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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Undecidability based on epistemological antinomies
Date: Tue, 30 Apr 2024 11:06:08 -0500
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On 4/30/2024 7:01 AM, Mikko wrote:
> On 2024-04-29 15:22:11 +0000, olcott said:
> 
>> 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
> 
> That page does not tell what a syllogism is. Instead, the page
>     https://en.wikipedia.org/wiki/Syllogism
> does.
> 

This is the part of the page on syllogism that links to that link
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

>> 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.
> 
> The result of the translation is not a syllogism and the conclusion
It <is> a syllogism with the non-sequitur error
as I have been saying all along

This seems to be related to what you are saying:
Proposition A is True.
Proposition A is False.
Therefore B
https://en.wikipedia.org/wiki/Principle_of_explosion

Translated into a syllogism:

All A are True
No A are True
Therefore B

*It is categorically impossible to show*
(a) How the above two categorical propositions entail B.
(b) That the above syllogism is not isomorphic to POE.
https://en.wikipedia.org/wiki/Categorical_proposition


> does not follow by the rules of syllogistc logic. Threfore you have
> not proven that the principle of explosion is true about syllogistic

I am proving the the POE is merely the non-sequitur error.

> logic. (Is is true about modern ordinary logic, which have different
> rules of inference.)
> 
>> 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.
> 
> The translation is not correct as the result is not a valid
> syllogism.
> 

The translation is correct and results in a syllogism with
the non-sequitur error as I have been saying all along.

>> 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.
> 
> A proof that starts with a false assumption is never sound. The

Yes and the false assumption of POE is that: (A and ~A) are true
When we reject that then the POE cannot exist.

> conclusion of the proof may be false if at least one of the premises
> is false. This is the idea behind indirect proofs: if one can prove
> False or any contradiction then one has proven that one of the permises
> is false.
> 

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