Wednesday, 16 March 2011

Question 40 - The Persons in Comparison to the Relations

Why this Question Matters.

Right at the start of his treatment of the Trinity Aquinas identified subsistent relation as the key concept in identifying and distinguishing the Persons of the Trinity. In the light of the material that he has developed since that introduction, he now returns to consider in greater depth the comparison of the Persons and the relational properties.


The Thread of the Argument

A1: Returning immediately to the theme of Question 28, Aquinas asks whether the relations in the Godhead can be identified with the Persons of the Trinity. The reason that he returns to this question is that he wants to address some of the possible problems and alternative approaches to the relational understanding of the Trinity, in the light of the theory that he has developed in the body of the treatise. Here Aquinas can recall that since the essence is the same as each Person (Question 39, Article 2) and each relation is necessarily the essence, we can identify the relations with the persons. Aquinas can apply the reasoning of this latter question to conclude that the relative properties are in the Persons and yet they are the Persons. In this way, Aquinas both argues against those who would attempt to drive a wedge between the relations and the Persons as well as preparing the ground for his contention in the next article that what distinguishes the Persons is founded in their relational properties rather than in what founds the relations.

The first objection suggested that if two things are the same, then the multiplication of one would imply the multiplication of the other. This would seem to rule out there being more than one relation in one Person; troubling if we reflect upon the paternity and common spiration in the Father. The answer to this objection allows Aquinas to amplify the point made in his reply: Person and relative property signify the same reality but differ conceptually. God’s simplicity excludes any composition of form and matter (therefore the abstract is to be identified with the concrete in God) and it excludes any composition of subject and accident (therefore any real attribute of God is His essence). The former means that, for example, God’s deity is God and it also implies that the Paternity of the Father is the Father: the relative properties and the Persons signify the same reality although their modes of signifying differ. The two identities together imply the identity of Person and relational property. The multiplication suggested in the objection need not happen: for example, the common spiration is not a single person subsisting per se but one property existing in two Persons in a way similar to the existence of one essence in two Persons (as seen in Question 30, Article 2).

The fact that Person and property signify the same reality and yet differ in their mode of signification allows us to understand that the relations determine distinct Persons in the Godhead yet do not determine distinct essences in the Godhead. The relational properties are only “in the essence” of God via this identity of Person, essence and relation; their signification only operates when considered as signifying something like a form in a subject.

A2: When we think of created things, and particularly when we thing about created things through the lens of Aristotle’s division of being into the categories, it’s hard to see that the relations are fundamental to the distinction between the Persons. In the Categories, being is divided into “substance” and the nine accidental categories, one of which is “relation”. This division implies that substance is, in a sense, primary and that relation is secondary: in this case, relation would appear to pre-suppose a distinction between substances. However, if we try to apply this reasoning to the relations in the Godhead and to the essence of God Himself, we have to be careful; the relations in the Godhead are subsistent and each the same as the essence. Putting this informally, we might ask whether God the Father is Father because he begets the Son or whether he begets the Son because He is Father. In contrast to other theologians of his day (Bonaventure, for example), Aquinas takes the latter view. The relational property of being Father is the primary source of what makes the Father a distinct Person; the fact that the Father is the originator of the Son and that the Son originates from the Father is secondary to the relational properties of being Father and of being Son.

In order to argue in support of this position, Aquinas identifies that the only possibilities for distinction in the Godhead arise from either origin or relation. There is in the Godhead, of course, no real difference between these, but they differ by their mode of signifying: origin signifies in the mode of an act and relation signifies in the mode of a form. In the created world, relation follows upon act, therefore Aquinas’s intellectual opponents apply this to the Trinity and argue that, for example, the Father is distinct from the Son because the one generates and the other is generated and that the relations follow after the fact. Aquinas identifies two major faults with this position.

The first problem is that in order to identify two things as distinct it is necessary to identify something intrinsic to them that provide a foundation for the distinction. Origin simply does not supply that intrinsic property, rather being a sort of trajectory from a thing to a thing that presupposes a distinction between them. Actually within a divine Person there are only two candidates that might provide the distinction: essence and relation. The former doesn’t distinguish, so it must be the latter that does. This line of reasoning explains Aquinas’s insistence in the first article that the relations are in the Persons.

The second problem is that positing the origins of the Persons as fundamental to the distinction between the Persons is prone to lead to the error of dividing something common to the three Persons. In other words, this approach leads to the idea of dividing the substance and therefore to tritheism.

A3: Even if we grant that it is the relations that make the Persons, is it possible that we might abstract the notion of relation from the notion of Person and still maintain a distinction between what would simply be hypostases of the Trinity? No: Aquinas insists that even when we are considering things as abstracted intellectually (as opposed to what is truly in reality) relation remains necessary for the distinction of the Persons. If we abstract away relation in our thinking, then Person evaporates from our thinking as well.

