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.

Aquinas on the distinction of spirits

In the Summa Contra Gentiles, book 4, chapter 24, Aquinas provides a number of arguments for the filioque (i.e., the claim that the Spirit is produced by two divine persons, namely the Father and the Son). In one of those arguments (n. 8 in the Taurini 1961 edition), he makes the following claim:

In things where the material distinction is removed (and a material distinction cannot have any place in the divine persons), no two things are found to be distinguished unless by some opposition.

Here Aquinas is saying that when it comes to non-material things (let’s just call them spirits), the only distinction is one between opposites. That is, any two distinct spirits are opposites in some way. Let's formulate this claim like so:

(A1) For any spirits x and y, x and y are distinct iff x and y are opposites.

Right away, I’m skeptical. A1 states that all spirits are opposites, but why should we believe that? You and I are distinct, but we’re certainly not opposites. Why can’t two spirits be distinct like we are, without being opposites? The angels Gabriel and Michael are distinct, but are they opposites? If so, in what way?

To explain why spirits are always distinguished by opposition, Aquinas says the following:

Those things that have no opposition to each other can be in the same thing at the same time. Hence, no distinction can be caused by them. Whiteness and triangularity are diverse, but they’re not opposites, so they can belong to the same thing.

This requires some unpacking. There are three points here, and each needs to be separated. That way, we can more clearly see what Aquinas is actually saying here.

(a) The first point to clarify is based on the comment that whiteness and triangularity can exist together in the same thing. The assumption is that some features can simultaneously exist in the same thing, but others cannot. Some features have no disagreement and are perfectly happy to be together, but others just can’t be in the same room, so to speak. Let’s say that the former type are ‘compatible’, and the latter type are ‘incompatible’:

(A2) For any x and y, x and y are compatible iff x and y can exist simultaneously in some z.

(A3) For any x and y, x and y are incompatible iff there is no z in which x and y can exist simultaneously.

To use Aquinas’s own example, whiteness and triangularity are compatible because one and the same thing can be both white and triangular. And indeed, we see white triangles all the time, so whiteness and triangularity are clearly compatible in this way.

Incompatible things, on the other hand, aren’t like this. If I ask a group of people to take sides on capital punishment, that will break up the group: some will be for the death penalty, and others will be against it. These are incompatible viewpoints, so they have to be held by different individuals/groups.

(b) The second point to clarify is based on Aquinas’s comment that compatible features cannot be the cause of distinction. The claim here is that incompatible features can, but compatible features cannot, be the cause of distinction. What does Aquinas mean by ‘cause’ here? To answer this, we need to distinguish between what Aquinas calls an ‘efficient cause’ and a ‘formal cause’.

The efficient cause explains how something comes to exist, while the formal cause explains how something is the particular kind of thing it is. Thus, the efficient cause of some x is the agent that brings x into being, but the formal cause of x is x’s defining characteristics (or ‘formal characteristics’, as the medievals put it), for those are the characteristics that make x the sort of thing it is.

For example, the efficient cause of a clay statue is the sculptor, for that’s who made it. Without the sculptor’s activity, the statue wouldn’t exist. But the formal cause of the statue is its statue-shape, for that’s what makes it a statue. After all, if the sculptor gave the clay a vase-shape, that’d make it a vase, not a statue.

So does Aquinas think incompatible features are efficient or formal causes of distinction? Surely he doesn’t think they’re efficient causes. Taking sides on capital punishment divides people into two groups, but the viewpoints themselves don’t literally twist people’s arms and force them into two groups. As the saying goes, viewpoints don’t kill people, people kill people.

But the ‘for’ and ‘against’ viewpoints are formal causes of division. Their formal/defining characteristics are such that one and the same individual can’t hold both viewpoints simultaneously. Thus, they require separate advocates: one to take the ‘for’ side, and another to take the ‘against’ side.

