Thursday, 7 October 2010


One of the important metaphysical concepts that Aquinas makes use of is that of a “relation”. He uses the concept in Ia q.13 in talking about how we are related to God and how God is related to us. When he comes to consider the Trinity, the notion of a relation becomes central. Aquinas will develop an exposition of the Trinity that maintains metaphysical coherence between the idea of God as “one” and God as “three” by identifying the “hypostases” (or “persons”) within God as “subsisting relations”.

This article is intended to give a brief overview of how medieval philosophers thought about relations as an aid to understanding how Aquinas uses the notion.

There is a superb article on “Medieval Theories of Relations”, by Jeffrey Brower, over at the online “Stanford Encyclopedia of Philosophy”.

In many ways, this article simply condenses and simplifies what is said there, so if the reader finds what is written here intriguing, puzzling or simply infuriating, relief may be had by going on to read Brower’s article.

We’re thoroughly used to using the notion of a relation in everyday language. For example:

  • “James is taller than Richard.”
  • “This potato is heavier than that tomato.”
  • “Hannah is my daughter.”

These examples seem quite benign, but when one starts to consider the metaphysics underlying such expressions of relation one is rapidly exposed to some surprising difficulties. For example, it would seem quite reasonable to think that “James is taller than Richard” expresses an objectively real fact about the world rather than simply being a consequence of how our minds organize their thoughts about the world. This being so, it would seem that a relation has to be some sort of real thing in the world as opposed to something that only exists in the mind. Where then does this relation exist? What is it? Does it have form and matter?

Medieval philosophers started their thinking about relations from Aristotle’s treatment in the Categories (which we mentioned in our Introduction to Metaphysics). In this work, Aristotle divided what we can express about things into two classes: substance and accident. Aristotle characterises substance as that which cannot be predicated of anything or said to be in anything – “primary substances”; or as that which can be predicated of something but cannot be said to be in anything – “secondary substances”. On the other hand, accidents are predicated of things in the sense of being (or inhering) in things. There is a primary division between being in a subject (accident) versus not being in a subject (substance).

So, for example, when we say that “that cat is white”, we are predicating something (whiteness) of some thing (“that cat”). The whiteness inheres in the cat as an accident, whereas the phrase “that cat” points to that particular cat rather than being predicated of it, and certainly does not inhere in the cat. So in our sentence, “that cat” points to a primary substance and “white” is an accident inhering in that particular cat. Similarly, in the sentence “that animal is a cat”, “that animal” points to a primary substance and “cat” is a secondary substance, a universal.

In the Categories, Aristotle went on to divide up the class of accidents into nine subclasses. One of these subclasses is what we are considering here, the notion of “relation”. Aristotle’s original Greek described “relation” as “pros ti” (“towards something”) and this description gives us an important clue about the metaphysical opportunities and problems associated with relation. The other eight accidental categories are all naturally associated with a thing-in-itself: we can happily say that “the ball is big” (the category of quantity) or “the ball is in the sandpit” (the category of place) but when we come to talk about relations involving the ball, we need something else there as well: the thing that enters into the relation with the ball: “the ball is bigger than the ant”.

When we think of our original examples, a sentence like “James is taller than Richard” seems to involve a number of aspects. First of all, each of the participants in the sentence has a particular height; the relation between the heights of James and Richard is said to be founded in the heights of each individual. Next, there is a comparison between the heights that dictates whether the relation holds or not. Finally there are the questions of where this relation exists as an accident and the sense in which we can say that the existence of this relation is real.

In the Categories, Aristotle held that a relation is not a separate thing to which the participants in the relation are jointly attached but is really explained by the foundational accidents involved. This idea bears a sort of similarity to Aristotle’s approach to universals; universals are instantiated in their exemplars, there is no Platonic third realm of universals where they have a totally separate existence. However, for Aristotle, relations (as universals) are still real entities with their own existence.

In the Middle Ages, although philosophers followed Aristotle in teaching that relations are real entities explained by foundational accidents, there was a dispute between those that held that relations amounted to no more that these foundational accidents (“reductive realism”) and those who held that although relations were founded on these foundational accidents, relations were sui generis accidents (“non-reductive realism”). These latter (including Aquinas) held that we should distinguish between such a thing as the accident of height and the accident of pointing-towards other heights founded upon the accident of height.

There’s a major distinction to be made between some modern approaches to relations, where they are considered to be things that hold between two or more things and the Aristotelian (and medieval) approach in which they inhere in one thing pointing towards another.

