Ok. I see. But then, what about the second premise? If A is false, wouldn't the second premise actually be not-A? — frank
I can't see that we are. — Michael
An argument is valid if and only if there is no interpretation in which all the premises are true and the conclusion is false. — TonesInDeepFreeze
That's not what he's saying. — Michael
All he had to do is say that there aren't any cases where both premises are true, therefore it's valid.
— frank
I said it over and over and over for you.
All you had to do is read the replies given you. And that's hardly the only point I explained for you. — TonesInDeepFreeze
You are claiming that he is asserting (1), when in fact he is asserting (2), as am I. — Michael
2. An argument is valid if there is no interpretation in which all the premises are true and the conclusion is false. — Michael
Question begging happens a lot. But, again, I can't think of an instance in public discourse.... As to complaints about formal logic, — TonesInDeepFreeze
I don't quite understand what you're trying to say here. — Michael
the reductio shows that the first premise is unsound but why is it unsound? It's unsound because it's logically contradictory. If A then not-A necessarily implies A and not-A, which tells me the argument must be invalid. — Benkei
The argument is an example of the principle of explosion — Michael
The inferences in OP's argument are right in line with the idea that if A is true then it is also false. — Count Timothy von Icarus
tautologies might be semantic, e.g. "bachelor's are unmarried men," or "triangles are three-sided." — Count Timothy von Icarus
(p→q) ⇔ (~q→~p) — Count Timothy von Icarus
At least in propositional logic, my understanding is that tautologies are defined in terms of form — Count Timothy von Icarus
A → ¬A does not mean A ∧ ¬A. It means ¬A ∨ ¬A
— Michael
How do you figure that? — frank
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