Besides, features depend on the things they belong to, not the other way around. A sports car has the feature of being red, but its red color depends on the car for its existence; the car doesn't depend on its red color. After all, I could re-paint my car, and the car would still exist, but if I destroyed the car, any color it might have would cease to exist too.

Consequently, features can't be the efficient cause of distinction. Features come on the scene too late, as it were, to cause any distinctions. For this reason alone, incompatible features can’t be the efficient cause of distinction (though they can be the formal cause of distinction).
I take it, then, that Aquinas thinks incompatible features are the formal cause, not the efficient cause, of distinction. When he says that two incompatible features F and G are the ‘cause’ of distinction, he means F and G formally require distinct things. He doesn’t mean that F and G efficiently cause distinct things to come into being.

(Note that this seems to be a priori or ‘self evident’ in the sense that the consequence is included in the antecedent. Here, incompatible features are defined as features that can’t exist in the same thing (A3 above). But to say that incompatible features are the ‘formal cause’ of distinction is just to say that incompatible features can only exist in distinct things.)

(c) The third point that needs clarification focuses on Aquinas’s claim that two features are compatible so long as they’re not opposites. We need to be careful here. How wide is Aquinas casting this net? He’s supposed to be talking only about spirits, but his example of whiteness and triangularity is taken from the material world. So is Aquinas talking about any two features (be they spiritual or material), or is he only talking about spirit features? If it’s the former, then Aquinas is saying this:

(A4) For any features F and G, F and G are compatible iff F and G are not opposites.

But if it’s the latter, Aquinas is saying this:

(A4*) For any spirit features F and G, F and G are compatible iff F and G are not opposites.

These are very different claims. The fact that Aquinas talks about whiteness and triangularity makes it tempting to think that he is affirming the former claim (namely, A4). After all, spirits are neither white nor triangular, so it certainly appears as if Aquinas is thinking that this rule applies to more than just spirits.

The problem is, Aquinas thinks A4 isn’t always true. Individual material substances are incompatible according to A3, but they’re not opposites. Socrates and Plato, for example, obviously can’t exist in the same thing, but they’re not opposites. Thus, Aquinas should reject A4.

Perhaps he holds A4* instead. That would support his initial claim (A1 above) that all spirits are distinct because they’re opposites. But if that’s right, I still wonder why Aquinas uses whiteness and triangularity as an example. Maybe it’s just a bad example, and that’s all there is to it.

Now, it’s well known that for Aquinas, material beings are distinct because they occur in different lumps of matter, but angels are distinct because they belong to different species. For Aquinas, a species gets divided up into different individuals when its instantiated in different lumps of matter, roughly similar to the way a cookie cutter’s shape gets replicated when it’s stamped into different lumps of cookie dough. (So Socrates is the human-species ‘stamped’ into this lump of tissue, and Plato is the human-species ‘stamped’ into that lump of tissue.) But angels don’t have any matter, so any given angel-species can’t be replicated by being ‘stamped’ into different lumps of matter. Thus, each angel is the sole member of its species. Moreover, each angel just is its species, much like how there’s nothing but the cookie cutter’s shape if there aren’t any lumps of cookie dough to take on that shape.

Given this, we might think that Aquinas believes that although distinct material beings (in the same species) aren’t opposites, distinct species are opposites. That would support the initial claim (A1), for although Aquinas is willing to accept that material things are distinct without being opposites, there is no matter in the realm of angels, so the only distinction there is one between species, and species are distinct only because they’re opposites.

But if that’s right, then what is it that makes species opposites? Every species is a complex of a shared genus and a unique specific difference. For example, the human species is composed of animality (the genus that humans share with other animals), and rationality (the specific difference that belongs uniquely to humans, and so distinguishes humans from other animals). Thus, any opposition between species would have to occur between the specific differences. After all, the genus is shared, and shared things can’t be opposites. But does Aquinas really think that specific differences are opposites?

