XPost: comp.theory, sci.math, sci.lang
XPost: comp.lang.prolog
From: polcott333@gmail.com
On 2/6/2026 8:33 PM, Richard Damon wrote:
> On 2/6/26 9:16 PM, olcott wrote:
>> On 2/6/2026 7:54 PM, Richard Damon wrote:
>>> On 2/6/26 8:13 PM, olcott wrote:
>>>> On 2/6/2026 6:23 PM, Richard Damon wrote:
>>
>> What is an expression of language that has no meaning?
>
> That is your problem, you can't figure out how to make it have the
> meaning you want.
{Meaningless} did not occur to you?
>
> The language of mathematics FULLY understand Godel's statment, but
you > need it to have no meaning.
>
Truth Conditional Semantics fails.
Proof Theoretic Semantics succeeds.
> Either you accept the language of methematics, which assigns meaning
> based on infinite sequences of operation, and thus is NOT compatible
> with your proof-theoretic semantic, or you admit that your system can't
> actually handle the meaning of the langugae that you claim to handle.
>
If these are not algorithmically compressed
that remain outside of the body of knowledge.
>>>
>>> Godel's proof shows the limitiation of Proof-Theoretic Semantics in a
>>> mathematical system.
>>>
>>
>> Not in the least little bit.
>
> Sure it does, you are just to ignorant to understand the problem
>
>>
>>> He creates a perfectly semantic statement
>>
>> In the wrong semantic system.
>
> In other words, you ADMIT that your system can't handle the semantics of
> basic mathematics,
>
It utterly replaces Truth conditional semantics with
proof theoretic semantics.
> After all, the final statement is just expressed using the language of
> basic mathematics.
>
Not at all. The truth predicates have entirely
different basis.
>>
>>> as a relationship that can be finitely tested for any number. He then
>>> ask a complete semantically reasonable question about that
>>> relationship, does a number exist that satisfies it, making an
>>> assertion that it does not.
>>>
>>> This SHOULD have meaning in a system that understands the mathematics.
>>>
>>> But, by the rules of proof-theoretic semantics, The statement can
>>> only be considered to be true if we could prove it, and false if we
>>> could prove its converse, or declared non-well-founded if we could
>>> prove that neither of those can be shown,
>>
>> Yes.
>>
>
> So, you ADMIT that you system is self-contradictory, by using Truth-
> Condition semantics but also rejects them.
>
My system has always used "proof theoretic semantics"
and this is many years before I even knew that term.
>>
>>>> *THE MEANING IN ALL FORMAL MATHEMATICAL AND NATURAL LANGUAGES*
>>>
>>> Then you accept the Formal Logic definition of "Truth" that means
>>> what can be demonstrated by an infinite sequence of steps, and thus
>>> reject you proposition that something is only true if it can be proven.
>>>
>>>
>>
>> We have been over this quite a few time now.
>> Anything requiring an infinite number of steps
>> is outside the domain of knowledge.
>>
>
> But not out of the domain of TRUTH.
>
> And our domain of knowledge accepts that domain of truth.
>
> Your problem is you don't understand the difference, because you just
> don't understand truth.
>
We have two entirely different foundations of truth
Truth conditional semantics
proof theoretic semantics
There truth predicates have an entirely different basis.
>>
>>
>>>>
>>>> *Good job, you got the most important point exactly correctly*
>>>> Non-well-founded means not truth-apt.
>>>
>>> So, you accept that your "Proof-Theoretic" system uses Truth-
>>> Conditional meaning, as you can't actually PROVE that something is
>>> Truth_Apt.
>>>
>>
>> ABSOLUTELY NOT EVER. WHERE THE HELL DID YOU GET THAT ???
>> ABSOLUTELY NOT EVER. WHERE THE HELL DID YOU GET THAT ???
>> ABSOLUTELY NOT EVER. WHERE THE HELL DID YOU GET THAT ???
>
> How does it determine that something is not well founded if you can't
> prove it.
>
> Your "Truth-Apt" needs Truth-Conditional interpretation or your last
> statement can't be correct.
>
It does not need Truth-Conditional interpretation
Truth-Conditional interpretation has always been
totally wrong-headed.
> The problem is that while you can determine SOME conditions that make a
> statement True, you can't determine if something is ~True, unless you
> can can actually prove that converse.
>
~Provable(x) ⇒ ~True(x)
>>
>> "true on the basis of meaning expressed in language"
>> Including formal mathematical languages and natural language
>> Where the meaning of expressions is only defined in terms
>> of other expressions makes the entire body of knowledge
>> that can be expressed in language nothing more than
>> computable relations between finite strings.
>>
>
> Then it accept Truth by infinite sequence of operations.
>
It accepts that they exist and rejects that their result is
in the domain of knowledge.
> And thus it accepts that Godel's G statement is true in PA, as by
> testing ALL Natural Numbers (an infinite number of numbers to test) we
> see that none of them satisfies the statement.
>
∀x (Provable(PA, x) ⇒ True(PA, x))
> Note, the Relationship being tested is just defined by normal
> mathematical operations, fully defined in PA. (It was BUILT in the meta-
> math, but to only use the operations defined in basic PA).
>
Truth conditional semantics is model theory that has
been rejected as erroneous. Gödel Incompleteness
cannot exist in Proof Theoretic Semantics.
--
Copyright 2026 Olcott
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
This required establishing a new foundation
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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