PeteOlcott wrote: ↑Wed May 24, 2023 1:30 am
"a contradiction is true" quoted above entails that the law of non-contradiction has been rejected.
No contradiction is being taken as true. It's a hypothetical.
IF 2 + 2 = 5 THEN I am the Pope.
That is a logically true statement based on the truth table for material implication. The antecedent is FALSE -- do you get that? -- the antecedent is FALSE. Therefore the implication as a whole is true, because any material implication with a false antecedent is true.
There is no claim that 2 + 2 = 5 is true. On the contrary. We note that 2 + 2 = 5 is false. We then look up the rows in the truth table for material implication in which the antecedent is false; and we note that in both cases, namely whether the consequent is true or false, the implication as a whole is true.
See
https://en.wikipedia.org/wiki/Material_ ... inference), in particular the truth table:
Code: Select all
P Q P → Q
= = =====
T T T
T F F
F T T
F T T
Likewise, P ∧ ¬P is false. Let me say that again. P ∧ ¬P is false. Why? Principle of non-contradiction, which is being AFFIRMED.
Therefore the material implication (P ∧ ¬P) → I am the Pope is a valid material implication, whose overall truth value is True.
Why does this simple point elude you?
In material implication, a FALSE antecedent always gives a TRUE material implication. "If 2 + 2 = 5 then I am the Pope." The material implication is true, exactly by virtue of the fact that 2 + 2 = 5 is false.
Nobody is saying P ∧ ¬P is true. Well YOU are saying it, but that's only because you don't understand material implication.
On the contrary, P ∧ ¬P is FALSE FALSE FALSE. That's the principle of explosion. It is NOT a denial of non-contradiction, it's an AFFIRMATION of non-contradiction.
PeteOlcott wrote: ↑Wed May 24, 2023 1:30 am
All Wikipedia changes are reviewed and reversed as needed.
I graffitied the wall of a building, because I expect the property owner will go to the expense of having it painted over. So no harm done, right?
PeteOlcott wrote: ↑Wed May 24, 2023 1:30 am
Because I directly linked to the source of most of the update I expect that it may be approved.
Like I said, the exact flaw with Wikipedia. "Anyone may edit." That policy giveth, and in this case that policy taketh away.