That seems to be the moral of the story here. Consider the human- and brute-species. These are distinct because the former has rationality and the latter does not. Rationality and irrationality seem to be opposites, so perhaps that makes sense. Maybe, then, Aquinas is using opposition to explain how species themselves are distinct.

Still, this leaves many questions unanswered. If specific differences are opposites, what, exactly, are opposites? How does one define ‘opposites’? Are there different kinds of opposites? If so, which kind do specific differences fall under?

In any case, now that we’ve gone through all that, we’re in a better place to summarize Aquinas’s argument. As I hope is clear by now, Aquinas argues that non-opposing features are compatible, so they’re perfectly happy to exist in the same thing. (Well, in the material world, material substances can be incompatible without being opposites, but we’re talking about the realm of spirits here.) Consequently, non-opposing features can’t be the formal cause of distinction between spirits, for there’s nothing about such features which demands that they exist in distinct things.

Opposite features, on the other hand, are incompatible, so they cannot exist in the same thing. On the contrary, opposite features can only exist in distinct things. Thus, opposite features must be the formal cause of distinction for spirits.

Unfortunately, A4/A4* are contentious. Neither A4 nor A4* are universally agreed-upon claims. Ockham, for example, thinks that angels are individuals just like Socrates and Plato, and all individuals are primitively distinct (without being opposites). So Aquinas’s argument is only as successful as A4/A4*, and not everybody buys A4/A4*.

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.)

Aristotle on Opposites 3: Possession and Deprivation

In the Categories 10, Aristotle outlines 4 kinds of opposites. In the last two posts, I covered the first two of these, namely 'correlatives' and 'contraries'. The third kind of opposites is possession and deprivation: possessing some feature that one should naturally have is the opposite of being deprived of it.

For example, sight and blindness are opposites in this way for animals, because animals naturally have the ability to see. When an animal can see, it possesses sight, but when it's blind, it's deprived of sight.

It's important to note that this only applies to natural features that things are supposed to have. We don't normally say that stones are blind, because stones aren't supposed to see. Only things that are supposed to have sight can be deprived of it, so sight/blindness are opposites for animals, but not stones, foot stools, and so on.

(To put this another way, being deprived of something is not the same as simply not having it. Stones don't have sight, but they're not blind. The sentence 'x is deprived of F' does not mean 'x does not have F'.)

Aristotle also says that possession and deprivation always refer to one thing that either possesses or is deprived of some natural feature. When we talk about sight and blindness and opposites, we're not talking about one animal that can see as the opposite of another animal that's blind. We're talking about the same animal either having sight or being blind. Sight/blindness are opposites for that one animal, not multiple animals.

This distinguishes possession/deprivation from correlatives. As I explained two posts back, correlatives always hold for two things, and they're reciprocal (if one thing is 'double', then another is 'half'). Possession/deprivation are not like this. If one thing can see, there's no guarantee that another is blind. If only one animal existed, it could still either see or be blind, and sight and blindness would still be opposites for that animal.

It's tempting to think that possession/privation are opposites in the way that contraries are. As I explained in the last post, contraries are the most different features that belong to the same kind (so 'white' and 'black' are contraries for color, 'hot' and 'cold' for temperature, and so forth). After all, what could be 'more different' than having some feature vs. not having it? But Aristotle says possession/deprivation are not contraries, and here are the reasons he gives.

Contraries are either (i) necessary and binary, or they are (ii) unnecessary and not binary. Possession/deprivation are binary, for something either has a natural feature or it doesn't. An animal can either see, or it's blind, but it can't be somewhere in between. (An animal might have poor sight, as I do, but I can still see. And sometimes an animal's sight is so bad that it is, for all intensive purposes, blind.) And the fact that possession/deprivation are binary rules out the possibility that possession/deprivation could be unnecessary contraries, for as I explained in the last post, no binary pair are unnecessary contraries.

