The structure of arguments

Often in philosophy, it helps to write an argument out as a set of claims which we call premises, leading to another claim which we call the conclusion. The premises are claims which give us reason to think that the conclusion is true. Here is one famous example:

These two claims give us reason to think the following conclusion is true:

This particular argument has two excellent traits, traits that all arguments ought to have. The first is that all its premises are true (if you ignore the fact that they are expressed in the present tense even though Socrates died long ago). The second is that the inference from its premises to its conclusions is a good one – or, as philosophers like to put it, the inference is valid. To say that an inference is valid is to say that it is guaranteed to be truth-preserving: if the premises of a valid inference are true, then this truth is bound to carry over to the conclusion. In the present example, the truth of the premises is indeed enough to guarantee that the conclusion is true. (To see this for yourself, try to imagine a world in which the two premises were true but in which the conclusion was false. You should find that such a world is impossible even to imagine.)

If an argument has the two desirable traits I have just described – i.e. all its premises are true and it is valid – then the argument is said to be sound. If it fails on either count – i.e. if it has one or more false premises, or if it contains an invalid inference – then it is unsound.

Notice that sound arguments, i.e. arguments with both desirable traits, are bound to have true conclusions, since the truth of the premises will be carried over into the conclusion. Having just one of the desirable traits is not good enough. Having premises that are all true is no use if, because the argument is invalid, this truth is not carried over into the conclusion. Nor is being valid of any use by itself: if the premises aren’t all true, there will be no truth to preserve, as the following example of a valid argument shows.

These notions (premise, conclusion, validity, soundness) are fundamental to presenting and evaluating arguments and, as you already know, arguments are fundamental to philosophy. In the next activity I will ask you to start putting them to work.