Aquinas considers how we make abstractions and identifies two fundamental types. When we consider a man as a rational animal, if we abstract the idea of rational from man and then remove the concept of rational, then we no longer have the concept of man but only the idea of animal. This example involves the abstraction of a universal from particulars. In contrast, if we consider the example of abstracting from a matter/form composite such as a bronze ring, abstracting and then removing the idea of a ring or circle still leaves us with bronze as a concept in the mind.

When we consider God, there are no universals and particulars and there is no composition of matter and form, but there remains the analogue of them by means of the different modes of signifying. Corresponding to the example of particulars and universals, abstracting and removing the properties leaves the common essence of God but not the hypostases which are analogical to particulars. When the properties that do not constitute the Persons are abstracted and removed in the sense of the matter/form abstraction, the concept of hypostasis remains. However, if the properties that constitute the Persons are removed, the concept of hypostasis vanishes. The point is that as the relational properties are subsistent, they “bring along with them” their corresponding supposits. One simply cannot be thought of without the other.

Those that argue that origin provides the foundation for relation might suggest that one can therefore abstract away the notion of relation whilst still leaving origin as the basis for the hypostases. However, in the first place Aquinas has shown the weakness of this position in the previous article and secondly since every hypostasis with a rational nature is a Person (following Boethius) it would be necessary to abstract way the rationality of the nature rather than the properties constituting the Person in order to be left with a hypostasis which is not a Person.

A4: In asking whether the characteristic (or notional) acts such as begetting and spirating are presupposed by the relations, Aquinas has the chance to summarize and elaborate upon his teaching from the earlier articles and the opportunity to distinguish between reality and how we may conceptualize that reality. Here he explicitly mentions the two possibilities: either the Father is the Father because He generates or the Father generates because He is Father. Aquinas favours the latter, but he is willing to make conceptual distinctions that explain the structure of the problem and the approach of other theologians.

Assuming that the relations in God really constitute the Persons and make them distinct then we can observe that origins in God can be signified actively (e.g. generation or spiration) or passively (e.g. being begotten or proceeding). This distinction allows us to observe that the origins as passively signified are conceptually prior to the properties of the Persons who proceed. When origins are signified actively, they are conceptually prior to any non-constitutive property of the Person. For example, the characteristic act of the common spiration is conceptually prior to un-named relation common to the Father and the Son. So in the conceptual realm, when we think of what constitutes the Person of the Father we can think in terms of a relation that presupposes the characteristic act of begetting but we can also think in terms of the relation constitutive of the Father being presupposed by the characteristic act. This process of distinction mirrors the conceptual distinction that one might make between the word “Father” signifying the divine relation of paternity and the subsistent Person.


Handy Concepts

  • The relations constitute and distinguish the divine Persons.
  • Person and property signify the same reality but differ in their mode of signification.
  • “God the Father begets the Son because He is Father” rather than “God the Father is Father because he begets the Son.”
  • We cannot abstract the idea of relation from the divine Persons in order to leave some kind of bare but distinct hypostases.
  • Distinctions can be made facilitating the conceptual priority of the characteristic acts over the relations.


Difficulties

  • Question 40 has gained the reputation of being one of the hardest questions to understand in the summa. Emery quotes Dondaine as saying that it considers “the most arduous problems in Latin Trinitarian theology”.
  • Aquinas’s conclusions in this question represent one side of an enduring split in Western theology between what one might approximately characterize as a Dominican school and a Franciscan school.
  • Article 4 appears to make distinctions between the real and our conceptual understanding of the real that almost contradict one another.

21 comments:

  1. But isn't there a contradiction lurking here?

    Aquinas writes: “In whatever multitude of things is to be found something common to all, it is necessary to seek out the principle of distinction” (ST 1.40.2). This makes perfect sense as a principle, because A and B are really distinct if and only if there is a principle of distinction that accounts for the difference between A and B, and the principle of distinction cannot be identical to what A and B have in common. The principle of distinction between A and B cannot be identical to what A and B have in common, because then you would have a logical contradiction, i.e. what A and B have in common is identical to what A and B do not have in common, which is the logical equivalent of saying that X = not-X.

    Now, Aquinas says that because “the persons agree in essence, it only remains to be said that the persons are distinguished from each other by the relations” (ST 1.40.2). And this fits perfectly with what I wrote above, because it is clear that the divine persons share the exact same divine essence in common, and since the principle of distinction cannot be what the divine persons share in common, then the divine essence cannot be the principle of distinction. Instead, Aquinas concludes that the principle of distinction is “the relations”.

    Here’s Emery on this line of thinking:

    “St Thomas is looking at the fact of distinction by means of relation alone, making it play a role analogous to that of a ‘principle of individuation’. In physical beings, the principle of individuation is the material which renders an individual, in relation to the species whose nature the individual has. All of them have, of course, the nature appropriate to the human species, but this humanity is, as it were, ‘multiplied’ in each one of them. It works out differently in the Triune God. The divine essence is numerically one: the essence is absolutely one and the same identical reality in the three divine persons. What makes the persons of the Trinity plural is not the common essence but relation as a personal property, a ‘quasi principle of individuation’.” (The Trinitarian Theology of St Thomas Aquinas, pp. 144-45).

    But there is a key complication of this line of thinking: the principle of distinction cannot be really identical to what the distinct beings have in common, on pain of logical contradiction. It necessarily follows from this that the divine persons cannot be really identical to the divine essence. However, this conclusion leads to two insurmountable problems for the Trinity.

    First, Aquinas has written that “relation really existing in God is really the same as His essence and only differs in its mode of intelligibility” and “in God relation and essence do not differ from each other, but are one and the same” (ST 1.28.2). So, we have a logical contradiction, because the divine essence cannot be really identical to the divine relations, because the principle of distinction cannot be really identical to what the distinct beings have in common, and the divine essence is really identical to the divine relations, because otherwise a key aspect of the Trinity would be false.

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  2. Second, Aquinas has written: “Everything which is not the divine essence is a creature” and “if it is not the divine essence, it is a creature” (ST 1.28.2). And this makes perfect sense, because, according to divine simplicity, the divine essence is Being Itself (ST 1.3.4), and only Being Itself does not depend upon anything else for its existence. Anything that is not Being Itself must depend upon something else for its existence, and anything that must depend upon something else for its existence is necessarily a creature. Thus, anything that is not Being Itself (i.e. the divine essence) is a creature. It would follow, therefore, that since the divine relations are not the divine essence, and everything that is not the divine essence is a creature, that the divine relations are creatures. Not only does this negate the Trinity, but it also has a number of absurd consequences, such as that the divine relations could not exist as cause until their effects first existed, that the divine relations must be composite entities, that the divine relations would exist in a relation of dependence upon creation, and so on.

    In conclusion, the only way for there to be a real distinction between the divine persons is if there is a principle of distinction, and this principle of distinction cannot be really identical to what the divine persons have in common, which means that it cannot be identical to the divine essence. But this conclusion contradicts core features of the doctrine of the Trinity, i.e. the divine persons are really identical to the divine essence and the divine persons cannot be creatures.

    Any thoughts?

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  3. Dear dguller, welcome to the blog! I'll have a think about your question and get back to you. Just a bit frantic at work at the moment getting papers written...

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  4. Here's a simpler way of making the same point:

    (1) A is really distinct from B iff there is a principle of distinction that (a) provides an account of the difference between A and B, and (b) cannot be really identical to what A and B have in common

    (2) The divine persons are really distinct from one another (in a non-physical and non-metaphysical way)


    (3) Therefore, there is a principle of distinction between the divine persons that cannot be really identical what the divine persons have in common (by (1), (2))

    (4) The principle of distinction that accounts for the real distinction between the divine persons is the divine relations

    (5) The divine persons share the exact same divine essence in common

    (6) Therefore, the divine relations cannot be really identical to the divine essence (by (3), (4), (5))

    (7) A is really identical to B if and only if A and B are notionally distinct

    (8) A is notionally distinct from B if and only if (a) A is not really distinct from B in any way, and (b) A differs from B only in the mind

    (9) Therefore, the divine relations cannot be notionally distinct from the divine essence (by (6), (7))

    (10) Therefore, the divine relations must be really distinct from the divine essence in some way (by (8), (9))

    (11) The divine relations are really identical to the divine essence

    (12) Therefore, the divine relations cannot be really distinct from the divine essence in any way (by (7), (8), (11))

    (13) Therefore, (10) contradicts (12)

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  5. Ah, it always seems as though the best and hardest questions come when time is short. I’m afraid it will be about a week before I can get round to giving your objection proper attention.

    In the meantime just an initial thought; I suspect the weakness in the objection lies with the very first step of your reformulation. Aquinas is looking for a notion of “individuation” that has satisfy some very tough axioms: in the first place it must apply to a simple immaterial substance that is pure act; in the second place it positively must not result in numerical individuation (lest the Trinity lapse into tri-theism). He identifies the unity of God as being a transcendental unity; similarly, he is looking for the principle of “individuation” within God to result in some sort “transcendental multiplicity”. I suspect that your formulation of what a principle of individuation is would fail Aquinas’s requirements. At the very least one would have to put the formulation through the mincer of the analogy of being before it could apply to the substance of God.

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  6. That's a fair point, but I think that the only relevant detail for my argument is that the principle of commonality between A and B cannot be really identical to the principle of distinction between A and B. Otherwise, you have the logical contradiction that what is common to A and B is really identical to what is not common to A and B, which is the equivalent of claiming that X is really identical to not-X.

    To continue to claim that the principle of commonality is really identical to the principle of distinction, and yet avoid this contradiction, one would have to infer that there is really only either the principle of commonality or the principle of distinction. If there were only the principle of commonality, then A and B would not be really distinct at all, but rather would be really identical. If there were only the principle of distinction, then you would have another impossibility, because at the very least, A and B must both be individuals of some kind, and that would have to be something they share in common.

    So, the only logical conclusion is that the principle of commonality between A and B cannot be really identical to the principle of distinction between A and B.

    But perhaps reframing the issue through the analogy of being would resolve this matter. I’ll await your more detailed response, whenever you have the time.

    Take care.

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  7. OK, I think I’m beginning to emerge from beneath a pile of work and I’ve cranked the “thinking about the trinity” starting handle…

    May I label your four posts 1, 2, 3 & 4 in order?

    It seems to me that the objections that you pose were clear to Aquinas – and probably also to Boethius and Augustine many centuries before him; if one attempts to treat the divine substance (immaterial, simple and pure act) in the same way that one treats material substance, then one simply runs into contradiction. So, if you start off with Aristotle’s Categories in the back of your mind as they apply to material being, and give a definition of a “principle of distinction” such as you give in 3 (1), it’s pretty clear it’s not going to work (for the reasons that you spell out in detail) when applied to the divine substance.

    I think that a similar fate befalls your “principle of commonality between A & B” from post 4: it appears fine when applied to material being, but it’s unclear that it even has meaning when applied to the divine substance. The big questions here concern what A & B could be. Of course, Aquinas wants them to be some sort of way of referring to the persons of the Trinity; but how might this work?

    Let’s just think about the being of the divine substance first of all; because we’re already in some difficulty considering the divine substance as substance. If one starts with the notion of substance in Aristotle’s Categories there are immediate problems: there substance is proposed as something in which other things (accidents) inhere but which does not inhere in other things. The thing is, although the second condition works, nothing inheres in the divine substance and the divine substance transcends the Categories. So, thinking of the divine substance as substance in the sense of the Categories already must involve some notion of analogy. (Incidentally, this also gives an indication of why Aquinas pushes the other Aristotelian approach to being through form and matter, act and potency.)

    So, what are we to do to come up with some notion of “distinction” between the persons of the trinity? First we must remember that we must avoid solutions that result in tri-theism (dividing the substance) or which result in the persons simply being distinct labels for the persons of the trinity (a conceptual rather than a real distinction) or which result in considering the persons of the trinity being considered under different modes of the economy (modalism). It is as well to re-read Ia.q31.a2 at this point to grasp the axiomatic conditions that Aquinas is requiring for this analogical notion of “distinction” as applied to the divine substance.

    [continued below...]

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  8. [continued from above...]

    So, if we now turn to Ia.q28.a2 we see Aquinas taking a close look at the accidental categories in order to see whether anything can be salvaged from them to apply by analogy to the divine substance. He identifies two aspects: firstly he notes that accidents exist in a subject; secondly he notes that they each have what he calls their “ratio”, which we might translate as their “specific character”. For all the categories of accident except for relation, the ratio of the accident derives from the subject. For relation, on the other hand, the ratio is derived from the very fact of its pointed-ness to other-ness. It is this that Aquinas leaps on as the key to the principle of distinction between the persons in the divine substance. When applied to the divine substance all the other accidental categories collapse: the being of the accident collapses into the substance of the subject; the ratio of accident collapses likewise, as the ratio is derived from the subject. When we consider relation, the being of the accident collapses into the being of the subject; but the ratio remains un-collapsed because it does not simply derive from the subject but from a pointing to other-ness.

    So when Aquinas applies the category of relation to the divine substance though analogy, he observes that although the being of the accident dissolves into the being of the substance, the ratio remains as a principle of distinction between the persons. One might wish to push this further to claim that the sources of revelation show us that simple, immaterial being in pure act (i.e. uniquely the divine substance) has relatedness as a metaphysical primitive. As Aquinas puts it (Ia.q28.a2) “…in God a really existing relation has the being of the divine essence and is wholly identical with it. But insofar as it is a pure reference, relation does not bear upon essence, but upon its opposed term”.

    If you have Emery’s book available to you, Chapter 5 (especially section 3) is quite good on these matters and repays close attention, preferably with a single malt Scotch in hand…

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  9. Gregory:

    Thanks for the comment.

    I don’t think that you’ve addressed the key problem, though. You seem to assume that the principle that I identified only applies to distinct entities that are subsumed under the categories, and thus should not apply to distinct entities that transcend the categories. But that cannot be true, because Aquinas himself uses the principle in his discussion of the Trinity at ST 1.40.2. He writes: “In whatever multitude of things is to be found something common to all, it is necessary to seek out the principle of distinction”. This principle clearly applies to the Trinity, because Aquinas uses this very principle in his discussion of the Trinity, which necessarily transcends the categories. In fact, his specific reason for identifying the distinct divine relations as the principle of distinction between the divine persons is precisely the fact that they are not shared in common between the divine persons, and the divine essence cannot be the principle of distinction precisely because it is shared in common. And therefore, it is necessarily true that the divine relations cannot be really identical to the divine essence.

    So, whether A and B transcend the categories or are subsumed under the categories, it is a necessary truth that if A is really distinct from B, then the principle of commonality between A and B cannot be really identical to the principle of distinction between A and B.

    To reject this principle is to embrace a logical contradiction.