But possession/deprivation aren't the same as necessary contraries either. Necessary contraries are such that one or the other of the pair must always be present in the appropriate sort of thing. But animals don't always have either sight or blindness. When animals are undeveloped (like when they're zygotes), they can't see yet. Still, at that time, they're not deprived of sight, for they aren't supposed to see yet. So although possession/deprivation are binary, they're not necessary in the way that binary contraries must be.

Aristotle on Opposites 2: Contraries

Last time, I talked about the first kind of 'opposites' that Aristotle talks about in the Categories 10, namely 'correlatives'. Correlatives are relational features that are reciprocal, like 'double' and 'half' (each refers to the other).

The second kind of 'opposites' are what Aristotle calls 'contraries'. These are what we typically think of when someone says, 'give me an example of a pair of opposites'. 'Hot' and 'cold', 'good' and 'bad', 'black' and 'white', 'healthy' and 'sick', things like that.

Here in Categories 10, Aristotle says two things about contraries.

(1) Contraries are not relational and reciprocal. They do not each relate to the other in the way that 'double' and 'half' do. If something's 'double', then there must be something else that's 'half'. A 10kg block couldn't be 'double' if it were the only thing in the universe, for there'd be nothing it could be the double of. But if something's hot, then there's no guarantee that something else will be cold. A candle could exist all by itself, and it'd still be hot. Hell, even if one thing is hotter than another, the cooler of the two still needn't be cold.

Of course, contraries like 'hot' can stand in various relationships -- this bit of heat might be double the temperature of that one -- but the contraries themselves are not relational features like correlatives are. Contraries are, I reckon, non-relational features.

(2) Contraries are divided into two broad groups.

(a) In the first group belong all that are necessary and binary. A pair of contraries is necessary if the appropriate sorts of things always have one or the other (but not both), and never neither. (I say 'the appropriate sorts of things' because contraries don't belong to just any old thing. Only certain kinds of things can have certain kinds of contraries. Animals can be healthy or sick, but stones cannot.) A pair of contraries are binary if those two contraries are the only options, and there's nothing in between.

For example, health and sickness are necessary and binary in this sense. Every animal must be either healthy or sick, but never neither, and it can't be somewhere in between. (Of course, we might say that an animal is 'in between' in the sense that it's partly healthy and partly sick, but that applies to different parts of the animal, not the same part.) Similarly, 'odd' and 'even' are necessary and binary for whole numbers (except zero). Every whole number (apart from zero) must be either odd or even, and it can't be somewhere in between.

(b) In the second group belong all contraries that are neither necessary nor binary. White and blackness, for example, are not necessary, nor are they binary. Animals can be white, black, or anywhere in between.

Aristotle speaks as if the division between (a) and (b) is exhaustive. All necessary contraries are binary, and all unnecessary contraries are not binary. There are no necessary contraries that are not binary, and there are no unnecessary contraries that are binary.

That's all Aristotle says in Categories 10. It doesn't give us a whole lot to go on. I still wonder what it is, exactly, that makes two things contrary? Elsewhere, Aristotle says that contraries are what are 'the most distant in the same genus' (Categories 6, 6a15-18). That is, if we take any particular kind of feature that comes in a variety of degrees, the two ends of the spectrum are the contraries. For example, color comes in different shades ranging from black to white, but since black and white sit at the ends of the color spectrum, black and white are the contraries for color.

But that won't do; not quite. Aristotle thinks some contraries are binary; for them, there's nothing in between, so there's no spectrum. Consequently, we can't talk about a 'spectrum', or a 'variety of degrees', or anything like that. Instead, we need to talk about contraries as the two most different features that belong to the same kind. So even if there were no colors except for black and white, black and white would still be contraries because they're the most different of any two colors. And that would work for any feature-kind, no matter how many different features belonged to that kind.

