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.

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: 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.)

Aquinas on Distinguishing Two Productions

In the last post, I talked about what Aquinas takes to be the basic components of any production. A production is a process whereby some material is fashioned into a product. The three basic components of such a process are these: there's the producer, there's the 'formal term' (the final form the product takes), and there's the 'receptive material' that gets fashioned into the product along the way.

As we saw in the quotation from the last post, Aquinas thinks two productions can only be distinguished by one of these three components. Let me restate that as follows: two productions P1 and P2 are distinct only if they differ with respect to (a) their producers, (b) their formal terms, or (c) their materials.

Consider (b) first: two productions are distinct if they have different formal terms. Let me try to explain this with the following scenario. Suppose that I am a cleaner who works for the sole sculptor within a hundred miles. This sculptor likes to work alone, so I only come in at night to clean. One night, I notice a clay statue on the table, but the next night I notice that the same lump of clay has been re-fashioned into a vase (I know it's the same lump of clay because the sculptor's only got one lump of clay at the moment; the next shipment has yet to come in).

Now, the only thing that's different between the two days is the shape/form of the clay. Apart from that, the clay (the receptive material) is the same, and the sculptor (the producer) is the same (after all, there isn't anyone else within a hundred miles who could've done the sculpting). Still, the fact that there are two different forms (the 'formal terms') provides enough information to tell me that there have been two productions, even if the producer and the material are the same: on the first day, the sculptor fashioned the clay into a statue, and on the second day, she fashioned it into a vase.

Now consider (c): two productions are distinct if they involve different lumps of material. Suppose that the next delivery of clay arrives, and that night I notice a that lump of red clay has been fashioned into a statue. On the next night, I notice that a brown lump of clay has been fashioned into what looks to me to be the exact same statue.

In this case, the producer is the same (it's the same sculptor who made both statues), and the forms are the same (both statues are identical copies), but the material is different: the first statue is made from red clay, and the second is made from brown clay. Still, the fact that there are different lumps of material is enough information to tell me that there have been two productions: on the first day, the sculptor made a statue out of red clay, and on the second day, she made one out of brown clay.

Now consider (a): two productions are distinct if they involve different producers. To get at this idea, we'll have to modify our hypothetical scenario a bit. Suppose that another sculptor moves in, and the two join up to form one esteemed sculpting firm. However, each sculptor likes to work alone, so they come in on alternate days. Suppose also that they're a bit manic, and so each one destroys whatever work the other one has left in the studio.

One night, I notice a statue made out of the last lump of clay (again, there's only one lump of clay left; the next shipment hasn't arrived). The next night, I notice what appears to be the exact same statue made from the exact same clay.

In this case, the material is the same (it's the same lump of clay), and the forms are the same (the statue has the same shape on both nights). But nevertheless, I know that two producers have been involved, and that's enough to tell me that two productions have occurred: on the first day, the first sculptor made a statue, but on the second day, the other sculptor smashed the previous statue into a lump, and then re-fashioned that lump into an identical statue.

Of course, these scenarios are contrived, but hopefully they illustrate how two productions are distinguished by their producers, formal terms, or materials. If two productions differ with respect to even one of these, that's enough to tell that there are two productions.

Now, I've talked as if we're looking for a way to notice a distinction between two productions, and I've been saying that if we notice a distinction between producers, formal terms, or materials, that gives us enough information to tell that there are two productions.

However, it's not clear that Aquinas is suggesting a criterion by which we can notice when two productions are distinct. Instead, he may be suggesting the cause of two productions being distinct. If that's what he means, then he'd be saying something like the following.

Consider (c) first: if a producer uses two lumps of material, that necessarily amounts to two productions (she makes one product out of one lump of material, and she makes another product out of another lump of material). That's not necessarily very plausible though. Surely I can use two lumps of material to make one product.

Now consider (a): if two producers produce, that necessarily amounts to two productions (one producer performs one production, and the other performs another act of production). This is not so plausible either. Surely two producers can cooperate to make one product. And besides, Aquinas believes the Father and Son together produce the Spirit, and does he want to say that the Spirit is produced by two productions? (Maybe he does; some scholastics do think that.)

Finally, consider (b): if a producer produces two formal terms, that necessarily amounts to two productions (she makes one product with a certain form, and she makes another product with a distinct form). That's much more plausible, for no one product could have two formal terms (a lump of clay can't have a statue shape and a vase shape at the same time, for example).

I reckon that from the list of (a), (b), and (c), (b) is the only plausible cause of distinction. (a) and (c) work fine as criteria of distinction, but surely a difference in (a) or (c) doesn't necessarily cause distinct productions.

Aquinas on the components of production

On a number of occasions throughout his various works, Aquinas defends the filioque (namely, the claim that the Holy Spirit is produced by two persons, the Father and the Son). At one point (SCG 4.24, n. 11), he says this:

'If the Holy Spirit were distinct from the Son, then they'd have to be produced by distinct productions or processions. Two productions, however, can only be distinguished by their principles, terms, or subjects.'

Never mind the first sentence. What interests me is the second sentence, for I think there's a nice bit of metaphysics here. I gather that Aquinas thinks the following three components are involved in any production:

(a) a principle,
(b) a formal term, and
(c) some receptive material (which Aquinas calls the 'subject').