    Furthermore, it all hinges on what a real distinction is. To me, a real distinction between A and B means that the distinction between A and B does not only exist in the human mind, and a notional distinction (or virtual distinction, if you are Garrigou-Lagrange) between A and B means that the distinction between A and B only exists in the human mind. Clearly, it is impossible for A and B to be really distinct and notionally distinct, because that would mean that the distinction between A and B is only in the human mind and not only in the human mind, which is a logical contradiction, and thus if A is really distinct from B, then A cannot be notionally distinct from B, and vice versa.

    Using this framework, we can look at the passage that you cited at ST 1.28.2. Aquinas says there that “in God a really existing relation has the being of the divine essence and is wholly identical with it”. I think that this means that the divine relations are really identical to the divine essence, which just means that there is a notional distinction between the two, i.e. any distinction between the two only exists in the human mind, because in reality, they are “wholly identical”. Furthermore, this means that it is impossible for the divine relations to be really distinct from the divine essence. As he writes elsewhere in ST 1.28.2, “in God relation and essence do not differ from each other, but are one and the same”. The only way that they differ is in their “mode of intelligibility” (ST 1.28.2) or “in our way of thinking” (ST 1.39.1), which is the definition of a notional distinction.


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  10. Keep that in mind. The divine relations and the divine essence are “wholly identical”, “do not differ from each other”, and are “one and the same”. But this leads to problems with the law of transitive identity. If A is really identical to C and B is really identical to C, then A is really identical to B. So, if the Father is really identical to the divine essence and the Son is really identical to the divine essence, then the Father is really identical to the Son. Unfortunately, that contradicts the claim that the Father is really distinct from the Son. The only solution is to reject the position that the divine relations are really identical to the divine essence, which means that they cannot be “wholly identical” or “one and the same” after all.

    And that means that the divine relations must be really distinct from the divine essence after all. This would preserve the principle that I mentioned above, as well as the law of transitive identity, and avoid logical contradictions. The problem is that Aquinas has also written that “[e]verything which is not the divine essence is a creature” and “if it is not the divine essence, it is a creature” (ST 1.28.2), which means that if the divine relations are really distinct from the divine essence, then the divine relations are creatures, which is absurd.

    So, some key logical, metaphysical and theological doctrine must be abandoned to preserve logical consistency. The question is, which one?

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  11. Gregory:

    And just to clarify one thing. I am defending the following principle:

    (P) If A is really distinct from B, then the principle of commonality between A and B cannot be really identical to the principle of distinction between A and B

    I claim that Aquinas endorses this principle as applicable whether A and B transcend the categories or are subsumed under the categories. We both agree about the latter, and the question is about the former.

    If you look at ST 1.40.2, Aquinas writes: “In whatever multitude of things is to be found something common to all, it is necessary to seek out the principle of distinction”. This implies that in any kind of multiplicity of entities that are distinct, their very distinction cannot be accounted for by what they have in common, but rather their distinction must be found in what they do not have in common, i.e. “the principle of distinction”. And this remains true whether the “multitude of things” transcends the categories or is subsumed under them. In fact, the entire discussion that occurs at ST 1.40.2 is about the Trinity, which transcends the categories, and thus it must be applicable to that which transcends the categories.

    He goes on to write that “as the three persons agree in the unity of essence, we must seek to know the principle of distinction whereby they are several”. This implies that the divine persons share the exact same divine essence in common, which he confirms elsewhere: “[T]he form signified by the name "God"--that is, the divine essence--is really one and common” (ST 1.39.4). So, the divine persons share the same divine essence in common. If it were possible for the principle of commonality to be really identical to the principle of distinction, then Aquinas could simply identify the divine essence as the principle of distinction that explains the real distinction between the divine persons, and move on to some other topic.

    But he does not do this. Instead, he rejects the position that the divine essence could be the principle of distinction, and says that “we must seek to know the principle of distinction whereby [the divine persons] are several”. This implies that what accounts for the real distinction between the divine persons must be other than the divine essence, because it must be other than what the divine persons share in common. And this is because it is impossible for the principle of commonality to be really identical to the principle of distinction.

    He ends up concluding that “since the persons agree in essence, it only remains to be said that the persons are distinguished from each other by the relations”. So, he identifies the principle of distinction with the distinct divine relations, and not with the divine essence at all.

    The important thing to notice in this discussion is that all the elements of (P) are there in ST 1.40.2:

    (1) There is a real distinction between the divine persons
    (2) The real distinction between the divine persons cannot be accounted for on the basis of what the divine persons share in common (i.e. the principle of commonality), but only on the basis of what they do not share in common (i.e. the principle of distinction)
    (3) There is a divine essence that is shared in common, and because it is shared in common, it cannot account for the real distinction between the divine persons
    (4) There are really distinct divine relations that are not shared in common between the divine persons
    (5) The real distinction between the divine persons is accounted for on the basis of the really distinct divine relations that are not shared in common between the divine persons
    (6) It is impossible that what the divine persons share in common is really identical to what the divine persons do not share in common (i.e. the principle of commonality cannot be really identical to the principle of distinction)

    So, on the basis of the above discussion, I think that we can conclude that (P) is applicable to the Trinity, because Aquinas himself applies it to the Trinity.

