Читать книгу The Philosopher's Toolkit - Julian Baggini, Julian Baggini - Страница 89

In addition, the law of non‐contradiction – a cornerstone of philosophical logic – is also a tautology. The law may be formulated this way:

Not (p and not‐p).

The law is a tautology since, whether p is true or false, the complete statement will turn out to be true.

The law of non‐contradiction can hardly be said to be uninformative, since it’s the foundation upon which nearly all logic is built. But, in fact, it’s not the law itself that’s informative so much as any attempt to break it.

Attempts to break the law of non‐contradiction themselves require contradictions, and it’s standardly accepted that contradictions are obviously, and in all circumstances, false. A contradiction flouts the law of non‐contradiction, since it asserts both that something is true and that something is false in precisely the same sense and at the same time – asserting, as it were, both p and not‐p. Given, however, that the law of non‐contradiction is a tautology, and thus in all circumstances true, there can be nothing more clearly flawed and senseless than asserting a contradiction in opposition to it – unless, that is, you’re a dialetheist in logic (see 3.10).

The principle of non‐contradiction has also been historically important in philosophy. The principle underwrote ancient analyses of change and plurality and is crucial to Parmenides of Elea’s sixth‐century BCE proclamation that ‘what‐is is and cannot not‐be’. It also seems central to considerations of identity – for example, in Leibniz’s claim that objects that are identical must have all the same properties.