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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Undecidability based on epistemological antinomies
Date: Mon, 29 Apr 2024 10:22:11 -0500
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On 4/29/2024 10:04 AM, Mikko wrote:
> On 2024-04-29 14:32:13 +0000, olcott said:
> 
>> On 4/29/2024 4:24 AM, Mikko wrote:
>>> On 2024-04-28 13:24:52 +0000, olcott said:
>>>
>>>> Translated into a syllogism:
>>>>
>>>> All A are True
>>>> No A are True
>>>> Therefore B
>>>
>>> Which inference rule of syllogistic logic permits that inference?
>>>
>>
>> (1) That is a correct translation from this POE argument:
>> Proposition A is True.
>> Proposition A is False.
>> Therefore B
>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>
>> (2) That as a syllogism it is the non-sequitur error proves
>> that the POE was the non-sequitur error all along.
> 
> What you call a "syllogism" isn't one as it has none of the forms
> of valid syllogism as listed by Aristotle.
> 

https://en.wikipedia.org/wiki/Categorical_proposition
proves that the premises are the categorical propositions
required by syllogisms, and these are isomorphic to the POE
premises. The fact that the conclusion is simply copied
proves that it was "translated" correctly.

When the POE argument is corrected translated into a
syllogism and this syllogism has the non-sequitur error
that then proves the POE argument also has this same error.

Assuming that (A and ~A) are true was the mistake of the POE proof.
We could equally assume that 2 > 5, thus 2 + 1 > 5.

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