However, this would mean that every two-membered feature-kind is a contrary. Would Aristotle accept that? I don't know. But more importantly, this would mean that all two-membered feature-kinds are necessary, for those kinds would be binary, and all binary contraries are necessary. Conversely, any more-than-two-membered feature-kinds would be unnecessary. I'm not sure whether Aristotle would accept this implication. Maybe he would. I don't know.

Before I finish, there are two little problems to bring up.

(i) A short while later in the Categories (see 12b37-13a2), Aristotle says that some contraries are essential constituents for certain kinds of things. For example, whiteness is an essential constituent of snow, because snow is always white. Doesn't this mean that whiteness is necessary for snow? If so, it should follow that whiteness belongs to a pair of binary contraries (for Aristotle has said that all necessary contraries are binary). But that's obviously false. There are other colors besides white and black. On the one hand, then, Aristotle says that all necessary pairs are binary, but on the other hand, he says some necessary pairs are not. Which is it?

(ii) Aristotle also says a little later (see 13a31-37) that contraries are variable: something can switch from one contrary to the other (a pot can become hot, then cold, then hot again). He makes this point in order to distinguish contraries from the third kind of opposites: namely, possessing a natural ability, and being deprived of that ability. Possession and deprivation, says Aristotle, are permanent (once blind, a man doesn't regain his sight), and since contraries are variable, they're not the same as possession/deprivation. Now, if some contraries are necessary constituents for certain things (as whiteness is for snow), then surely those are 'permanent'. Again, then, it seems that Aristotle is saying that contraries are 'variable', and that they're 'permanent'. Which is it?

Aristotle on Opposites: Correlatives

What are opposites? Any of us could give plenty of examples. 'Hot' and 'cold', 'good' and 'bad', and so forth. But what is it that makes these pairs of features opposites? And what is it that makes 'hot' the opposite only of 'cold' rather than, say, 'bad'?

Explaining a theory of opposites is no easy task, but Aristotle takes a shot at it in the Categories 10. There he says there are four kinds of opposites:

(a) correlatives (e.g., 'double' vs. 'half'),
(b) contraries (e.g., 'hot' vs. 'cold'),
(c) possession/deprivation (e.g., 'sight' vs. 'blindness'), and
(d) contradiction (e.g., 'Socrates is sitting' vs. 'Socrates is not sitting').

What about the first of these – what, exactly, are correlatives? Aristotle says the following:

'Pairs of opposites which fall under the category of relation are explained by reference of the one to the other, the reference being indicated by the preposition "of" or by some other preposition. Thus, "double" is a relative term, for that which is double is explained as the double of something'.
[11b22-33, emphasis mine, and I added the quotes around 'double'.]

Here's what I gather from this: every correlative is a relational feature. A relational feature relates one thing to another. How do we know when a feature relates one thing to another?

Well, Aristotle thinks it goes something like this. If we take some feature and try to explain what that feature is, we can only do so if we make reference to something else. For example, if I tried to explain to you what 'double' is, I'd have to talk about how something that's 'double' is twice as much as another thing. I couldn't really explain what 'double' is without also talking about what it's the double of.

In modern logic speak, we might say that relational features can only be expressed by two-place predicates. A two-place predicate is one that requires filling in two blanks to make sense. For example, the predicate 'is the double of' only makes sense if I fill in both of the following blanks: '_____ is the double of _____'.

I couldn't say '10kg is the double of...' and just drop off. You'd think I was either asking you to fill in the blank (as if I went around giving you pop math quizzes all day), or you'd think I got lost in thought and stopped mid-sentence (which I do). But you wouldn't think I uttered a complete sentence. A two-place predicate needs both blanks filled in.

(There are three-place, four-place, and n-place predicates too. A three-place predicate would be something like '_____ is half way in between _____ and _____'. I've got to fill in three blanks there, so it's a three-place predicate. But I think Aristotle believes that correlatives are best expressed by two-place predicates, so we can ignore all these n-place thing-a-ma-jigs for now.)

