Re: Undecidability based on epistemological antinomies V2 --H(D,D)--

On 4/28/2024 4:01 AM, Mikko wrote:

On 2024-04-27 13:50:08 +0000, olcott said:
 

On 4/27/2024 3:41 AM, Mikko wrote:

On 2024-04-26 16:21:21 +0000, olcott said:
>

That is like saying we cannot know that 2 + 3 = 5 because people
simply do not "believe in" numbers or arithmetic.

>
There really are that kind of people. They usually don't believe
that 2 + 3 = 5 because they learned it before they learned that
one can disbelieve. But people often disbelieve logical proofs
because they learned about proofs only when they already had
learned to disbelieve, and even then not very much about proofs,
just enough to disbelieve. Consequently, there are people posting
in various newgroups that they have found a solution to a problem
that is proven unsolvable.
>

>
Likewise most people have been indoctrinated to believe that the
errors of logic are not errors.

 Most? How many you asked? I have never heard anybody saying anything
like that.
 

When we encode the principle of explosion as a syllogism:
Socrates is a man.
Socrates is not a man.
Therefore, Socrates is a butterfly.

 That is not a valid syllogism.
 

Proposition A is True.
Proposition A is False.
Therefore B
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

The conclusion does not follow from the premises,
thus the non-sequitur error.
https://en.wikipedia.org/wiki/Principle_of_explosion

 Correct but not relevant as it is an example of a non-syllogism
and therefore does not demonstrage anything about the principle
of explosion.
 

I gave my better example of POE as a syllogism.

In logic, the law of non-contradiction (LNC) (also known as the law of
contradiction, principle of non-contradiction (PNC), or the principle of
contradiction) states that contradictory propositions cannot both be
true in the same sense at the same time, e. g. the two propositions "p
is the case" and "p is not the case" are mutually exclusive.
https://en.wikipedia.org/wiki/Law_of_noncontradiction
>
{A, ~A} ⊨ FALSE fixes this problem

 In ordinary logic {A, ~A} ⊨ FALSE is a valid infeference and so is
{A, ~A} ⊨ whatever, so what is "fixed"?
 

{A, ~A} only semantically entails FALSE thus if one is not moronically
stupid (or indoctrinated into nonsense) one can see there is no other
semantics left over that can be carried to the proposition.
Compared to other areas of mathematical logic such as proof theory,
model theory is often less concerned with formal rigour and closer in
spirit to classical mathematics. This has prompted the comment that "if
proof theory is about the sacred, then model theory is about the
profane".[3] https://en.wikipedia.org/wiki/Model_theory
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer