Avicenna on necessity and possibility

Avicenna famously says that God is 'necessary in himself', while all creatures are both 'possible in themselves' and 'necessary from another'.

There are two distinctions here.

1. The first distinction is between something that is 'necessary in itself' and something that is 'possible in itself'. God is 'necessary in himself', while everything else is 'possible in itself'.

It would be a mistake to interpret this as a distinction between necessary and contingent beings, as if that which is 'necessary in itself' exists in every possible world, while that which is 'possible in itself' exists in some but not all worlds.

This would be wrong not only because Avicenna doesn't believe in possible worlds (for Avicenna, there are no possible worlds -- just the one, necessary world), but also because Avicenna thinks everything that is 'possible in itself' is produced necessarily. Since anything that's produced necessarily would exist in every possible world, it would be incoherent to also say that it would exist in some but not all worlds.

(Averroes thinks Avicenna is suggesting just that, so he accuses Avicenna of incoherence. But Averroes' interpretation is incorrect.)

So we should not think that to be 'possible in itself' means to be 'contingent'. Rather, we should take it to mean just what Avicenna says: that which is 'necessary in itself' exists without being produced, while that which is 'possible in itself' exists because it is produced.

And that, I think, is the bottom line. That's all that Avicenna means when he talks about being 'necessary in itself' and 'possible in itself'. There's nothing there about modality.

Now, Avicenna says some other things about being 'necessary' or 'possible in itself', but I don't think they take away from my point. They are as follows.

(a) Something is 'necessary in itself' if its non-existence entails a contradiction. In other words, something that is 'necessary in itself' is the sort of thing that simply must exist. Consequently, it exists on its own, so it need not, and in fact it cannot, be produced. (It just exists on its own, and you can't produce what already exists.)

(b) By contrast, if something is produced, then it cannot be 'necessary in itself'. If it were 'necessary in itself', then it would exist on its own, so it could not be produced. But since it is produced, it must not be 'necessary in itself'.

(c) Further, since it's produced, it must not be 'impossible in itself', for impossible things cannot exist at all.

(d) Its existence, then, must be within the bounds of possibility. So it is 'possible in itself'.

But as I said, I don't see how any of that takes away from the basic point: for Avicenna, to be 'necessary in itself' means to exist without being produced, and to be 'possible in itself' means to exist because its produced. And that's all it means.

Some people talk as if Avicenna thinks there is a realm of 'possibles' standing in front of God, and God chooses what to actualize.

But I don't think that's right either. Avicenna uses the word 'possible' only because that which is produced is neither 'necessary' nor 'impossible' in itself, and the only word left is 'possible'. But unfortunately, the word 'possible' suggests contingency, a realm of 'possibles', etc.

I think a better label would be 'not necessary in itself'. Avicenna's real point is just that a product is produced; it's not the sort of thing that just exists without being produced. As Aquinas nicely puts it in Sent. 1.8.3.2: 'That which acquires its existence from another does not exist necessarily in itself, as Avicenna proves'.

So to say that something is 'necessary in itself' means nothing more than that it exists without being produced, and to say that something is 'possible in itself' means nothing more than that it exists because it is produced. That's it. No modality here.

2. The second distinction, however, does have to do with modality. This is a distinction between something that is produced necessarily and something that is produced contingently (or, in Avicenna's terminology, between what is 'necessary from another' and what is 'possible from another').

For those who believe in possible worlds, we could put the point like this: a product is 'necessary from another' if it's produced in every possible world, but it is 'possible from another' if it's produced in some but not all worlds.

Note that just because something is produced does not entail whether it is produced necessarily or contingently. To put it in terms of possible worlds again, a product might be produced in every world, or it might be produced only in some.

This is why I say that the distinction between being 'necessary' or 'possible in itself' is not a distinction between necessary and contingent beings. It is just a distinction between being produced or unproduced. The distinction between being necessary or contingent comes up here, i.e., in the distinction between being 'necessary' or 'possible from another'.

For reasons I don't want to go into here, I should note that Avicenna's distinction between being 'necessary' or 'possible from another' is only a logical distinction. Avicenna believes that every product is produced necessarily, so there is nothing that is genuinely contingent in Avicenna's universe. So the distinction is just logical.

Nevertheless, the point still stands: to be produced is one thing, and to be produced necessarily or contingently is another. Again, to put it in terms of possible worlds, a product cannot exist in a world all by itself: if it exists in a world, it must exist with its producer. But that says nothing about how many worlds a product exists in. It might exist in none (if it was never produced), it might exist in some if it's produced contingently), or it might exist in all (if it's produced necessarily).

Obviously, the distinction between being 'necessary' and 'possible from another' only applies to products. It cannot apply to something that is 'necessary in itself', for such things are not produced, so there's no option to be produced 'necessarily' or 'contingently'. Only products can be produced 'necessarily' or 'contingently'.

Consequently, anything that exists without being produced has only the one feature: that of being 'necessary in itself', while anything that is produced has two features: that of being 'possible in itself', and that of being 'necessary' or 'possible from another'.

William of Ware: a lesser mind?

Medieval philosophy does not consist only of Anselm, Aquinas, Scotus, and Ockham. There were many, many more philosophers back then. But not all of them were anywhere near as sharp as those I just mentioned.

Scotus's alleged teacher is a character by the name of William of Ware. I don't really know much about William except that he followed Henry of Ghent's claim that the divine essence is like the quasi-matter or subject of the Son's generation. And I only know this because I read about it in an article.

So I was re-reading that article the other day, and for the first time I decided to pay attention to one of the quotations from William (before I had always just skipped over it). This paragraph struck me as such a bad piece of philosophy that it made me think William might be one of those lesser minds that are simply not as bright as the Anselms and the Ockhams. Maybe I'm wrong about this; I've only read this one little paragraph. But I had the thought nonetheless.

Here's the paragraph. William writes:

'In book 5 of The Physics, the Philosopher argues as follows to show that generation is not motion: "what is moved, is; what is generated, is not; therefore, generation is not motion". In the first premise, the word "what" is taken subjectively for the subject of motion. Therefore, it must be taken in the same way in the second premise, for if it were taken to refer to the end point of the generation [i.e., the substance that's generated], then there would be a variation in the argument, and it would not go through'. [Vienna, 1424, fol. 29vb]

The implied conclusion here is that the subject of generation -- i.e., matter -- is generated. Let me explain this in more detail.

Aristotle tries to distinguish generation and motion on the grounds that generation causes something that didn't exist to come into being, and motion causes something that already exists to move. The thrust of the quotation from Physics 5 is clearly that what's generated didn't exist before, while what's moved did.

But William looks at the logical form of the argument. Here it is:

(1) What is moved, exists [before the motion].
(2) What is generated, does not exist [before the generation].
(3) Therefore, generation is not motion.

As William points out, this argument is only valid if the term 'what' stands for the same thing in both (1) and (2). If it stands for different things in (1) and (2), then it commits the fallacy of equivocation.

Now, on a standard scholastic-Aristotelian analysis, motion and generation are both types of change. A change occurs when something x acquires a new property F that it didn't have before.

Motion fits this definition because an object moves when it acquires a new place, and so the object is x, and its new place is the acquired F. Generation also fits this definition because a living organism is generated when a lump of matter acquires a substantial form, so the lump of matter is x and its new form is the acquired F.

With this in mind, William points out that in premise (1), the term 'what' clearly stands for x, i.e., the subject that acquires a new F (where, in the case of motion, x is the object that moves, and F is the new place it moves to). But since 'what' in premise (2) has to stand for the same thing, it must also stand for x, i.e., the subject that acquires a new F (where, in the case of generation, x is the lump of matter, and F is the form it acquires).

So if we substitute the subjects of motion and generation for 'what' in (1) and (2), we get this:

(1*) The object that is moved, exists [before the motion].
(2*) The lump of matter that is generated, does not exist [before the generation].

William then looks at (2*) and infers that a lump of matter is generated, for (2*) states that the lump of matter did not exist before the generation, whereas (1*) states that an object that's moved does exist before it's moved.

So the conclusion here, as William sees it, is that matter is generated. (Or, to put it slightly more generally: the subject of a generation is itself generated.)

