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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Why Tarski is wrong --- Montague, Davidson and Knowledge Ontology
 providing situational context.
Date: Fri, 21 Mar 2025 20:01:50 -0400
Organization: i2pn2 (i2pn.org)
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On 3/21/25 6:44 PM, olcott wrote:
> On 3/21/2025 2:30 PM, Keith Thompson wrote:
>> Richard Heathfield <rjh@cpax.org.uk> writes:
>>> On 21/03/2025 08:11, Mikko wrote:
>>>
>>> <snip>
>>>
>>>> Another part of human knowledge is that there are fools that try to
>>>> argue against proven theorems.
>>>
>>> Well, if it ain't proven it ain't yet a theorem. But is that enough?
>>>
>>> The background to the work of Church, Turing, Gödel and the like is
>>> Hilbert's second problem: "The compatibility of the arithmetical
>>> axioms", and the background to /that/ problem is that in the late 19th
>>> century mathematicians were occasionally coming up with proofs of X,
>>> only to discover in the literature that not-X had already been
>>> proved. The question then was which proof had the bug?
>>>
>>> But what if they were /both/ right? It was an obvious worry, and so
>>> arose the great question: is mathematics consistent?
>>>
>>> And Gödel proved not only that it isn't, but that it can't be.
>>>
>>> Fortunately, to date inconsistency has tended to surface only in
>>> corner cases like the Halting Problem, but Gödel's Hobgoblin hovers
>>> over mathematics to this day.
>>
>> My understanding is that Gödel proved that there are statements
>> that are true but not provable.  It's still not possible for both
>> X and not-X to be provable.  If proofs exist for both, at least
>> one of the proofs must be flawed.
>>
> 
> It seems that the short version is that G can be
> expressed in math yet cannot be linked to its
> semantic meaning in math. We need meta-math for this.
> 
> In my system of the entire set of human general knowledge
> that can be expressed in language G is linked to its
> semantic meaning.
> 
> 

No, G is fully connected with its BASIC semantics meaning in the 
language of math. What it isn't connected to is the special meaning 
injected into it structure from the metalanguage used to construct it.

But, we can still create MORE possible assignments of values (since the 
possiblities are uncountable) and your system can't know them all, we 
can still create a "meaning" that it can't know of.

The problem is that since logic systems need to be finite to meet the 
nornal definition of them, they can enumerate their axioms, as that 
enumeration creates axioms that would need to be enumerated.

This is the power of metasystem, they can enumerate the logic system, 
and still be finite, as the enumerations didn't go into the original 
system, so don't need to be enumerated.

Thus, your system can't contain the knowledge in the metasystem, and 
thus can't "know" of that meaning, it can't "defend" itself from it.