## C1 If the tuna industry is not regulated more stringently the tuna population will vanish

It might be a bit difficult to imagine CI and P3 true, and then ask whether C2 could be false. But in fact, when we considered this argument earlier, we used a method which makes it easier. We shall now make this more explicit, as it is very important when considering arguments that have as much logical complexity as this argument (or more). Note that C2 is a conditional. What a conditional asserts, roughly, is a certain relation between the antecedent and consequent - that if the antecedent is true then so is the consequent. So the question we want to answer is this: if the premises of the argument were true, then would this purported relationship hold? To answer this question we suppose, not only that the premises of the argument are true, but that the antecedent of the argument's conclusion is also true. And then what we want to know is whether, under those suppositions, the consequent of the argument's conclusion would also have to be true.

So here goes. Suppose CI and P3 are true, and that the tuna industry is not (going to be) regulated more stringently (this is the antecedent of C2). We can now reason as follows (using our easier-to-understand, 'if-then' version of CI): we have assumed that the tuna industry is not regulated more stringently; therefore, according to CI, the tuna population will vanish. But in that case, according to P3, the tuna industry will collapse altogether. But that is precisely what the consequent of the C2 says. So we see that if CI and P3 are true, then it does follow, from the antecedent of C2's being true, that the consequent of C2 is true also. So the argument is valid.

The same sort of technique is useful where the conclusion of an argument is a generalisation. Consider this argument.

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