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.)

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.