Aquinas on different kinds of correlatives

Aquinas says that the Son and Spirit are opposites, but we can ask: what kinds of opposites are they? In the last post, I explained why Aquinas thinks that of Aristotle's four kinds of opposites, the Son and Spirit are only opposites in the way that correlatives are opposites. However, there are different kinds of correlatives, so Aquinas needs to say something about the different kinds of correlatives.

To that end, Aquinas says that correlatives come in two kinds: those based on ‘quantity’, and those based on ‘action’. (Note that Aquinas surely has book 5 of Aristotle's Metaphysics in mind here.) Let’s look at each in turn.

(a) Quantity. The term ‘quantity’ is a little misleading in this context, and Aquinas's comments ehre can be a little obscure. Here's the stuff to keep in mind. Instead of ‘quantity’, it would probably be more helpful to talk about ‘sameness’ and ‘difference’. Let me explain.

Whenever two things are the same in some way, they are said to be ‘one’ in that way. For example, Socrates and Plato are the same kinds of things: they are both humans. Thus, we can say that they are ‘one in kind’. In this sense, sameness is based on situations where two things are ‘one’ in some way.

But when two things are different in some way, they are said to be ‘many’ in that way. Socrates and Felix the cat, for example, are different kinds of things. One is a human, and the other is a cat. Thus, we can say that they are ‘many in kind’ (in the sense that there are many (more than one) kinds of things there). In this sense, difference is based on situations where two things are ‘many’ in some way.

Now, talking about ‘one’ and ‘many’ makes it sound as if we’re talking about quantities — either one or many — and so Aquinas (following Aristotle) classes this kind of sameness and difference under the broad heading of ‘quantity’. But really, he is thinking of two things being the same (being ‘one’) or different (being ‘many’) in some way.

Aquinas next points out that there are only three ways that something can be ‘one’ or ‘many’ (same or different).

(i) First, two things can be the same or different with respect to substance. This is what the medievals (and us too) call identity and distinction. That is, when some x and y are they very same thing, they are identical, but when they are two things, then they’re distinct. For example, Cicero and Tully are identical, for ‘Cicero’ and ‘Tully’ are just two names for one and the same person. But Cicero and Plato are distinct, because Cicero and Plato are two separate persons.

(ii) Second, two things can be the same or different with respect to quantity. This is what the medievals (and us too) call equality and inequality. Note that here Aquinas is talking about ‘quantity’ in the strict sense (as in, the second of Aristotle’s categories). When two things are the same size/weight/some other quantity, then they are equal with respect to quantity, but otherwise they’re unequal. For example, two 10kg blocks are equal in weight, but a 10kg block and a 5kg block are unequal in weight.

(iii) Third, two things can be the same or different with respect to quality. This is what the medievals (and us too) call similarity and dissimilarity. When two things are the same in color, temperature, or some other quality, then they are similar with respect to quality, but otherwise they’re dissimilar with respect to quality. For example, the white table in my kitchen and the white walls in my living room are similar in color, but black cows and red cows are dissimilar in color.

At this particular point in his text then, when Aquinas talks about correlatives that are founded on ‘quantity’, he is talking about two things being ‘one’ or ‘many’ (same or different) in one of these three ways. Aquinas does not always talk about ‘quantity’ correlatives like this. More frequently, he talks about ‘quantity’ in the stricter sense, in which case he is talking about equality and inequality (type (ii) above). Here, I’ll just say ‘sameness-correlatives’ when I mean the broader kind based on ‘one’ and ‘many’, and I’ll reserve the word ‘quantity’ for the strict sense that pertains to equality and inequality.

(b) Action. The second kind of correlative is based on action. These sorts of correlatives occur between two things where one acts in some way on the other. In these cases, one thing x acts on another thing y, and a specific relationship occurs between the two that is based on that action.

Aquinas gives ‘mover’ and ‘moved’ as an example. When one thing moves another, there is a reciprocal relationship there: one thing does the moving, and the other gets moved. The mover/moved relationship is based on the mover’s activity that causes the movement.

Aquinas also gives ‘master’ and ‘slave’ as an example. The idea is that a master/slave relationship is based on the activity of governing and being governed: the master governs the slave, and the slave is governed by the master. Another example Aquinas gives is ‘father’ and ‘son’, for the father/son relationship is based on the father’s reproductive activity that brought the son into being: the father does the producing, and the son is produced.

Aquinas on what kind of opposites the Son and Spirit are

In the last post, I talked about Aquinas's claim that all distinct spirits are opposites. He wants to use this to show that the Son and Spirit are distinct by opposites too. To do so, he goes through Aristotle's four kinds of opposites (see my earlier posts on that), and he argues that of Aristotle’s four kinds of opposites, only the first (viz., correlatives) applies to the Son and Spirit. To see this, let’s start with contradictions and work our way backwards.