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  12. Again, my apologies for taking so long to reply; research grant writing is taking its toll…

    There’s quite a lot of stuff in what you’ve written, and I’m afraid that I’ll only be able to deal with some of your points. I hope that what I do address is helpful.

    Let’s look at the argument from the transitivity of “equality”. I think the first thing you’ve got to realize is that this argument against the trinity was well known in the Middle Ages. After all, Islamic and Christian philosophers paid careful attention to what each other were writing!

    The problem with applying it to the case of the trinity begins with a reflection upon what “equality” means; after all, there are good reasons for the fact that “equality” is not a real relation! Whenever you say A=B, you’ve got to have a good think about what each symbol might stand for.

    In mathematics we’re very used to A & B being algebraic expressions, or more generally descriptions of or pointers to mathematical objects. In this case equality can already mean a range of things: “B ends up being the same algebraic expression as A when you apply a set of manipulative rules to B”; “When A is evaluated on its free variables, the same value is obtained as when B is evaluated on the same free variables”; “A is a distinct description of the same mathematical object as B”. And so forth.

    When we apply the concept of equality in the physical world, we’re often concerned with accidental qualities of (first) substances. “The weight of A is the same as the weight of B”, where A & B are distinct (first) substances. Similarly, “A and B have the same colour”, “A & B are the same size”. When we get into the realms of pointers to (first) substances, equality is still under control: “the queen of England” is equal to “Elizabeth Windsor” is equal to “that lady walking over there” seem un-troubling. These sorts of notions of equality lead us to be perfectly happy with the idea that equality is reflexive, symmetric and transitive defining an equivalence relation with equivalence classes consisting of some sort of singleton.

    But this last example also hints at difficulties that may lie ahead: “the queen of England” is a pointer to a (first) substance and we talk of equality with “Elizabeth Windsor” when we say that these are distinct pointers that point to the same (first) substance. But what happens if we try to apply equality directly, as it were, to first substances? There’s something very fishy about trying to say “James is equal to James” or “this person I am thinking about is equal to this person I am thinking about”. In trying to apply the concept of “equality”, something seems to break in the transition between descriptions of (first) substances and (first) substances themselves. If we try to make the argument that A=B & B=C implies A=C, then this works fine if we’re talking to pointers to (first) substances, but it’s less clear that the individual terms have any meaning if they are the (first) substances themselves.

    So there’s something disquieting about “equality” even for finite being. The problem gets worse when we try to think of the simple pure-act being that is the divine substance, especially in relation to relation. Terms like “Father” & “Son” and “Holy Spirit” are pointers to real relations and we may take “God” as a pointer to the divine substance. We already have the analogy of being in operation in recognizing that “relation” is not accidental in the simple pure-act being. So, the question to the interlocutor arguing that transitivity of equality dismantles the notion of trinity is: “what do the terms of your argument mean?” It was reflection on this question that assured medieval philosophers that the argument dissolves in a confusion of terms.

    [continued...]

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  13. [continued...]

    If I may turn to your definition (P), I’m afraid that I think you are simply misreading Aquinas if you read him as supporting this axiom in Ia.q40.a2. Reading through your supporting text suggests that you are not taking into account the terminological precision that Aquinas is insisting upon and which he has established by the time we get to Ia.q40. Let me give you some examples. Notice how Aquinas uses the word “commonality” (“aliquid commune” in the Latin) and shuns the verb “to share”. We might informally say that “the Father shares the divine essence with the Son”, but once we’re into being precise we have to remember that the Father is the divine essence and the Son is the divine essence as regards substance; they don’t “share” anything, they “are” each the divine substance as substance. Similarly, when Aquinas is talking of a multitude, he is already including what he has termed a “transcendental multiplicity” in the scope of the discussion. In applying the notion of “multitude” to the trinity he is already thinking in terms of analogy with what we understand “multitude” to mean in finite being. If I may quickly slip in a quote from one of Emery’s other books:

    “It is necessary even to affirm that the three persons are their identical divine nature. Between the divine persons and the divine nature, there is no real difference, but only a conceptual distinction. The sole real distinction that is found in God is the distinction between the persons themselves (and not between the persons and the divine nature).” Emery “The Trinity” pg. 106.

    What Aquinas is trying to do here is establish that subsistent relation is the basis for real distinction in something substantially simple. Aquinas’s description of the trinity boils down to an assertion that the sources of revelation tell us that the unique example of simple-pure-act substance is inherently relational. We can only get a “thin” grasp on this by means of analogy with finite being. The major obstacle to getting a grasp on this analogy is that for finite being “relation” is an accident; for simple-pure-act being it is not. So it is extremely important that when we consider the term “really distinct” in regard to the trinity, we do not accidentally equivocate on its meaning (an equivocation that I think is present in (P)). One meaning relates to distinction as substance (which cannot occur in the divine substance); the other to distinction as relational (which does occur in the divine substance). In the unique simple-pre-act being that is God, relation being subsistent, and forming the basis for “distinction as relational”, is akin to the divine substance uniquely having relational “modes” of existence.

