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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --Mendelson--
Date: Sat, 27 Apr 2024 11:18:21 +0300
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On 2024-04-26 15:28:08 +0000, olcott said:

> On 4/26/2024 3:42 AM, Mikko wrote:
>> On 2024-04-25 14:27:23 +0000, olcott said:
>> 
>>> On 4/25/2024 3:26 AM, Mikko wrote:
>>>> epistemological antinomy
>>> 
>>> It <is> part of the current (thus incorrect) definition
>>> of undecidability because expressions of language that
>>> are neither true nor false (epistemological antinomies)
>>> do prove undecidability even though these expressions
>>> are not truth bearers thus not propositions.
>> 
>> That a definition is current does not mean that is incorrect.
>> 
> 
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...(Gödel 1931:43-44)
> 
>> An epistemological antinomy can only be an undecidable sentence
>> if it can be a sentence. What epistemological antinomies you
>> can find that can be expressed in, say, first order goup theory
>> or first order arithmetic or first order set tehory?
>> 
> 
> It only matters that they can be expressed in some formal system.
> If they cannot be expressed in any formal system then Gödel is
> wrong for a different reason.

How is it relevant to the incompleteness of a theory whether an
epistemological antińomy can be expressed in some other formal
system?

-- 
Mikko