(d) First then, are contradictions. Aquinas claims that the Son and Spirit are not opposites by contradiction. That is, the Son and Spirit are not opposites in the way that ‘Socrates is sitting’ and ‘Socrates is not sitting’ are. Why not? One obvious reason is this: the Son and Spirit are not sentences, and contradictions only apply to sentences. But that’s not what Aquinas says. Instead, he says that a contradiction distinguishes ‘beings’ from ‘non-beings’.

By ‘beings’ and ‘non-beings’, Aquinas has in mind the beings that affirmative and negative statements describe. An affirmative statement asserts that some state of affairs exists. A negative statement, by contrast, asserts that some state of affairs does not exist. Thus, affirmative statements describe ‘being(s)’, and negative statements describe ‘non-being(s)’.

Okay, so affirmative and negative statements describe states of affairs that do and do not exist. But why should that mean the Son and Spirit can’t be distinguished by contradiction? Unfortunately, Aquinas says no more than what I’ve already said, namely that the Son and Spirit aren’t distinguished by contradiction because contradiction distinguishes ‘beings’ and ‘non-beings’. Apparently, he thinks the conclusion is obvious, but it takes some explaining (it does for me, anyways).

Consider the following. Can’t I say that ‘the Son is begotten by the Father’ and ‘the Spirit is not begotten by the Father’? Wouldn’t that be enough to distinguish them? Similarly, if I said ‘George Bush Jr. is the President of the United States’ and ‘I am not the President of the United States’, wouldn’t that be enough to distinguish myself from the President?

Well, the problem here is that these are faux contradictions. Both pairs of statements are true, so they don’t count as contradictions, strictly speaking. As I explained in my previous post, contradictions are such that one of the sentences must be true and the other false. If two sentences are true, then there’s really no contradiction there.

Indeed, Bush Jr. really is the President, and I’m really not the President, and there’s nothing contradictory about that. Likewise, the Son really is begotten by the Father, and the Spirit really isn’t (he’s spirated, not begotten), and there’s nothing contradictory about that either.

A genuine contradiction would be this: ‘the Son is begotten by the Father’ and ‘the Son is not begotten by the Father’. Those two sentences are opposites by contradiction, not ‘the Son is begotten by the Father’ and ‘the Spirit is not begotten by the Father’. But the genuine contradiction can’t apply to the Son, for the false sentence is simply false. The Son is begotten, and that’s all we can say. But the Son being begotten says nothing about the Spirit. So genuine contradictions don’t really help us distinguish two things.

(c) Second, Aquinas says that the Son and Spirit are not distinguished by possession and deprivation. The reason is that possession and deprivation distinguish the perfect from the imperfect. Again, Aquinas says no more than this, for he assumes that the conclusion is obvious. And for me anyways, this time it is a little more obvious.

In this context, ‘perfection’ refers to fully realized potential, so something is ‘perfect’ only when it fully realizes its potential, and it’s ‘imperfect’ until its potential is fully realized. Possession and deprivation imply this sort of perfection and imperfection. A blind animal can’t realize its capacity to see, so it’s ‘imperfect’ with respect to sight. A seeing animal, on the other hand, is fully realizing its capacity for sight, so it’s ‘perfect’ with respect to sight.

In the Godhead, of course, nothing can be imperfect. There is no unrealized potential in God, so every divine person has everything it has the capacity for. Thus, there simply is no ‘deprivation’ in God, and therefore, there can’t be opposition between ‘possession’ and ‘deprivation’ in the Trinity. This kind of opposition is simply not possible in the divine case, so it can’t distinguish the Son and Spirit.

(b) Third, Aquinas says the Son and Spirit are not distinguished by contraries. As I explained above, contaries are non-relational features like ‘hot’ and ‘cold’ or ‘white’ and ‘black’. For Aquinas (and for Aristotle), these sorts of features are forms. Something is hot, for example, because it has the form of ‘heat’, and that form is what makes it hot.

Consequently, a difference between contraries amounts to a difference between forms. A hot thing and a cold thing differ with respect to hot and cold because one of them has the form of ‘heat’, and the other has the contrary form of ‘cold’.

For Aquinas though, there is just one form in God, and that’s the divine essence. The three persons all share that one divine-essence-form. Thus, the persons cannot differ by having different forms, and so the Son and Spirit cannot be opposites by having contrary forms.

(a) That leaves only correlatives. The Son and Spirit must, then, differ by having correlative features. As I explained above, correlatives are relational features that are reciprocal, like ‘double’ and ‘half’. So the Son and Spirit must each have a relational feature that is reciprocal with respect to the other’s relational feature.

However, there are lots of different kinds of correlatives, and so Aquinas still needs to show which kind of correlative the Son and Spirit differ by.