" here. And I also
reject the use of "indicates" wrt to them.

My goal is to have accepted definitions as my only basis.

Oh! I just noticed it's a new statement with "by some criterion measure"
which makes it excellent. I retract my rejection.


[snip]

This is a grammatically correct English sentence:
"flpm erf09-25k (*&j^*&NJ*&jkNef", reject.

That's impertinent.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/14/2025 6:51 AM, Tristan Wibberley wrote:

On 13/12/2025 19:50, olcott wrote:

On 12/13/2025 1:33 PM, Tristan Wibberley wrote:

On 13/12/2025 16:44, olcott wrote:

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

I continue to reject the use of "accept" and "reject" here. And I also
reject the use of "indicates" wrt to them.

My goal is to have accepted definitions as my only basis.

Oh! I just noticed it's a new statement with "by some criterion measure" which makes it excellent. I retract my rejection.

Good.

This is my first post on the halting Problem https://groups.google.com/g/sci.logic/c/V7wzVvx8IMw/m/ggPE6a-60cUJ

I worked for 15 years mostly on the basis of intuition.
Then 2 more years creating fully operational code. Then
3 years of discussing this code.

Now I am finally getting around to anchoring these
intuitions and my working code in standard definitions.

My current working code.
https://github.com/plolcott/x86utm/blob/master/Halt7.c

I had to refrain from learning the standard definitions
before now or they would have boxed me into the standard
views.

My insights are entirely from slight nuances of meaning
that are abstracted away in the standard definitions.

I had to carefully reverse-engineer the exact details
of what was actually happening before I could see what
nuances of meaning were being left out. Initially I
had to use my own non-standard terminology to do this.

This is my first principle
All Turing machines only compute the mapping
from input finite strings to some value.

Second Principle
Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

Third Principle (rough draft)
Turing machine halt deciders only report on
the behavior of Turing Machines through the
proxy of finite string inputs. The behavior
specified by the finite string input overrules
any other behavior.

[snip]

This is a grammatically correct English sentence:
"flpm erf09-25k (*&j^*&NJ*&jkNef", reject.

That's impertinent.

Sometimes required to put things in sharp focus.
I just proved that reject is a valid operation.
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 14/12/2025 16:16, polcott wrote:

This is my first principle
All Turing machines only compute the mapping
from input finite strings to some value.

I maintain that's wrong. it should be "compute only".

You previously said it means the same either way around but that's not
true for "only" even if it's true for many adverbs because of a
syntactic ambiguity due to the many parts of speech "only" can fulfil.

[only compute] [the <something>]
[compute] [only the <something>]

the first can actually be wrong if nonterminating programs (ie, keep
operating without making progress producing a result) are not said to
compute, which I'm told they are not. Those turing machines do not
compute so it can't be that compute is the only thing they do.

That the only thing they compute is <something> could be true depending
on the <something>, which is another matter.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/14/2025 3:00 PM, Tristan Wibberley wrote:

On 14/12/2025 16:16, polcott wrote:

This is my first principle
All Turing machines only compute the mapping
from input finite strings to some value.

I maintain that's wrong. it should be "compute only".

All Turing machines compute only the mapping
from input finite strings to some value.

Computable functions are the basic objects of study
in computability theory. Informally, a function is
computable if there is an algorithm that computes
the value of the function for every value of its argument. https://en.wikipedia.org/wiki/Computable_function

Now we tie that to a model of computation:
Turing machines computable functions only compute
the mapping from input finite strings to some value.

*I might just use this as the new first principle*
Turing machine Deciders compute the mapping from
input finite strings to an accept or reject value
by some criterion measure.

You previously said it means the same either way around but that's not
true for "only" even if it's true for many adverbs because of a
syntactic ambiguity due to the many parts of speech "only" can fulfil.

[only compute] [the <something>]
[compute] [only the <something>]

the first can actually be wrong if nonterminating programs (ie, keep operating without making progress producing a result) are not said to compute, which I'm told they are not. Those turing machines do not
compute so it can't be that compute is the only thing they do.

Your correction is correct.

That the only thing they compute is <something> could be true depending
on the <something>, which is another matter.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/14/2025 4:43 AM, Mikko wrote:

On 13/12/2025 18:44, olcott wrote:

At the most fundamental level:
All Turing machines only compute the mapping
from input finite strings to some value.

