Re: Undecidability based on epistemological antinomies

On 2024-05-02 13:17:24 +0000, olcott said:
 

On 5/2/2024 3:11 AM, Mikko wrote:

On 2024-05-01 15:19:54 +0000, olcott said:
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On 5/1/2024 4:06 AM, Mikko wrote:

On 2024-04-30 16:06:08 +0000, olcott said:
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On 4/30/2024 7:01 AM, Mikko wrote:

On 2024-04-29 15:22:11 +0000, olcott said:
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On 4/29/2024 10:04 AM, Mikko wrote:

On 2024-04-29 14:32:13 +0000, olcott said:
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On 4/29/2024 4:24 AM, Mikko wrote:

On 2024-04-28 13:24:52 +0000, olcott said:
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Translated into a syllogism:
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All A are True
No A are True
Therefore B

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Which inference rule of syllogistic logic permits that inference?
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(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
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(2) That as a syllogism it is the non-sequitur error proves
that the POE was the non-sequitur error all along.

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What you call a "syllogism" isn't one as it has none of the forms
of valid syllogism as listed by Aristotle.
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https://en.wikipedia.org/wiki/Categorical_proposition

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That page does not tell what a syllogism is. Instead, the page
   https://en.wikipedia.org/wiki/Syllogism
does.
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This is the part of the page on syllogism that links to that link
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

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THat's right. That section says what the form of a syllogism is.
Your "syllogism" has not that form.
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*This part is correct*
Each part is a categorical proposition, and each categorical proposition contains two categorical terms.
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*This part is incorrect only because the POE expression is incorrect*
"Each of the premises has one term in common with the conclusion:"

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There is nothing incorrect in that. In every syllogism each of the
premises has one term in common with the conclusion. That this is
not true about yor "syllogism"

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Only because this error already exists in the POE argument,
thus the same error is transferred to the syllogism when the POE
argument is accurately translated into the syllogism.
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simply means that your "syllogism"
is not true. (Etymologically the term "syllogism" is reference to
the common words.)
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By retaining the same lack of a common term as the POE expression we
see that the POE expression has the non-sequitur error.

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No, but we do see that your "syllogism" is not a syllogism.
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It is the exact same invalid syllogism with the non-sequitur
as the POE argument that it was translated from.

 It is an ivanlid syllogism as the conclusion does not follow by any
valid inference rule of syllogistic logic.

However, the conclusion
follows by classical logic. One can prove about every inferences of
the form
   Premise1
  Premise2
  ----------
  Conclusion
 that it is a valid inrerence of ordinary logic if
   ¬Premise1 ∨ ¬Premise1 ∨ Conclusion
 is a tautology of propositional logic then. From this theorem follows
that your invalid "syllogism" is a valid inference of ordinary logic.