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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable
Date: Mon, 19 Aug 2024 11:36:16 +0300
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On 2024-08-18 11:47:36 +0000, olcott said:

> On 8/18/2024 5:32 AM, Mikko wrote:
>> On 2024-08-17 14:45:45 +0000, olcott said:
>> 
>>> On 8/17/2024 9:40 AM, Richard Damon wrote:>>>
>>>> No, you said that "ALL THEY DID" was that, and that is just a LIE.
>>>> 
>>>> They developed a full formal system.
>>>> 
>>> 
>>> They did nothing besides change the definition of
>>> a set and the result of this was a new formal system.
>> 
>> Yes they did. They did show that the new system is similar enough to
>> the old systems to be called "set theory" and sufficiently useful.
>> 
> 
> They redefined the notion of a set in set theory and that
> by itself got rid of Russell's Paradox. Mostly this disallows
> a set to be a member of itself.

The new notion is restricted to their new system. The general informal
notion of "set" is unaffected. Some sets, e.q. Quine's atom that
contains itself and nothing else is not a set in Zermelo's theory
but is an example of a set according to the general notion.

> I redefine the notion of formal system in math and logic
> and this by itself gets rids of undecidability. Mostly this
> rejects self-contradictory expressions.

Math and logic are not formal systems that could be replaced with
other formal systems. The notion of formal system cannot be redefined.
You can construct a new formal system where formal system is formally
defined but that definition has no consequences outside that syatem.

-- 
Mikko