In any case, my point is that a relational feature is explained with reference to something else (it's explained with a two-place predicate), and every correlative is like this. Thus, 'double' is a relational feature because you have to explain it as the double of another thing. Likewise, 'half' is a relational feature because you have to explain it as the half of another thing. The same goes for other correlatives like 'parent' and 'offspring', 'taller' and 'shorter', and so on.

Another thing I gather from the quotation above is this: correlatives are reciprocal. That is, each one refers to the other: for any pair of correlatives R and R*, if x is related to y by R, then y is related to x by R*. Every correlative is like that. If x is the double of y, then y is half of x. If x is the parent of y, then y is the offspring of x. If x is taller than y, then y is shorter than x.

So that's correlatives. A pair of features are correlatives iff (i) each of the pair is a relational feature, and (ii) each of the pair are reciprocal. As Aristotle sees it, correlatives are one kind of opposites. 'Double' is the opposite of 'half'. 'Parent' is the opposite of 'offspring'. 'Taller' is the opposite of 'short'.

One last thing. We should be careful not to confuse the correlatives themselves with the things they correlate. Suppose I have a 10kg block and a 5kg block. Obviously, the first is double the second in weight, and the second is half the first in weight. But what are the actual 'opposites' here? The blocks? The weights?

It seems to me that the genuine opposites are the relationships the blocks have to each other (namely, the relationships of being double and half). The blocks (and their respective weights?) are 'opposites' only in virtue of their double/half relationships.

(Strictly speaking, perhaps the blocks are opposites in virtue of the double/half relationship, and the weights are the foundation/basis for that relationship. But still, aren't 10kg and 5kg opposites?)

Aquinas on the Filioque

In the last two posts, I talked about what Aquinas thinks are the essential ingredients or components of any production, and how he thinks those components allow us to distinguish two productions. As I explained, for Aquinas, every production will involve (a) a producer, (b) a 'formal term' (which is the final form the product takes), and (c) the receptive material that gets fashioned into the final product along the way. And given these, Aquinas thinks we can distinguish two productions if they differ with respect to at least one of these components.

Aquinas uses all of this, of course, to distinguish the Son from the Spirit, and so I might as well wrap this up by quickly going over that. Immediately after the quote I gave two posts back (the one from SCG 4.24, n. 11), Aquinas goes on to argue that we can only distinguish the Son and Spirit by their producers, not 'formal terms' or 'receptive material'. He reasons as follows.

First, we can't distinguish the Son and Spirit by (c) their receptive material, he says, because the Son and Spirit aren't material things, so there aren't two lumps of material there.

(Note that some scholastic authors, Henry of Ghent in particular, disagree with part of Aquinas's claim here; for Henry of Ghent, the divine essence is like a lump of quasi-material that all the persons are made from. Of course, there's just one such lump, so we couldn't distinguish the Son and Spirit based on that.)

Second, we can't distinguish the Son and Spirit by (b) their 'formal terms' either, because for Aquinas, the Son and Spirit have the very same form, namely the divine essence.

(Again, note that not all scholastic authors accept this. Henry of Ghent, again, thinks the personal properties (not the divine essence) are the forms of the persons, and those are all different.)

Third, that leaves (a) their producers. The Son and Spirit must, then, have different producers. Therefore, Aquinas concludes, the Son must be produced by one person (the Father), and the Spirit must be produced by two (the Father and Son together).

(Note also: This argument could equally conclude that the Son is produced by the Father alone, and the Spirit is produced by the Son alone. That'd amount to different producers too. But Aquinas would respond that if the Son were the sole producer of the Spirit, we might as well just call the Son 'father' and the Spirit 'son', for 'father-son' really means 'one producer-one product'. But that would be no good. The notion that 'father-son' relations only apply to 'one producer-one product' scenarios is precisely the point that Aquinas is trying to prove here, so he couldn't slip that in before he's proved it.)