Think of production as a process whereby some material gets fashioned into a product, much like how a lump of clay gets fashioned into a statue. Here, (a) the 'principle' is the source of the production, and in this sense it's the starting point of the whole process; (b) the 'formal term' is the final form the product takes, and so in this sense it's the end point of the whole process; and (c) the 'receptive material' is the stuff that gets fashioned into the final product along the way.

Of course, that's a rough way of putting it, so let's discuss each of these components in a little more detail. I'll start with the last item on the list and work my way backwards.

First, then, is the last on the list: the (c) 'receptive material'. We think of 'material' as stuff like wood, clay, or iron, but for Aquinas the meaning is a bit wider. Something deserves the label 'material' only if it has the capacity (in medieval-speak: a 'passive power') to be acted upon in some way. Aquinas calls it the 'subject' because it receives the activity of the producer. So, for example, a lump of clay has the capacity to be shaped into statues, vases, and the like, so clay is 'material' in this sense. But Socrates can be sunburnt, so he is like 'receptive material' for the sun's activity too. For Aquinas, the term 'receptive material' extends to quite to a few objects in the material world.

Further, the receptive material has to be the right kind of stuff, where 'the right kind of stuff' is anything that has the capacity to be fashioned into the particular kind of product in question. Materials have certain kinds of capacities ('passive powers'), but not others, so not all materials can be made into just any old product. Clay makes for great statues, but horrible nails. Organic tissue, on the other hand, makes for great animal bodies, but horrible statues.

Also, the receptive material has to be distinct from whatever product it's fashioned into. The very same lump of clay can become a statue, then a vase, and so it's clearly not the very same thing as the statue or the vase. If it were the same as the statue, it'd be destroyed when the statue is, but that's obviously not the case. I can smash a clay statue, but I'm still left with a lump of clay, even though the statue is no more.

As for (b) the 'formal term', different scholastic authors define this in different ways (Ockham, in particular, provides a distinctive definition in Ord. 1.5.3). But for Aquinas, it's the final form of the product. The 'formal term' is called the end point (terminus) of a production because it's the final form the product takes. When I sculpt a statue, my lump of clay takes on a succession of different shapes, but eventually I get to the one I'm after. The 'formal term' is that final shape that I finally get to, and that's why it's the 'end point' of a production.

(Sometimes a lump of matter doesn't go through a series of intermediate forms. Instead, it's immediately turned into the product in question. Living organisms are generated this way: a lump of organic tissue immediately becomes the organism in question as soon as it gets the organism's form. But even in cases like this, the product's form is the 'end point' of the production.)

As for (a), the term 'principle' has a broad meaning in scholastic writings, and it basically means 'source'. Of course, there are lots of way for one thing to be the 'source' of another, so there are lots of different kinds of principles. So what kind of principle does Aquinas have in mind when he talks about the 'principle' here?

I think there are two candidates here. First, a cause is one kind of principle. (Here I mean an 'efficient cause'. Aquinas also calls the 'formal' and 'material' causes 'principles', but those don't seem to be good candidates for what Aquinas is talking about here, so I'm only looking at the 'efficient cause', i.e., whatever acts to bring about an effect.) If we take 'principle' in this sense, then the 'principle' (efficient cause) of a production is the producer – i.e., the thing that actually does the producing.

But another kind of principle is a power source (or what I call a 'power-pack'). A power-pack, in this context, is some constituent or 'metaphysical part' of a producer that provides it with the power to produce the product in question. The idea here is that certain things have certain power-packs, and those power-packs give them certain powers. Consequently, something can only produce a particular kind of product if it has the right kind of power-pack.

On many an occasion, scholastic authors use the term 'principle' to refer to a 'power-pack' (see especially distinction 7 of the Sentences Commentaries), and so I suppose it's possible that Aquinas has the 'power-pack' in mind here when he talks about the 'principle' of a production.

So which is it? Does 'principle' mean 'producer' or 'power-pack'? I think that Aquinas must mean 'producer' here. I have two reasons for saying this. First, when some later authors present Aquinas's argument (and I'm thinking of Henry of Harclay in his Ord. Quest. 6), they just use the term 'producer' instead of 'principle'. Now, later authors often misconstrue Aquinas if it suits their purposes, but this particular reading is perfectly sensible, so I see no reason to doubt it.

Second, Aquinas's argument simply wouldn't work unless he meant 'producer'. He goes on to argue that we can only distinguish the Son and Spirit by (a) their principles, and from this, Aquinas concludes that the Son and Spirit must have different producers (the Son comes from one producer, and the Spirit comes from two producers). This wouldn't work if Aquinas didn't mean 'producer'. If he meant 'power-pack', he could only conclude that the Son and Spirit come from different 'power-packs', not different 'producers'.

A production, then, is a process whereby a producer (the 'principle') takes a lump of 'receptive material', and fashions into a product by giving it a particular form (the 'formal term'). This provides an abstract account for many different kinds of production: a statue is produced when a lump of clay is given a statue shape; a human being is produced when a lump of organic tissue is given a human form; 'tan Socrates' is produced when Socrates is given a tan color; and so on.