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

A further elaboration of this comes from the
notion of computable functions and Rice's
Theorem:

Turing machine deciders compute functions from
*finite string inputs* to {accept, reject} values
according to whether the input has a syntactic
property or specifies a semantic property.

Every property a Turing machine can compute is a syntactic property.
A Turing machine sees only its input. It does not see any neaning of
the input. Therefore it has no access to semantic properties. A
semantic property can be computed only if it is equivalent to a
syntactic property.

If that was true then Rice's theorem would be
wrong before it even got started.

In computability theory, Rice's theorem states
that all non-trivial semantic properties of
programs are undecidable. A semantic property
is one about the program's behavior https://en.wikipedia.org/wiki/Rice%27s_theorem
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except as noted in
the sig.

On 14/12/2025 16:16, polcott wrote:

On 12/14/2025 6:51 AM, Tristan Wibberley wrote:

On 13/12/2025 19:50, olcott wrote:

On 12/13/2025 1:33 PM, Tristan Wibberley wrote:

On 13/12/2025 16:44, olcott wrote:

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

I continue to reject the use of "accept" and "reject" here. And I also >>>> reject the use of "indicates" wrt to them.

My goal is to have accepted definitions as my only basis.

Oh! I just noticed it's a new statement with "by some criterion measure"
which makes it excellent. I retract my rejection.

Good.

This is my first post on the halting Problem https://groups.google.com/g/sci.logic/c/V7wzVvx8IMw/m/ggPE6a-60cUJ

I worked for 15 years mostly on the basis of intuition.
Then 2 more years creating fully operational code. Then
3 years of discussing this code.

Now I am finally getting around to anchoring these
intuitions and my working code in standard definitions.

My current working code. https://github.com/plolcott/x86utm/blob/master/Halt7.c

I had to refrain from learning the standard definitions
before now or they would have boxed me into the standard
views.

My insights are entirely from slight nuances of meaning
that are abstracted away in the standard definitions.

I had to carefully reverse-engineer the exact details
of what was actually happening before I could see what
nuances of meaning were being left out. Initially I
had to use my own non-standard terminology to do this.

This is my first principle
All Turing machines only compute the mapping
from input finite strings to some value.

My second correction of three that are needed (I will return to the
third later once I've thought more):

"value" is not defined, a first principle must be elementary (introduces
terms of art but does not depend on them).

Here are two alternatives to illuminate the matter, but I think they're
not good enough:

1st alternative: You need a prior principle defining "value". That's not entirely intuitive though we pretend it is, like so much that you
correctly find to be a problem.

2nd alternative: All Automatic Turing Machines compute only an output
finite string from an input finite string.

They're wrong because a turing machine has a state (m-configuration),
whose change--and given a constant initial state then also itself--is,
in effect, computed.

The 3rd alternative is contingent as noted, a contingency whose premise
I think you suppose:

3rd alternative, admissible when considering an ATM to be a physical
machine rather than a mere formal system: An Automatic Turing Machine is
one of those things restricted--at least in part--such that it computes
nothing more than an output finite string along with its own halting
state from an input finite string along with its own pre-nominated
initial state.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 15/12/2025 01:46, olcott wrote:

On 12/14/2025 4:43 AM, Mikko wrote:

On 13/12/2025 18:44, olcott wrote:

At the most fundamental level:
All Turing machines only compute the mapping
from input finite strings to some value.

Turing machine Deciders are a subset of this
where the value indicates accept or reject a
finite string by some criterion measure.

A further elaboration of this comes from the
notion of computable functions and Rice's
Theorem:

Turing machine deciders compute functions from
*finite string inputs* to {accept, reject} values
according to whether the input has a syntactic
property or specifies a semantic property.

Every property a Turing machine can compute is a syntactic property.
A Turing machine sees only its input. It does not see any neaning of
the input. Therefore it has no access to semantic properties. A
semantic property can be computed only if it is equivalent to a
syntactic property.

If that was true then Rice's theorem would be
wrong before it even got started.

No, the Rice's theorem does not imply that the Rice's theorem be wrong.

In computability theory, Rice's theorem states
that all non-trivial semantic properties of
programs are undecidable. A semantic property
is one about the program's behavior https://en.wikipedia.org/wiki/Rice%27s_theorem

Where non-trivial means 'not equivalent to a syntactic property'.
--
Mikko
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