Wednesday, December 24, 2008

Aristotle on Opposites 4: Contradictories

In the Categories 10, Aristotle describes four different kinds of opposites. I talked about the first three of those in the last three posts. As for the fourth, Aristotle says that contradictories are opposites.

Contradictories are pairs of statements, one of which is an affirmative sentence of the form 'x is F' (as in, 'Socrates is sitting'), and the other of which is a negative sentence of the form 'x is not F' (as in, 'Socrates is not sitting'). Negative sentences can also be expressed as 'it is not the case that x is F' (as in, 'it is not the case that Socrates is sitting').

(I use the word 'sentence' here instead of 'proposition' because I don't know if Aristotle believes in propositions -- i.e., eternal, abstract statement-like entities that somehow describe the world or worlds. I'd also be happy to use the word 'statement' too.)

Right off the bat, it's clear that contradictions belong to a separate class of opposites than the other three (namely: correlatives, contraries, and possession/deprivation). Contradictions are sentences, but the rest apply to some feature of things. Correlatives are relational features, contraries are non-relational features, and possession/deprivation apply to natural features, but none of these are sentences.

Further, Aristotle points out that if we do try to express the other kinds of opposites with language, we express them with predicates, not full sentences. 'Double', 'hot', and 'having sight' are predicates, and predicates don't contradict anything. Only sentences can be contradictory. ('Hot' doesn't contradict anything, but 'that thing is hot' contradicts 'that thing is not hot'.)

But can't we formulate contradictory sentences about any of the other kinds of opposites? Take sight and blindness. Can't we say 'Socrates is blind' and 'Socrates can see', and aren't those contradictory sentences?

According to Aristotle, the crucial characteristic of contradictions of this: it's always the case that one of them is true, and the other is false. We can, of course, form contradictory sentences from the other kinds of opposites, but it's not always the case that one is true and the other is false.

There are cases, for example, where both 'Socrates can see' and 'Socrates is blind' are false. When Socrates is a zygote, he can't see yet, so he neither has sight nor is blind. Similarly, if Socrates doesn't exist, there is no Socrates to be blind or to see. The same holds for correlatives and contraries too.

But with genuine contradictions, one is always true and the other is false. For example, 'Socrates is sitting' and 'Socrates is not sitting' are contradictons, and one is always true and the other is always false, no matter what. If Socrates exists, then one will be true and the other false (depending on whether Socrates is sitting or standing). Likewise, if Socrates doesn't exist, then 'Socrates is not sitting' (or better: 'it is not the case that Socrates is sitting') is true. There simply is no Socrates, so it's not the case that he's sitting.

(Thus, for contradictions, we can identify this general rule: if the subject of the contradictory sentences does not exist, the negative sentence is true; if the subject does exist, then one or the other is true.)

The key here is that contradictions always involve a negative statement, and the negative statement is always true when the subject doesn't exist. The other kinds of opposites can't be reduced to mere negative sentences. On the contrary, they all amount to some positive state of affairs.

For example, 'double' and 'half' are positive states of affairs: something is double, and something is half. 'Hot' and 'cold' are too, for something is hot and/or something is cold. 'Sight' and 'blindness' are also positive states of affairs: either something can see, or something is there, but it can't see. (As I said in the last post, being deprived of something is not the same as simply not having it.)


Thomas Wright said...

I don't have much of substance to say; I only wonder why you fear using "proposition" and naturally assume a proposition must be some abstract thing.. that seems odd. There are plenty of nominal theories about propositions lingering about... I think Aristotle would be quite content to call them propositions.

JT Paasch said...

Good comment. On a nominal theory, Aristotle might allow his comments to apply to such propositions.