## Supposing the conclusion false

Another way to assess the validity of an argument is to suppose the premises are true but the conclusion false. If we can see that this is impossible, then, according to the definition of validity, the argument is valid;

if we can see that this is possible, then we know that the argument is invalid. So consider the first argument about the Italian footballers. To suppose the conclusion false is to suppose that there is at least one Italian striker who does not tackle well. If he does not, then by P2 he is not a good defender. But then he is an Italian striker who is not a good defender, which contradicts PI. So if the conclusion is false, it is impossible for the premises to be true. So the argument is valid.

Do the same with the second argument about the Italian footballers. We now imagine an Italian striker who does not tackle well. According to PI, he must be a good defender. But P2 does not force us, or enable us, to draw any further conclusion about this Italian striker. It tells us that if he tackles well, then he is a good defender, but it does not tell us anything about the case where he does not tackle well: it does not say that if he does not tackle well then he is not a good defender. So the falsity of the conclusion is perfectly consistent with the two premises being true. For all the premises say, our striker might be a good defender for other reasons - he might be very quick and energetic, good at clearances, and so on. So the argument is invalid.

This method can be used on any argument, not just those whose conclusions are conditionals or generalisations. But it is especially helpful in those cases.

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