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

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.

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.

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"?
--
Mikko