Are Scotus's haecceities really unrepeatable?

In my last post, I explained that the only way I can see that a thisness (haecceity) would be unrepeatable would be if the thisness involved some identity reference to the individual in question. Otherwise, I can't see how cloning it would result in a contradiction.

Does Scotus think a thisness involves some identity reference to the individual in question? I don't see how he could think this. Two reasons.

(1) First, identity reference is a relation, and Scotus argues that thisnesses are absolute (non-relational) entities. So it's hard to see how Scotus could say that a thisness is constituted by any reference to the individual.

I wonder, then, if a thisness is supposed to be an absolute entity, why couldn't God clone it? Why couldn't God clone any absolute entity? I can't see why not.

(2) Second, Scotus believes that relations supervene on the things they relate. That is, they are posterior to the things they relate, so if they supervene on an individual, then the individual is already individuated. In short, relationships cannot do any individuating, for they show up on the scene too late, as it were, to do any individuating.

Indeed, to say that Socrateity is the property of being identical to Socrates already presupposes that Socrates is an individual. Otherwise it would make no sense to make an identity reference to Socrates as the individual that he is.

This, I think, is a particularly powerful desideratum here. Take the view of the venerable Robert Adams. He argues that a thisness is just the property of being identical to oneself, and this explains nicely why a thisness is non-qualitative (unrepeatable) property: reproducing it would generate a contradiction.

But what I don't understand is how it does not presuppose the individual in question. If Socrateity is the property of being identical to Socrates, then doesn't that presuppose that Socrates is already an individual? How could we say x is identical to Socrates if we didn't already think of Socrates as an individual?

As Scotus would put it, identity relationships (and in fact all relationships) are naturally posterior to the things they relate, so they show up on the scene too late, as it were, to do any explaining.

One might further suggest, I suppose, that identity relationships are just figments of the imagination. When I think 'Cicero is identical to Tully', I'm imagining Cicero and Tully as if they were different individuals: I have a picture of Cicero in my mind, and I have a picture of Tully in my mind too, and then I connect them and say 'those are the same person'. But in reality, there are not two persons there. There's just one dude, so the 'identity relationship' is really not some sort of entity that exists 'out there' in Cicero/Tully. It's just a (true) connection I've drawn in my mind.

So also with Socrateity: the fact that Socrates is identical to Socrates would be a fact that supervenes on the fact that Socrates is Socrates. But doesn't that already presuppose that Socrates is already the individual Socrates that he is? How could I possibly refer to him if he wasn't?

In any case, it seems to me that Scotus cannot answer any of these questions. He says a thisness is a positive, absolute entity, but if it is an absolute entity, why couldn't it be cloned (by God at least)? I think Scotus has to take thisnesses as entities that are just (somehow) primitively unrepeatable. And that doesn't really explain very much.

But perhaps that is the meat and potatoes of Scotus's position. If so, then Scotus would be saying: we simply cannot explain individuation, for we always presuppose the individual in question. Consequently, it must be the same in reality: there must be some sort of entities 'out there' in the world which are, in and of themselves, (somehow) unrepeatable.

What makes a haecceity unrepeatable?

My question is this: what is it about a thisness (haecceity) that makes it so unrepeatable? Take Socrateity. Why couldn't God create another one, an identical copy or clone?

As far as I can tell, if we assume that God is omnipotent (by which I mean that God can bring about anything that does not involve a contradiction), then the only way that a thisness could not be cloned is if doing so brought about a contradiction.

Suppose, for instance, that we assume (as some modern metaphysicians do) that a thisness is the property of being identical to oneself. In that case, Socrateity would be the property of being identical to Socrates. Now suppose that God created a clone of Socrates, and cloned his Socrateity as well. Let's call this clone 'Harold', and let's call the Socrateity-clone 'Haroldeity'.

Since Haroldeity is a clone of Socrateity, it would be the property of being identical to Socrates. Thus, Harold would be identical to Socrates. But Harold is not identical to Socrates. On the contrary, he is just a clone of Socrates. Thus, Harold would turn out to both be identical to and non-identical to Socrates, and that's a contradiction. So God could not clone Socrateity if it amounted to being identical to Socrates, for cloning that property would result in a contradiction.

One might take this example and generalize: the only way that cloning a thisness will result in a contradiction is if the thisness involves some sort of intrinsic reference to the individual in question. For ultimately, the contradiction is going to involve being identical to vs. not being identical to the individual in question. (It would be irrelevant if the resulting contradiction amounted to being identical and not being identical to Beulah the cow. We're talking about Socrates here, so the contradiction is going to have to pertain to him.)

So, one might think, if a thisness lacks any sort of reference to the individual in question, then it could be cloned after all.

What are haecceities?

One of the major questions that I wonder about is this: what is the difference between haecceities and quiddities (or 'thisnesses' and 'suchnesses')?

One option is to say this: a suchness is qualitative, whereas a thisness is not. But what does that mean? My pre-theoretical intuitions are this: something that is qualitative has some sort of content, whereas something that is non-qualitative does not (it's more abstract -- whatever that means). 

But it's hard to come up with examples for that sort of distinction, and that tells me that my pre-theoretical intuitions are just confused.

Another option is to say this: a suchness is repeatable, whereas a thisness is not. That is, a suchness can be instantiated more than once, whereas a thisness cannot. There can only be one of any given thisness.

That is how most analytic philosophers these days distinguish 'qualitative' and 'non-qualitative' properties. Anything that is repeatable is qualitative, and anything that is not is non-qualitative.

But still, what are some examples? It's hard to come up with an example of a non-qualitative property or constituent. Any entity I can think of is the sort of thing that could be repeated: God could create another identical copy of it, for instance.

So why couldn't God create an identical copy of a haecceity? What makes it so unrepeatable?

Scotus: haecceities must be some positive entity

Medieval philosophers offered a variety of theories about individuation -- that is, about the formal cause of individuation. Here are two popular medieval options.

(1) Some proposed that individuals are individuated by their unique set of incidental features. For instance, if we ask why you and I are different, the proponent of this theory would say that you and I have different heights, weights, shapes, colors, and so on, and this particular set of features that I have is unique: no other individual has these features, just as no other individual has your particular set of features.

This view obviously rests on the identity of indiscernibles: any things that have the exact same properties are indistinguishable, and hence the very same thing. So, for instance, if someone else looked exactly like me in all respects, you couldn't tell us apart, and for that reason we would be same individual.

One might object, of course, that we could easily distinguish me and my twin because I am sitting here, in this chair, and my twin is sitting there, in that chair. In other words, we occupy different regions of space-time.

But the advocate of the theory in question would say that space and time are also part of our incidental features, and so me and my twin would not have the very same features after all. We would have a lot of them in common, but we would not have our spatial and temporal features in common, and for that reason we would not be the same individuals.

Max Black famously questioned this theory. There's no reason, he proposes, that we couldn't imagine two exactly similar identical spheres in parallel dimensions. (I must admit that I have never understood this. Even if they have all the same features, they are still indexed to different dimensions, and so wouldn't they differ with respect to that? I confess that I don't get how Black's example is a genuine counter-example.)

(2) Others proposed that two individuals differ because they are made up of different chunks of materials. So, for instance, me and my twin might have all the same features, except I am made of this chunk of material, and he is made of that chunk of material.

(This theory seems to assume that different chunks of material are distinct -- either primitively, or in virtue of the fact that they occupy different regions of space. But again, couldn't one suppose: what if these two chunks of material had the same spatial and temporal properties? How would they be distinguished then? I think that most advocates of this theory would have to maintain that different chunks of material cannot occupy the same region of space-time simultaneously.)

Scotus argues that neither of these two theories actually explain individuation. For Scotus, each of these theories presupposes individual entities. The first theory assumes that incidental features are already individual, and the second theory assumes that chunks of material are individual. But that still leaves us wondering: how are incidental features or chunks of material individuated? So as Scotus sees it, neither of these theories have really explained individuation after all.

In fact, Scotus goes through all the major theories that he knows of and points out that they all presuppose some individual entity, and for that reason, he rejects all of them.

Scotus then concludes that we must assume that individuation comes about by some primitively individual entity -- and this is called a haecceity. We don't know what this entity is, but it must be a positively real thing, and it must be individual in and of itself. Since all of our theories about individuals assume individuality already, we must postulate some primitive individuator.

Individuation is a question of the formal cause

When scholastic philosophers discuss individuation, their basic question is this: which of a thing's constituents make it the individual that it is? This question deserves some comment. As the schoolmen see it, we are looking for what they call the 'formal cause', not the 'efficient cause'.

The efficient cause is the agent that brings the effect in question into being. For instance, when a sculptor makes a statue, the sculptor is the efficient cause here, for the sculptor is the person/agent who effectively brings the statue into being. In short, the efficient cause is the producer of the effect.

The formal cause, on the other hand, is some feature or constituent of the product itself that explains why it is the sort of thing it is. For instance, the formal cause of a statue being a statue is the shape of the statue. Without it's shape, it wouldn't be a statue, so that very shape is the 'formal cause' of the statue being a statue.

When the schoolmen talk about individuation, everybody agrees that the efficient cause of the individual is its producer. But that seems perfectly obvious. If you want to know who produced this particular statue, the answer is the sculptor who actually produced it.

But when it comes to the formal cause, the schoolmen disagree. Again, here they are looking for some feature or constituent (or combination thereof) in the individual itself that explains why it is the individual it is.

More precisely: here we are looking for some set of features or constituents that cannot exist in some other individual. Suppose I ask every member of a group to take a side on capital punishment. Some will be for it, others will be against it, but in this case, taking the 'for' or 'against' side will separate these individuals into distinct groups, for nobody can be 'for' and 'against' capital punishment at the same time.

Taking the 'for' or 'against' side here would be an example of something that is the 'formal cause' of distinction: it's the sort of thing that cannot exist in more than one individual at the same time, and so when individuals take the 'for' or 'against' side of capital punishment, they necessarily get separated into groups. So also when it comes to individuals. The schoolmen are looking for some feature that cannot exist in more than one individual at a time, much like how being 'for' or 'against' capital punishment cannot exist in one and the same individual at the same time.

Christology and Heresy

I did a short and simple series of posts on the Incarnation over at trinities.org. Here are the links:

Christology and Heresy - 1 
Christology and Heresy - 2
Christology and Heresy - 3
Christology and Heresy - 4
Christology and Heresy - 5

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.