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A similar version of this question was answered before, (An invalid argument, the conclusion of which is a tautology) but I'm still a bit confused about why this is not possible. Like the other asker, I am responding to an exercise from an Intro to Logic text.

I thought of this example for a possible invalid argument with a tautology as its conclusion:

Monday was a sunny day

Tuesday was a rainy day

... On Wednesday, it will either rain or not rain.

I think this argument would be inductive, so wouldn't that make it deductively invalid? It doesn't seem like in all cases the truth of the premises would lead to a true conclusion, but since its conclusion is a tautology in this case, does that fit the definition of validity anyway?

Mauro ALLEGRANZA
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  • Comments are not for extended discussion; this conversation has been moved to chat. – Geoffrey Thomas Feb 08 '21 at 10:46
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    According to the convention in current textbooks on FOL, "argument" is just a list of premises followed by the conclusion. It is called "valid" if the conclusion is true whenever the premises are on any substitution of non-logical terms. So if the conclusion is a tautology the argument is automatically "valid", the truth of premises is irrelevant. This does not follow the common use of "argument" as a sequence of steps according to some rules, inductive or deductive, but unfortunately it is entrenched now. – Conifold Feb 08 '21 at 10:57
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    In short: "follows from" does not mean "is proven by". Validity is just a guarantee that whenever all of the premises are true, then the conclusion shall be too. – Graham Kemp Feb 09 '21 at 23:27
  • There is a good answer to the same question on the Math Stack Exchange here: https://math.stackexchange.com/questions/1373918/different-definitions-of-a-valid-argument – Bumble Feb 10 '21 at 14:40

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