Medieval philosophers were also willing to recognize a distinction between propositions and situations that define real relations (so called “relations according to being” or “relationes secundum esse”) and propositions and situations that simply express relative terms (“relations according to speech” or “relationes secundum dici”). In other words, a distinction was made between what serves to relate things and what simply stands in some relation. For example, if we were to come across a decapitated body with its head by its side, we might say “this is a head” and “this is a body”. “Body” and “head” would appear to be relative terms related to each other, but do “this is a head” and “this is a body” express real relations? The problem is that if so this would appear to identify substances with relations, but according to Aristotle relations are accidents. The solution is to recognize that these relative statements are describing parts of substances and not relations. If we were to go on and say “this is the head of that body” we would now be expressing a relation between two substances whose accidental situation indicates that they originally came from one substance. Aquinas refers to this distinction in Ia q.13 a.7 ad1.

Let’s consider another problem: think about the relation of “equality”. “James is the same thing as James” seems to express an obvious fact about reality. If this relation is a real thing, which we’ll call “R1”, then we can immediately observe that “R1 is the same thing as R1”. This is itself a real relation which we’ll call “R2”. We can then apply this reasoning to R2 to get R3, and so on. We soon see that our simple notion of the relation of equality implies an infinite sequence of “real things” associated with one apparently simple relational statement! This would seem the sort of hopeless mess that would have William of Ockham rubbing his hands in glee. The way out of this conundrum is to observe that when we say “James is the same thing as James”, we’re not really saying anything about James. We could quite happily substitute the word “James” with any “x” that named a substance and we’d still have a true statement. Statements like this do not express real relations (“relationes reales”) but what the medieval philosophers called “relations of reason” (“relationes rationes”). In this example, we notionally posit a relation founded on the unity of the substance concerned.

There are also problems in other directions and Aristotle seems to have identified some of these problems in his Metaphysics, suggesting that he himself knew that the treatment in the Categories would not ultimately be sufficient for all circumstances. Much of the medieval debate about relations amounts to a debate about how to relate the theory of relations given in the Categories with that advanced in the Metaphysics and then how to square this resolution with the data of revelation about God.

As we saw, our original examples given above seem to be based on accidents in both the objects appearing in the relations concerned. “James is taller than Richard” depends upon a fact about James’ height and a fact about Richard’s height and a comparison between the two. However, this need not be the case.

  • “Richard is thinking about Fiona.”

This sentence seems to express a relation between Fiona and Richard that only depends upon some fact about Richard (that he is currently thinking about Fiona). There would seem to be nothing about Fiona that is involved in this relation. (If one argues that “Fiona is known by Richard” is the underlying fact about Fiona that grounds this relation, one should consider that this is just another way of saying “Richard knows Fiona”).

  • “I have arrived at a position to the right of the column”.

Similarly, this sentence provides another example where it is a fact about me that founds the relation rather than any fact about the column. In both of these examples there is a profound asymmetry. Medieval philosophers dealt with these examples by using the idea of a “relation of reason” that we saw above. They considered that even if there were no case for considering one side of the relation being real (or extra-mental) we should consider it as if it were so, projecting the mental relation onto the subject concerned. In examples such as these, there is both a real relation and a relation of reason involved. Philosophers such as Aquinas were quite happy to consider that certain relations did not introduce something in extra-mental reality. The discussion in Ia q.13 a.7 gives a clear example of Aquinas exercising these concepts of real relation and relation of reason simultaneously.

  • “I am thinking about those two chairs.”

This sentence would seem to set up a relation between two chairs (as well as a relation between me and the two chairs). But surely this relation expresses no facts inherent in the chairs themselves. Here we have an example where the relations involved are purely those of reason.

Finally, we come to the examples that motivated much discussion in the middle ages about the nature of relation and about whether the notion of relation put forward by Aristotle was adequate when dealing with the metaphysics of theism.

  • “God the Son is the son of God the Father.”
  • “The Holy Spirit proceeds from the Father and the Son.”

We already know from Aquinas that when we talk about God, we often talk analogically. Does this apply here, when we talk about relations involving God? Or are these statements literally true, and if so, how are we to understand them?

If we take the statement “Jesus is the Son of God” as being true, then it appears to set up a relation between God the Father and the God the Son. If we were to consider this relation to be purely one of reason, then we would fall into the heresy of Sabellianism (the idea that the distinction between the persons of the Trinity is purely notional). If we were to suggest that the relation is real in the Son and a relation of reason in the Father, then we would be falling into the error of Arianism (that the Son of God is a creature) because the reality of the relation in the Son would correspond to an accident in the Son which would imply that the Son was a creature. If the relation were real in both God the Father and in God the Son then we would seem to have set up accidents in both of them, contrary to the doctrine of divine simplicity.

Aquinas’s solution is simple and bold: when we consider relations concerning the divine persons, those relations can correspond to substances rather than accidents. Aquinas will spend much of Questions 27-43 of the first part of the summa developing the idea that the persons of the Blessed Trinity are subsisting relations within the Godhead.


  1. Wow - I wish I'd had you around when I was studying philosophy; thank you!

  2. That's very kind of you Ed! I hope the stuff I write is correct...

  3. Sounds right to me as I try to write 12,000 words on relation in the Trinity.

  4. 12K words? Oof! Is it for a Master's thesis?