It may seem bizarre that a valid argument could have at least one premise that is necessarily false at first glance, but I think it is fairly intuitive if one thinks in terms of truth-preservation. — Count Timothy von Icarus
...prioritizing truth-functional process over logical telos. — Leontiskos
With a false antecedent, the consequent is vacuously true. — Benkei
violates the LNC — Benkei
All he had to do is say that there aren't any cases where both premises are true, therefore it's valid. — frank
No, with a false antecedent the conditional is true, sometimes described as 'vacuously true'. It's the conditional that is deemed true when the antecedent is false. — TonesInDeepFreeze
But that situation, where the antecedent is denied, is irrelevant because the second premise assumes A to be true. And it necessarily follows from the first premise that not-A is simultaneously true. This is self-contradictory and violates the LNC. — Benkei
Here's an example in ordinary langauge with the same form.:
1.Life therefore death
2.Life
Therefore
3.Death.
Both valid and sound it seems — Janus
I suppose accusations of hypocrisy are nearby. "Your anti-racism is itself a form of racism." "Your anti-capitalism materially benefits you." "Your piety is actually vanity." Generalize those and instead of saying, hey here's a case where the claim is A but it's really ~A, you say, every A turns out to be ~A. Now it's a rule.
Perhaps I misunderstood you. I had taken "it" and "the inference" to be the argument in the OP. Hence it appeared you were saying the argument in the OP was invalid.It violates the LNC, which is foundational and introduced by Aristotle before modus ponens so he certainly didn't intend that the inference can work. — Benkei
What I want is an example where this conditional is actually false, but is relied upon as a sneaky way of just asserting ~A. — Srap Tasmaner
Well, while I think Srap has a good point about our being able to live without A→~A in most situations, I think it is important that statements like "nothing is true," are able to entail their own negation—that logic captures how these claims refute themselves. — Count Timothy von Icarus
It may seem bizarre that a valid argument could have at least one premise that is necessarily false at first glance, but I think it is fairly intuitive if one thinks in terms of truth-preservation. If the premises were true, it would preserve truth. But the "truth" of a false premise cannot be preserved.
And it's a good thing that it is valid because we often can reason from necessarily false conclusions in valid arguments to identifying false premises. — Count Timothy von Icarus
Everything that runs is an animal.
My refrigerator is running.
Therefore, my refrigerator is an animal.
Works great formally if you're allowed to us "R" for "that which runs" in both premises. — Count Timothy von Icarus
What is the conditional? — TonesInDeepFreeze
analogous predication — Count Timothy von Icarus
A = "George is going to open the store tomorrow"
So, by substitution:
George is going to open the store tomorrow implies George is not going to open the store tomorrow. — Moliere
Can we substitute salva veritate into an ironic statement? — Banno
I don't know what you mean.
You mean substitute "George will open the store" with "If George will open the store then George will not open the store"?
Why make that substitution? I don't see how that is what the ironic speaker is saying. — Moliere
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