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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 16:51:02 -0500
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In-Reply-To: <2235385edf766f66cd1261b54db6573b0d8f691c@i2pn2.org>

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.
> 

It never could.

> 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.


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