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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Sat, 29 Mar 2025 17:00:03 -0500
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On 3/29/2025 1:18 PM, Richard Damon wrote:
> On 3/29/25 9:53 AM, olcott wrote:
>> On 3/29/2025 4:51 AM, joes wrote:
>>> Am Fri, 28 Mar 2025 15:07:22 -0500 schrieb olcott:
>>>> On 3/28/2025 8:46 AM, Richard Damon wrote:
>>>
>>>>> Ok, so therefore it includes all the "laws of mathematics" and the
>>>>> "rules of inference" and thus, the system is capable of creating the
>>>>> rules and properties of the Natural Numbers, so it supports the proofs
>>>>> of Godel and Tarski, and thus there are statements in that sytstem 
>>>>> that
>>>>> are True but unprovable and no definition of the Truth Predicate can
>>>>> handle those,
>>>>
>>>> Yes it will showed the formal system can be defined that have all kinds
>>>> of issues because they were defined incoherently.
>>>
>>> How is arithmetic (which is all it takes for Gödel's proof) incoherent?
>>>
>>
>> To the best of my knowledge arithmetic itself cannot
>> be incomplete unless it can be shown that the sum of
>> two finite strings of digits cannot be derived.
>>
> 
> Depends on what you consider "Arithmetic". If you just mean "sums" and 
> the like, then maybe it can't be incomplete, because it can't ask 
> questions that ask for proofs.
> 
> Once you include first order logic with things like There exist a number 
> such that ..., then you can perform Godel's proof and find that there is 
> at least one statement that is true but can not be proven in the system.

When semantics is fully integrated into syntax and all
proofs apply truth preserving operations to basic facts
then ~Provable(X) and True(X) cannot possibly co-exist.

Within this system of general knowledge that can be
expressed in language Tarski is refuted and undecidability
is impossible.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer