Relations as basic – the Bradleyan descent

I think both steps (1) and (2) of Della Rocca's argument are problematic as I will show in this paper: (1) treats relations as addenda to the relata which seem to exist independently of the relation. This is one way of thinking about relations – a way we will see very clearly also in Aristotle's account of relation. But it is by no means the only one as Della Rocca suggests for his argument; I will give several examples below of relations that cannot be thought along these lines. Subsequently, I will demonstrate problems with step (2), with the way in which Della Rocca gets the infinite regress going. This does not mean, however, that the core concern Della Rocca raises is not a real concern; it is in fact one dealt with in many debates about metaphysical foundationalism and coherentism.

Before I demonstrate this descent of Bradley's regress, I will first stay on the positive side and show how the kind of relations Della Rocca sketches are indeed problematic and have been shown to be worrisome already in ancient times, starting from Parmenides.

Della Rocca ties his argument against any distinctions to Parmenides and his monism, since a strict monism is the only position that, following Della Rocca's main argument, will ultimately be left for us. Parmenidean monism is based on his rejection of any distinctions. According to Della Rocca, this is in turn based on Parmenides' rejection of all forms of relations.⁵

The notion of relation is indeed a notion that is very problematic in ancient philosophy: Parmenides does not allow for any relations, and Plato and Aristotle point out problems with them. The main worry seems to be that if something is a relation or relational, then it seems to have only derivative existence, but no full being. We can see this in Plato's characterisation of Forms as being simple in itself while sensible things only exist in relation to Forms, or in Aristotle's account of accidentals, which can only exist in relation to some substance. Della Rocca stands in this long tradition of raising problems for the very notion of relation. Since Aristotle is the thinker who shows the problems relations may raise most explicitly, we can think of Della Rocca as an Aristotelian in this sense. However, like Aristotle, Della Rocca only takes certain kinds of relations into view which will turn out not all that there is to relations. But let us look at the problems Plato and Aristotle raise with respect to relations first.

Plato, like Parmenides, attempts to conceive what truly is, for him the Forms, as possessing no complexity, no distinctions. For Plato there is, however, a plurality of what-is, of Forms, and so the freedom from distinctions only concerns each Form internally: each is of one kind (monoeidês), simple, not composed, and indivisible (see, for example, Phaedo 78b-d). The late Plato, however, changes this, as we can see in the Sophist. There he not only demonstrates that Parmenides has problems even formulating his position of monism (244c8-d9), but also that we have to think of what truly is as being internally complex and thus as containing some form of relation (in the so-called megista genê passage, Sophist 254c1-259d8).

In the Euthydemus Plato plays with paradoxes we get into if we think of relations as simple properties⁶: the sophist Euthydemus shows, for example, that if we understand the relational predicate “being the father of y” (so a two-place relation “x is the father of y”) as a one-place predicate, simply as “being the father”, then we can derive from the claim that Michael Della Rocca is not the father of Socrates that he is no father full stop (poor Ben and Ethan Della Rocca). Today, we often do not strictly distinguish between relations and properties in that we take relations as objects of multi-place predicates or simple predicates as one place relations. But the problem the Platonic passage raises is still the same: understanding something multi-place as one-place means we loose the connection to the particular relatum to which the relation is tied.⁷ This is important since we will see below that there are in fact relations that are not tied to a particular relatum and are universal in this sense, but these are not the family relations discussed in the Euthydemus.

In the Parmenides in the so-called “Greatest Difficulty” passage (133a-134e), Plato seems to distinguish between two ways of being, relative being and absolute being. Something has relative being if what it is, its nature, can only be determined with respect to something else. But if a Form is relative, it seems it could only be relative in relation to another Form, while sensible things can stand in relation only to other sensible things. Plato illustrates this point with the example of the master–slave relation: the “Form” of Slavery can only stand in a relation to the “Form” of Mastery, while a particular slave will only stand in a relation to a particular master.⁸ The upshot of this argument, the greatest difficulty for the theory of Forms as depicted so far in this dialogue, is that it seems no individual sensible thing can stand in a relation to a universal Form, and thus no participation relation seems to be possible. But it is of course the participation relation, the fact that sensible things participate for what they are in their respective Forms – a beautiful flower, for example, is beautiful because it participates in the Form of beauty – that seems to be a main reason for assuming Forms.⁹ What is more, according to this argument, our specific human acts of cognition can never cognize Forms, but only a specific individual thing. Thus Forms turn out to be unknowable for us, and gods who possess knowledge as such cannot know human affairs.¹⁰

What is important for our topic is that Plato here looks at relations as such – mastery or slavery as such – and clarifies that mastery as such only stands in relation to slavery as such, not to a specific slave; and a specific master is master not in relation to slavery as such, but to a specific slave. We get a clear linkage of specific relations with specific relata, universal ones with universal relata.

The father example shows Plato discussing the fact that relations cannot be understood as one-place predicates and that a relation needs to be tied to a specific relatum – a father always has to be the father of somebody particular, such as Michael Della Rocca being the father of Ben and Ethan Della Rocca, otherwise we get into paradoxes. By contrast, an Aristotelian is interested in another aspect of such relations, namely that being a father is a mere accident, and does not yet specify what the thing talked about ultimately is¹¹: Michael Della Rocca is first and foremost Michael Della Rocca, a human being, this is his substance; and only in addition is he a father. There was a time when he was not a father; being a father is temporal and metaphysically posterior for Aristotle, prior is him being a human being. (Furthermore, Michael Della Rocca may become part of a relation even if not doing anything, for example, if he were to become an uncle).

We see that according to Aristotle, whatever is relative to something is first and foremost something else. It has its own nature and, in addition, it is also relative to something else. Thus a relation is always derived from the relata. The relata have to be given in the first place in order for a relation to obtain; the relation can then be added or taken as the sum of the relata. This is the reason that for Aristotle relata are least of all true beings.¹³

Furthermore, it is rather loose if I talk about Aristotle's discussion of relation, since what he in fact talks about in his Categories as well as his Metaphysics is about what is pros ti, literally “what is with relation to something”, “what is relative”. Thus he is not talking about relations as such, but about the relata, what possesses a relation, the relative. In Metaphysics Delta 15 Aristotle distinguishes between different kinds of pros ti – a relative according to number (like half and double), or a relative of doing and having done (like cutting and being cut), or a relative in the sense of measure in relation to what is measured.

Thinking of what is relative, rather than of relations also means that relations like “A > B” and “B < A” which are the same relation just expressed differently, are two different relations for Aristotle, one being the “bigger than”, the other the “smaller than” relation, similar to the “being half” and “being double” relation Aristotle discusses explicitly.

This emphasis not on the relation but on the relatum, that is already expressed in the term “pros ti”, shows that Aristotle thinks of relations as something that is additively built, as a sum from its part: we start with some A that is of nature x and then turns out also to have a relation to B. This starting point from relata seems very close to what Della Rocca has in mind.¹⁴ Also Aristotle certainly makes Della Rocca's assumption (1) above (though he does not go on further to (2)).

Aristotle's Categories show that what is relative is not only derivative for him but also problematic.¹⁵ There he defines the category of pros ti a second time, for the first definition ultimately extends into the category of substance (8a28ff.) and thus cannot be adequate.¹⁶ Aristotle not only lists master and slave as relatives there, but also knowledge and what is knowable; and he takes up the worry that second substances, i.e. kinds and genera, may seem to be relative.

Relations like the ones we find in Aristotle (being a father, being double) are always tied to particular relata. These kind of relations are indeed dependent on their relata in the way Aristotle, Bradley, and Della Rocca suggest. There seem to be no general relations of these kinds, but only of specific relata. In this respect, Della Rocca seems to be like an ancient thinker, though not like Parmenides, but more like Aristotle.

Relations like “being a father” is the kind of relation Della Rocca is talking about, but it is not all there is to relations. Hegel, who ironically was an important influence on Bradley, seems to be the first thinker to show clearly that there are other kinds of relations that cannot be thought of in an additive way such that we have A and B and in addition also the relation of A and B.¹⁷

The short sketch of Plato's and Aristotle's treatment of relations above shows that we need to get clearer first what is in fact understood by a relation here. Della Rocca seems to focus on relations where A and B give me R, since he treats R as posterior to A and B. He treats relations as addenda, as decorum if you like, as something that can, but need not be added to the relata A and B. Behind the thought that relata A and B add up to relation R is the implicit assumption that parts have priority over wholes so that we get R as a mere result of A and B. The whole, the relation, is thought of as the sum of its parts. There are, however, also relations where A and B on their own do not give me the result, where the whole has priority over the parts.

Furthermore, with the father-son relation and all kinds of family relations the individual relata are important – we saw that if we leave them out, Della Rocca will stop being a father. But there are other kinds of relations, where the relata are not important and prior since different relata can be used (we may think of such relations as universal in this sense)¹⁸; and if I posit one relatum, its correlate will simply come about.

In the following I will give several examples of relations that cannot be understood in the way Della Rocca understands relations, that is as an addendum to its relata. In this way I will argue against step (1) of Della Rocca's Bradleyan regress. We will see instances where the “relata” would not be what they are without the relation so that it would be false to say that the relation is grounded in its relata or where the relation is prior and different individual relata can be plugged in. I will give counter examples to the way Della Rocca treats relations from the social, musical, and scientific realm – these are just the areas where such examples immediately came to my mind, but presumably there are many other examples in other realms.

So far I have dealt with the first step (1), that Della Rocca takes in his argumentation against relations, his assumption that relations are always grounded in relata. We saw above that Della Rocca seems to assume such relations for his argument and leaves out relations we know from music or the sciences where the relations are more basic than their relata. We will now consider how Della Rocca gets from the initial relation R to the infinite regress and thus move on to his second step (2).

Della Rocca claims that relation R is grounded in its relata, A and B, and thus stands itself in a grounding relation R' to them. R' in turn is grounded in its relata – A and B on the one hand, and R on the other. I do not see that Della Rocca explicitly clarifies what exactly he understands by “grounding” (independent existence, metaphysical or epistemic priority, or yet something else?). He seems to assume that a relation R is grounded in A and B iff R (the result) would not be there, in case A and B were not there²⁹; and he seems to think of it as a metaphysical or ontological relation.

R' is a relation where one of the relata, that which does the grounding, here A and B, is (presumably metaphysically) prior to the other relatum, to what is grounded, here R. Call this an imbalanced relation for ease of reference. By contrast, the relation we started out with between A and B is neutral and not tied to any kind of priority, call it a balanced relation. Now some of the examples Della Rocca gives are indeed imbalanced relations such that some C is prior to some D, such as a substance being prior to its attributes. So perhaps it is just that an imbalanced relation has to be assumed as a ground not only for other imbalanced relations, but also for balanced ones (and a more specific relation may be the basis for less specific ones). Be this as it may, what is important in the step here is that (a) the two relations R and R' are in fact very different, and (b), it is unclear how we should get from R to R'. R is a balanced relation, while R' is an imbalanced one.

In this way Della Rocca thinks we still get into a regress if we deal with facts, rather than objects. But what Della Rocca does here, as Bradley did in his object talk, is to treat relations or relational facts as the same kind of beings as relata, be they objects or facts. He presupposes that there is no difference in the behavior of relata and relations and thus misses the point of relations. It is only treating relations as the same kind of thing as their relata that allows Della Rocca to pump up another relation into the system: if a relation or relational fact R is grounded in fact F or substance S then it must also depend on a grounding relation (or a grounding relational fact) R' in addition to F and S.³⁰ But we only need another relation R' if we treat R as being of the same kind as F or S (only in understanding R as at least a quasi-object or quasi-relatum would the grounding question rise again, would a path be demanded),³¹ otherwise the regress (or circle) does not get started.

This demand for another relation due to the fact that our original relation R is treated like a relatum shows that Della Rocca is not, contrary to his explicit claim, following Ockham's razor. On the contrary, he is using the opposite operation, what I would call “Della Rocca's Multiplier”.

Della Rocca thinks that people can only stop the regress by restricting the PSR. He claims in his “Tamers” paper against Kant's restriction of the PSR that “any response to the regress argument will appeal to brute facts in one way or another, i.e. will turn on denying the PSR”. I do not think this is right. My response to his regress argument turns not on denying the PSR, but rather on pointing out that relations cannot be thought in the same way as their relata can and that here the millennium old move of philosophers, to make distinctions between different things, is the way to avoid such a regress.

However, the concern Della Rocca points to with his argument, namely the question whether there is an ultimate basis for all the grounding, whether the why or how questions ever comes to an end, is a real concern. And it is front and centre in debates about foundationalism and coherentism. Do we ultimately have to assume something which is not grounded in something else, but rather self-grounded and if so how can we understand this self-grounding? Or should we rather assume that all grounding ultimately is done in one big, non-vicious circle, along the lines we find it in different versions of coherentism³² and for most basic concepts in Hegel's Science of Logic?

We saw that the main argument of Della Rocca's book that is at the bottom of his rejection of any distinction, the Bradleyan regress against relations, is itself a problematic argument, since it treats relations in the same way as its relata and thus misses what is specific about relations. Della Rocca assumes relations to be grounded in relata, treats relations as behaving in the same way as its relata, substantivizes them and thus requires a further relation for it to be grounded in its relata. And this further relation needs another relation of grounding etc., starting “Della Rocca’s Multiplier”.

Furthermore, Della Rocca presupposes a particular kind of relation which can be seen along the lines of thinking about relatives that we found in Aristotle. This is, however, by no means the only way to think about relations and misses out many relational phenomena and concepts we know from the sciences, mathematics, and music. In these fields, we saw examples of relations that have to be captured as wholes whose natures cannot simply be determined by the nature of their parts. Rather, as we saw in mathematics, there are relations, like functions, where different relata can be plugged in; or in quantum physics it is relations that are determined and the objects derivative. So there is a whole group of “Relations First” phenomena. And it may only be with middle-sized objects, if at all, that relations are dependent on and wholly derivative of their relata.

Della Rocca gives the question of ultimate grounding the specific flavour to ask what happens to the PSR. He claims that there is no natural end to PSR reasoning and that all restrictions of the PSR are not well-founded and lacking. And he seems to assume that only restrictions of the PSR need to have a reason but not pushing our PSR question always further. But an unrestricted PSR leads to infinite talking or to silence, both of which Della Rocca's book does not embrace (even if chapter 12, and perhaps 13, point into the direction of silence). So perhaps it is not so much the restriction of PSR reasoning that needs a reason, but the assumption of an unrestricted PSR itself.