Aquinas on the origination relations of the Son and Spirit

According to Aquinas’s argument thus far, if the Son and Spirit are distinct, then they must have opposite features. The only kinds of opposite features they can have are the correlative features of ‘being the producer of’ and ‘being the product of’ that arise from instances of origination.

Consequently, if the Son and Spirit are distinct, they must each have one of those features. So if we take this argument seriously, Aquinas is saying that all three persons must be distinguished by the features 'being the producer of' and 'being the product of'. Those are the only options. So each divine person must either be the producer of, or produced by, another person.

This goes for the Son and Spirit too. If they are to be distinguished from each other, one must be the producer, and one must be the product. But which is which? Is the Son the producer, or is it the Spirit?

Aquinas simply says that the Son must be the producer of the Spirit, not the other way around, for nobody says that the Spirit produces the Son. Rather, everybody says that the Spirit is given by and from the Son.

Aquinas may be referring to Anselm here. In De processione 15.2 (Schmitt, 215), Anselm argues that either the Son is produced by the Son, or the Son is produced by the Spirit, and since nobody thinks the Son is produced by the Spirit, then it must be that the Son produces the Spirit. Henry of Harclay, when commenting on this particular argument in Aquinas, thinks Aquinas is just plain quoting Anselm here. And that may be.

But in any case, we have finally reached the end of this first argument for the Filioque in the SCG. Whew.

Aquinas on what kinds of correlatives distinguish the Son and Spirit

It's been some time since I've posted, as I've been busy writing a paper on Arius and Athanasius. That's pretty much done now, so I can jump back into what I've been posting about for the last couple of months, namely one of Aquinas's argument from the Summa Contra Gentiles on the filioque. This argument is fairly complicated, so I've been posting on it for some time now.

Up to this point, Aquinas has argued that spirits can only be distinguished as opposites, and the only kinds of opposite features that can distinguish the Son and Spirit are correlative opposites (like 'double' and 'half', or 'father' and 'son'). But then Aquinas wonders which kind of correlative opposites distinguish the Son and Spirit. In the last post, I explained that Aquinas says there are two basic kinds of correlatives: sameness-correlatives and action-correlatives. Sameness-correlatives are 'being the same as' (or 'being different from') with respect to substance (i.e., identity and distinction relations), quantity (equality and inequality relations), or quality (similarity and dissimilarity relations). Action-correlatives obtain between things that do an action and things that have that action done to them. Okay, so that's where we got to last time. Let's move on.

Given these two kinds of correlatives, which kind applies to the Son and Spirit? Aquinas says the first kind (sameness-correlatives) doesn't apply. Long before Aquinas’s day, Augustine established that the Father, Son, and Spirit must all be the same in substance, quantity, and quality. That is, they are all the same substance (they are all the very same God), they are all equal in magnitude or greatness, and they are all qualitatively similar (all have the same divine attributes).

Aquinas accepts this Augustinian rule, and so the divine persons can’t be different in any of those ways. Consequently, they can’t be opposites in any of those ways either. If two things are the same, they’re not opposites. Cicero and Tully are not opposite substances because they’re the same substance; two 10kg blocks are not opposite in weight because they have the same weight; and two white objects are not opposite in color because they’re the same color. So the divine persons are not opposites with respect to sameness-correlatives.

That leaves the second kind of correlatives, i.e., those based on action. But here, Aquinas makes an odd statement:

When it comes to correlatives based on action or passion, one of the pair of correlatives is in a subject that’s unequal in power [to that of the other’s subject]. The only exception are correlatives based on origination, for there nothing is designated as the ‘lesser’. Rather, in cases of origination, we find something that produces another which is similar and equal to it in nature and power.

Aquinas seems to be saying that most of the time, when one thing acts on another, one of them has more power than the other. But there’s a special case where this doesn’t happen, and that’s called ‘origination’. In cases of origination, one thing produces another, and the producer and the product are the same kinds of things (similar in ‘nature’, as Aquinas puts it), and they have the same degree of power.

What I don’t get about this is the claim that an action always involves one thing that has more power than another. What about when living organisms beget offspring? In those cases, Aquinas is happy to say that the producer and the product are the same kinds of things, and so they would also be equal in power. Humans are humans, and they have the exact some innate powers, irrespective of whether they’re fathers or sons.

Perhaps Aquinas is thinking about the raw materials that a producer uses to make a product. Raw materials don’t have any of the powers they have once they’re fashioned into a product (raw steel isn’t drive-able, but a car is), and so of course the producer has more power than the raw materials it uses to make a product. Or maybe Aquinas is thinking of offspring that need to develop their powers. Human zygotes don’t initially have the same powers as their parents. They have to develop those powers.

More generally, perhaps Aquinas is thinking that every action involves an agent and a patient, where the agent has active powers (powers to do something), and the patient has passive powers (powers to have something done to it). Thus, for every standard case of action down here on earth, the agent is more powerful than the patient.

But if that’s right, then Aquinas thinks ‘origination’ is a very specific kind of production that occurs only in the Trinity. Natural generation here on earth would not count as ‘origination’. Only in the Trinity is the producer and the product totally equal in power, for that’s the only instance of production that doesn’t involve any ‘moment’ when the patient (an underdeveloped product or the raw materials) has less power than the producer.

There might be something else going on here too. In most cases of production, producers cause their products to come to exist. That is, products depend on their producers for their existence. One would think that this applies in the Trinity too. If the Father produces the Son, then surely the Son depends on the Father for his existence.

However, the Son is supposed to have aseity -- and part of what it means to have aseity is not to depend on anything for existence. How then, can the Son both have aseity and be produced? This is a difficult issue, and I don’t intend to go into it here. The point is just that Aquinas might be thinking that products normally don’t have aseity, but in the divine case, the products (the Son and Spirit) do have aseity, and so he uses a special word -- ‘origination’ -- to talk about that special kind of divine production.

Still, that seems a stretch. Aquinas makes no mention of aseity or existential dependence here. Instead, he talks about the producer and the product being the same in kind and power. So I would think my former comments about power are closer to the mark.

In any case, Aquinas concludes from this that ‘origination’ is the only action that applies to the Son and Spirit, and so the only kinds of correlatives that can apply here are those based on origination. And presumably, these correlatives are the features of ‘being the producer of’ and ‘being the product of’ for an instance of origination. Finally, then, Aquinas has identified the opposite features in question. These are the features that distinguish the Son and Spirit.

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.

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?)