if the A in the antecedent is false, the A in the consequent should be false too — frank
This is just what the word "valid" means. I think you think it means something else. — Michael
this argument is not valid becasue all the premises are true and that conclusion is false.. — Hanover
There is no interpretation in which all the premises are true. Therefore, the argument is valid.
— frank
That's not what he's saying. — Michael
Given that frank and I were talking about the definition of "valid", I (mis)understood him as claiming that you were saying "an argument is valid if and only if there is no interpretation in which all the premises are true". — Michael
These are two different claims:
1. An argument is valid if there is no interpretation in which all the premises are true
2. An argument is valid if there is no interpretation in which all the premises are true and the conclusion is false. — Michael
You say that because you're not linking your first argument to your second. — Hanover
this arises from the principle of explosion, a law of classical logic stating that inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all.
He's just using the definition of validity:
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
There is no interpretation in which all the premises are true. Therefore, the argument is valid. — frank
It depends on the length to which we "interpret" an argument and how you interpret "interpret." — Hanover
If you have an argument in which there is an interpretation where both premises are false, but there are no cases where both premises are true, then the argument is valid. That wouldn't be a case of explosion. — frank
The reason that there is no interpretation where both premises are true is because the premises are inconsistent, i.e. that their conjunction is a contradiction. As such, any conclusion follows and the argument is valid. — Michael
They can never both be true only if they are inconsistent. If they are consistent then they can both be true. — Michael
Checking the validity of one argument using another is done all the time. — Hanover
Notice that 1 and 2 are saying the same thing — frank
Question begging happens a lot. But, again, I can't think of an instance in public discourse.... As to complaints about formal logic,
— TonesInDeepFreeze
Small point. Public discourse often (usually/always?) uses rhetorical logic - Rhetoric. Not ever to be confused with "formal" logic. — tim wood
Any argument with inconsistent premises is valid, according to Tones. Weird indeed. It requires a strained reading of the fine print of portions of definitions of validity, taken out of context. Earlier posters usefully leveraged the word "sophistry."
(Note that this is different from the modus ponens reading of the OP and it is different from the explosion reading of the OP. The effect of explosion requires explicit argumentation. The OP, for example, is susceptible to explosion, but it is not wielding explosion. Tones is just doing a weird, tendentious, definitional thing.) — Leontiskos
I think, though, we can allow a somewhat negative connotation because reliance in argumentation on degenerate cases is often inadvertent or deceptive. "There are a number of people voting for me for President on Tuesday [and that number happens to be 0]." — Srap Tasmaner
"Therefore, an argument with contradictory/inconsistent premises cannot have a false conclusion while the premises are true" [Paraphrase of Tones] — Leontiskos
I'm saying that if you can interpret the same argument and obtain contradictory conclusions, then the argument is not "valid" under this definition of "valid": — Hanover
these mean two different things:
1. A → ¬A
2. A → (A ∧ ¬A) — Michael
Tones' is literally applying the material conditional as an interpretation of English language conditionals — Leontiskos
1. A -> not-A
2. A
Therefore,
3. not-A.
Is this argument valid? Why or why not? — NotAristotle
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