Philosophy 1200 Lecture Notes - Lecture 26: Modus Ponens, False Premise, Logical Form

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An argument is invalid if it is possible for an argument of the same form to have true premises and a false conclusion. It is for this reason that we look at all possible combinations of truth values for the simple statements. An argument is valid if it is not invalid; i. e. there is no way (row) to make the premises true and the conclusion false. Recall that an argument is valid if the truth of the premises guarantees the truth of the conclusion. It can be the case that the conclusion of an argument is true, but it does not follow from the premises. So it is not enough that an argument has true premises and a true conclusion for it to be valid. For an argument to be valid, its structure must connect the premises and the conclusion in such a way that any argument with the same structure could not have true premises and a false conclusion.

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