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  14. Gregory:

    Again, my apologies for taking so long to reply; research grant writing is taking its toll…

    No need to apologize.

    If we try to make the argument that A=B & B=C implies A=C, then this works fine if we’re talking to pointers to (first) substances, but it’s less clear that the individual terms have any meaning if they are the (first) substances themselves.

    I don’t see why. It just means that A, B and C are just different terms for the exact same underlying reality, whatever that underlying reality is. In other words, you have a situation in which different terms have different senses, but the same underlying referent. It would be analogous to the divine attributes, each having a different term, a different sense, but ultimately the exact same underlying referent. The distinction between the divine attributes solely exists in the human mind, and not in objective reality. That is what makes it a notional distinction, and not a real distinction, after all.

    And I also don’t see why it is incoherent to say that A is identical to A. That is actually a basic truth of logic and metaphysics.

    The problem gets worse when we try to think of the simple pure-act being that is the divine substance, especially in relation to relation. Terms like “Father” & “Son” and “Holy Spirit” are pointers to real relations and we may take “God” as a pointer to the divine substance. We already have the analogy of being in operation in recognizing that “relation” is not accidental in the simple pure-act being. So, the question to the interlocutor arguing that transitivity of equality dismantles the notion of trinity is: “what do the terms of your argument mean?” It was reflection on this question that assured medieval philosophers that the argument dissolves in a confusion of terms.

    I’m not too sure about that. I think that you have a variety of terms, a variety of senses, and the question is whether those terms and senses have the exact same underlying referent. The way that I look at it is that if the underlying referent is simple, then it has no parts, and thus any term and sense must have the exact same underlying referent, i.e. the simple being in question. It is only if the being is composite that the different terms and senses can have different referents.

    For example, the Morning Star and the Evening Star have different terms and senses, and the question arises about their referent. One can say that they have the exact same referent, i.e. the planet Venus, but this is technically incomplete, because they actually refer to different spatiotemporal parts of Venus, specifically different orbits of Venus and how Venus appears to observers on the Earth. So, the Morning Star refers to one spatiotemporal part of Venus and the Evening Star refers to another spatiotemporal part of Venus. This makes sense only because Venus is a composite being. Venus itself is a spatiotemporal being that is spread out over space-time in the physical universe, and the terms that we use can either refer to the entirety of Venus, i.e. its entire space-time existence, or to a part of Venus, i.e. one particular aspect of its space-time existence, e.g. a part of its orbit around the Sun as seen from the Earth.

    None of this works for a simple being in which there can only be a single referent, no matter how many terms and senses our minds can come up with. In that case, all the terms and senses ultimately have the same referent. That is what I take Aquinas to mean when he says that the divine relations and the divine essence are “wholly identical”, “do not differ from each other”, and are “one and the same”, such that the only difference between them is in our minds. In other words, any distinction between the divine relations and the divine essence only exists in our minds, and is projected upon them by our minds, but does not actually correspond to anything real in existence.

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  15. It is precisely because Aquinas believes that the divine relations and the divine essence ultimately refer to the exact same underlying reality that allows him to use the law of transitive identity, specifically when discussing the Trinity. At ST 1.42.5, he writes:

    “The Father is in the Son by His essence, forasmuch as the Father is His own essence, and communicates His essence to the Son not by any change on His part. Hence it follows that as the Father's essence is in the Son, the Father Himself is in the Son.”

    This argument presupposes the validity of the law of transitive identity. It basically argues that if the Father is the divine essence, and if the divine essence is in the Son, then the Father is in the Son. So, Aquinas clearly agrees with using the law of transitive identity in reasoning about the Trinity, and yet it is prohibited from making the inference that the Father is the Son. Why? It is based upon the exact same argument that Aquinas clearly accepts as sound.

    Notice how Aquinas uses the word “commonality” (“aliquid commune” in the Latin) and shuns the verb “to share”. We might informally say that “the Father shares the divine essence with the Son”, but once we’re into being precise we have to remember that the Father is the divine essence and the Son is the divine essence as regards substance; they don’t “share” anything, they “are” each the divine substance as substance. Similarly, when Aquinas is talking of a multitude, he is already including what he has termed a “transcendental multiplicity” in the scope of the discussion. In applying the notion of “multitude” to the trinity he is already thinking in terms of analogy with what we understand “multitude” to mean in finite being.

    The issue is what A and B have in common, and what A and B do not have in common. Necessarily, what A and B have in common cannot be identical to what A and B do not have in common. That is what (P) is supposed to ultimately be all about, and I find it difficult to believe that Aquinas would reject this principle. After all, to reject (P) is to embrace a logical contradiction, i.e. that what A and B have in common is identical to what A and B do not have in common, which is logically impossible. Furthermore, to reject (P) would be to allow for the possibility that A and B can have everything in common, and yet be really distinct, which is also impossible. So, it is not possible to coherently reject (P).

    What Aquinas is trying to do here is establish that subsistent relation is the basis for real distinction in something substantially simple.

