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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 15:58:46 -0500
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On 3/29/2025 3:21 PM, joes wrote:
> Am Sat, 29 Mar 2025 08:53:04 -0500 schrieb olcott:
>> 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.
> And you think arithmetic should be incomplete or what?
> 

When Provable(X) means applying truth preserving operations
to basic facts thus deriving True(X) then True(X) and ~Provable(X)
cannot possibly exist.

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