Now, that, it seems to me, is absolutely crazy. Apparently, William is here taking an argument from Aristotle so literally (in terms of its logical form) that he reaches a very un-Aristotelian conclusion. One of the foundational claims of Aristotelian philosophy is precisely that every change (even generation) requires a substrate or subject that persists throughout the change. If you claim that the subject of a generation is itself generated (as William is here), you have traveled very far from Aristotle indeed.

Surely William can see this. You would think that instead of denying a fundamental Aristotelian claim, he would instead say that Aristotle's argument is (at worst) either invalid or (at best) not to be taken so literally.

And indeed, the argument is, in fact, invalid. Premise (1) states that the subject of motion exists before the motion (or at least independently of the motion), while premise (2) states that the product of generation (i.e., the whole organism that's generated) does not exist before the generation (or at least not independently of the generation). But those two claims in no way entail the conclusion (3) that motion is not generation. So William could have had a nice point here if he would have just shown that Aristotle's argument is invalid when taken too literally.

But instead of doing that, William took the crazy route. Bad scholastic philosophy, if you ask me. As I said above, this is an example of the lesser minds you can find in medieval philosophy. The better minds like Scotus and Ockham would never even dream of such bad philosophizing.

Per se unity

The scholastics often follow Aristotle in saying that the matter and form in a living organism have 'per se unity'. What's that?

Well, the basic idea is that different ingredients can be tied together more or less loosely. Consider the following cases.

(i) Items in a pile of trash are tied together extremely loosely. It doesn't take a lot of force to separate them, and the items aren't held together in a pile because they each have some intrinsic power to join together.

(ii) Socrates and his pale color are tied together more tightly than a trash pile, but not so tightly that they can't be taken apart, so to speak. After all, Socrates can get a tan, in which case Socrates and his pale color are no longer together. It doesn't necessarily take a lot of force to separate them, for natural processes like getting a tan can do the job; we don't need God stepping in here. Also, Socrates and his pale color do have intrinsic powers to join together. Socrates has the (passive) power to be pale, for example.

(iii) Matter and form are supposed to be tied together far more tightly than either of the previous two scenarios. The way that matter and form come together to form 'one thing' is, for the Aristotelians, a paradigm case of unity. But like case (ii), it doesn't necessarily take a lot of force (like God) to separate matter and form, for natural processes like copulation and decomposition can do the job. And like case (ii), matter and form do have intrinsic powers to join together. Matter, for example, has the (passive) power to acquire a form.

The problem is, it's incredibly difficult to define 'per se unity', at least for the scholastics (it's also difficult for Aristotle, but I'm not interested in that here). There are a number of difficulties here.

I can define accidental unity like this: when a substance x (like Socrates) and an accident F (like his pale color) are tied together, x can survive the gain and loss of F. In other words, F does not determine the identity or persistence conditions of x. So x and F are tied together loosely enough that they can separated without x being destroyed.

One is then tempted to say that per se unity occurs when some x and F are tied together so tightly that they can't survive being taken apart. But that doesn't work. Here are some counter examples.

(a) Living organisms gain and lose matter all the time. Particles are constantly flying out of and into me, and biological cells are continually dying and being regenerated. I see no reason why an organism can't survive a total replacement of its matter. Aristotle, I think, says this somewhere (though I can't remember where, and I may be mis-remembering this fact). The scholastics also think so, but for an additional reason: they believe the body is restored (replaced?) after death, and most believe that God could miraculously replace a sick person's heart with a new, healthy heart, so mutatis mutandis for the whole body.

(b) Matter can survive the loss of a form, and indeed this is what happens in every normal case of change down here on earth. For example, when water is turned into steam, the scholastics (following Aristotle) would say that a chunk of matter first has the form of water, and then it loses that water-form and acquires a steam-form; but the matter is the very same throughout the whole process. As with all Aristotelian changes, the matter (by definition) persists throughout the change.

(c) For the scholastics, the soul can survive the loss of its body. They believe the soul survives for a time without its body, after it dies. Right now I have my body, but when I die, my soul gets separated from my body, and then it gets reacquainted (over coffee, probably) with a body in heaven.

So matter and form aren't inseparable. For all intensive purposes, it looks to me like they're tied together in exactly the same way that a substance and an accident is. Matter can survive the gain and loss of a form, and a form (like the human soul) can survive the gain and loss of matter.

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.