    And I’m claiming to have an argument based upon Thomist principles that this is impossible. After all, if (P) is true, then what the divine persons have in common cannot be identical to what the divine persons do not have in common. Since the divine persons have the divine essence in common, and the divine persons do not have the divine relations in common, then the divine essence cannot be identical to the divine relations. And that flatly contradicts Aquinas’ claim that the divine essence must be identical to the divine relations.

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  16. The major obstacle to getting a grasp on this analogy is that for finite being “relation” is an accident; for simple-pure-act being it is not. So it is extremely important that when we consider the term “really distinct” in regard to the trinity, we do not accidentally equivocate on its meaning (an equivocation that I think is present in (P)). One meaning relates to distinction as substance (which cannot occur in the divine substance); the other to distinction as relational (which does occur in the divine substance). In the unique simple-pre-act being that is God, relation being subsistent, and forming the basis for “distinction as relational”, is akin to the divine substance uniquely having relational “modes” of existence.

    I don’t think that will work, though. Aquinas himself agrees that the divine essence cannot be the principle of distinction that accounts for the real distinction between the divine persons. And why not? Precisely, because “the three persons agree in the unity of essence”, which is “something common to all”, and thus cannot be the principle of distinction. In other words, if X is common to A and B, then X cannot be the principle of distinction, which means that the principle of distinction must be not-X, i.e. not what is common to A and B. There is no equivocation here at all, and this idea applies to any A, B and X, whether A, B and X are in God, or are in creation, because Aquinas uses it in his discussions of both.

    The bottom line is that if the divine essence is common to the divine persons, then the divine essence cannot be the principle of distinction, because the principle of distinction must itself be distinct from what the divine persons have in common. Otherwise, the divine essence could be the principle of distinction, which is a position that Aquinas wisely rejects. It therefore follows that the principle of distinction must be other than the divine essence. If the principle of distinction is the distinct divine relations, then it necessarily follows that the distinct divine relations must be other than the divine essence, which means that the distinct divine relations cannot be identical to the divine essence. After all, if X is other than Y, then X cannot be identical to Y.

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  17. To simplify matters, look at the following proposition:

    (1) What the divine persons have in common cannot be identical to what the divine persons do not have in common

    Do you agree or disagree with (1)?

    If you agree with (1), then if the divine persons have the divine essence in common and the divine persons have the divine relations not in common, then it necessarily follows that the divine essence cannot be identical to the divine relations.

    If you disagree with (1), then it follows that (a) it is possible that what A and B have in common is identical to what A and B do not have in common, which is a logical contradiction equivalent to affirming that X is identical to not-X, and (b) it is possible that A and B can have everything in common and yet be really distinct, which is impossible.

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  18. Gregory:

    Any further comments?

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  19. Very busy at the moment with professional life! I hope to get back to you some time over the Xmas break.

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  20. Back at last; but I’m afraid that I am probably going to disappoint you – at least temporarily.

    I must admit that I’m finding corresponding in the reply boxes to blog posts to be very frustrating; especially to a discussion so interesting and detailed as this one. For your last series of four blog post, for example, I find myself wishing to comment in detail on most lines! It is precisely the detail (and it is important detail) that gets lost in this type of medium. I think you are badly misreading Aquinas in these sections, especially in not seeing that your counter-arguments were obvious to Aquinas. But to justify this bold assertion I need to go into greater depth than this medium supports.

    I have been planning for quite some time to add an independent website to this blog; one component of this will be a proper discussion forum where we can better lay out these arguments. In addition this will be much more amenable to conversations in which there are more than two voices. So, if you will have patience with me, I will transfer this thread to the new forum and perhaps we can start anew? I hope this will be done within the next three months.

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  21. No problem, Gregory. Take your time.

    Here's a simpler version of my argument:

    (1) C is a principle of unity between A and B iff A and B share C in common iff C is present in A and C is present in B


    (2) C is a principle of distinction between A and B iff A and B do not share C in common iff C is present in A and C is absent in B
    (3) A principle of unity between A and B cannot be identical to a principle of distinction between A and B
    (4) The divine persons share being God (= the divine essence = Being Itself) in common
    (5) Therefore, being God (= the divine essence = Being Itself) is a principle of unity between the divine persons (by (1), (4))
    (6) Therefore, being God (= the divine essence = Being Itself) cannot be identical to a principle of distinction between the divine persons (by (3), (5))
    (7) If A is not identical to being God (= the divine essence = Being Itself), then A is a creature
    (8) Therefore, a principle of distinction between the divine persons is a creature (by (6), (7))

    You clearly want to reject (8), because it violates core theological truths, and so you must reject one or more of the premises. Which will you reject? You cannot reject (1) or (2), because those are just definitions of what a principle of unity and a principle of distinction are. You cannot reject (3), because that would result in a logical contradiction, i.e. what A and B have in common is identical to what A and B do not have in common. You cannot reject (4), because the divine persons share being God in common. And you cannot reject (7), because it is true that if something is not God, then it is a creature.

    I really don't know what you would do, but I look forward to your response.

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