Читать книгу The Philosopher's Toolkit - Julian Baggini, Julian Baggini - Страница 53

We saw in 1.4 that one of the most interesting things about arguments is that their logical success or failure doesn’t entirely depend upon their content, or what they claim. Validity is, again, content‐blind or topic‐neutral. The success of arguments in crucial ways depends upon how they structure their content. The following argument form is valid:

1 All Xs are Ys.

2 All Ys are Zs.

3 Therefore, all Xs are Zs.

For example:

1 All lions are cats. (true)

2 All cats are mammals. (true)

3 Therefore, all lions are mammals. (true)

With this form, whenever the premises are true, the conclusion must also be true (1.4). There’s no way around it. With just a small change, however, in the way these Xs, Ys, and Zs are structured, validity evaporates, and the argument becomes invalid – which means, again, that it’s no longer always the case that if the premises are true the conclusion must also be true.

1 All Xs are Ys.

2 All Zs are Ys.

3 Therefore, all Zs are Xs.

For example, substituting in the following terms results in true premises but a false conclusion.

1 All lions are cats. (true)

2 All tigers are cats. (true)

3 Therefore, all tigers are lions. (false)

This is an instance of showing invalidity by counterexample (1.5, 3.12). If this form were valid, it wouldn’t be possible to assign content to it in a way that results in true premises but a false conclusion. The form simply wouldn’t allow it. This is an important point. As we work our way through various fallacies in this book, pay attention to whether or not the fault in reasoning flows from a faulty form or something else.