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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: The philosophy of computation reformulates existing ideas on a
 new basis ---
Date: Sat, 2 Nov 2024 06:43:02 -0500
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On 11/2/2024 4:09 AM, Mikko wrote:
> On 2024-11-01 12:19:03 +0000, olcott said:
> 
>> On 11/1/2024 5:42 AM, Mikko wrote:
>>> On 2024-10-30 12:46:25 +0000, olcott said:
>>>
>>>> ZFC only resolved Russell's Paradox because it tossed out
>>>> the incoherent foundation of https://en.wikipedia.org/wiki/ 
>>>> Naive_set_theory
>>>
>>> Actually Zermelo did it. The F and C are simply minor improvements on
>>> other aspects of the theory.
>>
>> Thus establishing the precedent that replacing the foundational
>> basis of a problem is a valid way to resolve that problem.
> 
> No, that does not follow. In particular, Russell's paradox is not a
> problem, just an element of the proof that the naive set theory is
> inconsistent. The problem then is to construct a consistent set
> theory. Zermelo proposed one set theory and ZF and ZFC are two other
> proposals.
> 

My view is that the same kind of self-reference issue that
showed naive set theory was inconsistent also shows that the
current notion of a formal system is inconsistent. When we
handle this self-reference differently then this issue is
resolved.

When a formal system is ONLY a sequence of truth preserving
operations applied to a consistent set of expressions that
have been stipulated to be true then expressions that would
otherwise show incompleteness are rejected because they have
no path to true or false.

> The foundation of all these theories is classical logic.
> 

The key error of classical logic is that it diverged from the
model of the syllogism where there is always a path to true or
false or the syllogism is ill-formed.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer