So then any argument that has no true premises is valid. That's weird. — frank
There is no question. He does not presuppose it. — TonesInDeepFreeze
I did not claim that validity requires that there is no interpretation in which the premises are all true. — TonesInDeepFreeze
We’re just saying that the conclusion follows from the premises – that if the premises were all true, then the conclusion also would have to be true. — Gensler, Introduction to Logic, Second Edition, p. 3
Oh. So then any argument that has no true premises is valid. That's weird. — frank
Gensler:
"An argument is valid if it would be contradictory (impossible) to have the premises all true and conclusion false."
It is impossible to have both A -> ~A and A true. Perforce, it is impossible to have the premises all true and the conclusion false. — TonesInDeepFreeze
I did not claim that validity requires that there is no interpretation in which the premises are all true.
— TonesInDeepFreeze
And I never said you did (you are falling into the fallacy of affirming the consequent). — Leontiskos
Your claim is, "Whenever the premises are inconsistent, the argument is valid." — Leontiskos
That is the second time you put quotes around words I didn't say. — TonesInDeepFreeze
"A sentence Phi is a consequence of a set of sentences Gamma if and only if threre are no interpretations in which all the sentences in Gamma are true and Phi is false." (Elementary Logic - Mates)
"An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false." (The Logic Book - Bergmann, Moor and Nelson). — TonesInDeepFreeze
"a major topic in the study of deductive logic is validity. This is a relationship..." — TonesInDeepFreeze
It's called paraphrase — Leontiskos
These are not conclusive in favor of your reading, and you would need to quote the context around these sentences given the way you have shown yourself willing to ignore context. — Leontiskos
"it is not possible for the premises to be true and the conclusion false" is not uncontroversially fulfilled by a set of inconsistent premises. — Leontiskos
It's remarkable that you can't stand to be wrong to the degree that you don't heed even your own cites! — TonesInDeepFreeze
The idea that it is a relationship already excludes your reading. If a relationship between A and B must be established, then one must know something about both A and B. — Leontiskos
If there is no assignment in which all the premises are true, then the argument is valid.
That is very different from what you mentioned. — TonesInDeepFreeze
Any argument with inconsistent premises is valid, according to Tones — Leontiskos
Yep.If you look at the argument in the OP, there can never be a case where both premises are true. — frank
Any argument with inconsistent premises is valid, according to Tones — Leontiskos
However, 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
Just to note: tautology is semantic and contradiction is syntactic.
When I say A sarcastically, I mean ~A, of course. And that is equivalent with A -> ~A. But I don't present it like that at all. I just say A and there is an implicit premise that when I say it, I mean its negation. I don't know how even modal logic could capture that. Or maybe, I am saying that A is true in an alternative world and false in the actual world, but even that seems far-flung.
Getting back to Srap Tasmaner, he's looking for a use of A -> ~A in everyday discourse. I don't think your proposal works, since people don't acutually say things of the form A -> ~A to convey sarcasm. It seems to me that you followed an interesting idea, but it doesn't do the job here. — TonesInDeepFreeze
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