Are All Properties Relations?

Are All Properties Relations?

For some reason, philosophers tend to prefer properties to relations: the former are deemed more real, more concrete. To the contrary, I will argue that all properties are relations; so, if relations are unreal, so is the world. Fortunately, they are not, but that is not my concern today.[1] We have a wide range of properties to consider, so brevity will be our policy. The idea will be that all properties, so called, are polyadic, never monadic. Actually, it is not so difficult to establish this once we look more closely; we are under a kind of illusion on the question. Let’s start with sensible qualities: colors, sounds, smells, tastes, and feels. Here we can quickly announce that these are all tacitly relational; they are all relations to perceivers—ways things appear to perceivers. The external object appears a certain way in experience and this is what the property consists in; traditionally, it is regarded as a disposition to produce experiences in perceivers. The ontological form of “x is red” is “x appears red to y” (I am not being fussy about quotation). This is an excessively familiar story, so I won’t labor it; I am merely stressing the relational nature of this analysis. In the case of primary qualities, we can be equally brief: shape is a matter of relations between edges or surfaces or points, while size is relative to other objects (“x is big” means roughly “x is bigger than most things”). Mass is defined as resistance to motion under applied forces (like being pushed). Dispositions and powers are relations to other objects, as in a disposition to dissolve in water. Electrons and protons are particles that repel other particles with the same charge. Gravitational force is a relation between massive bodies. Chemicals and metals are defined by molecular and atomic structure, which involve relations between particles. Animal species are defined anatomically or by the ability to mate: the former involves spatial relations and the latter sexual relations. We should note that in all these cases the words used are grammatically once-place predicates, but the corresponding reality involves relations of different kinds: for example, the word “gene” and the structure of DNA. Language is no guide to reality here.

But there are less obvious cases: mental, mathematical, logical, semantic, moral, aesthetic. Are beliefs relational? Not to other people, to be sure, but internally they are—they are relations to propositions. This is a familiar idea: belief is a relation between a believer and what is believed. In turn the proposition is related to the world it is about. Some philosophers have maintained that intentionality is the essence of the mental, and this is clearly relational. Mental events are also causally related to the environment and behavior, and these have been thought essential to their nature (externalism and behaviorism). The mind is full of relations that constitute the nature of mental states. Mathematical properties are also relational: to be even is to be divisible by 2, all numbers are related to other numbers in various ways, numbers either precede or succeed other numbers in the series of natural numbers. Logic is relational in an obvious way: premises are related to conclusions by entailment—validity is a relational concept. To be a premise is to occur in an argument. Meanings involve the relation of reference and relations to other words (synonymy, antonymy). Morality is a matter of consequences or duties, both being relational—consequences for others and duties to others. Beauty is either in the eye of the beholder or a matter of the structure of the object (a painting or a musical composition)—this involving relations of various kinds. No property is relation-free. The world doesn’t neatly divide into monadic properties and polyadic relations—that is a superficial view. Scratch the surface and swarms of relations pop out. You can’t make a world by first installing the monadic properties and then adding the polyadic relations; the former require the latter. No relations, no properties. Language may make it seem like there are two separate categories of being here, but actually there are not. The world (any world) is a relational place.

Are there any exceptions? It is certainly hard to find them, contrary to first impressions, but there may be some stubborn holdouts. Anything come to mind? I think there is one area where relationality is hard to discern: pain. It may well be said that pain is not intentional and not a relation to a proposition; it is just a sentient thing being in a simple monadic state. Pains are free-standing properties of organisms, that’s all. For what are they relations to? However, this objection is not unanswerable: we may cite the body as the relevant relatum. I have a pain in my foot or head—there is no pain felt nowhere. How does this work for mental anguish, though? But isn’t it directed to reality in some vague way? Also, it might be argued that pain must involve a relation to the brain. The case is messy and controversial, but it shouldn’t be thought to undermine the whole metaphysical picture sketched above. It would be very odd if all of nature but pain had a relational ontology. Still, the case shows that this metaphysics is not trivially true; there are conceivable counterexamples. Maybe non-relational properties are at least logically possible. What is striking is how relational reality turns out to be on close examination. So, we had better hope that relations are real or else nothing is. My own feeling is that it is a surprise to discover that relations are as vital to reality as they seem to be.[2]

[1] See my “Relational Realism”.

[2] The notation of standard logic encourages a false dichotomy between properties and relations (an untenable dualism): we write “Fx” and “Gy” and distinguish these from “xRy”, as if we are plumbing the ontological depths. Thus, the talk of “properties and relations”, as if these were mutually exclusive. A kind of symbol-object fallacy ensues, wherein we suppose that the objects are as discriminating as our notation. In reality, what are called properties are disguised relations—relations masquerading as properties. Perception and language conspire to produce this illusion—this dualism of properties and relations. It even leads to denying relations full reality. The word “gold” and the look of gold make us think that gold is a non-relational attribute, whereas beneath the surface gold is a bunch of tightly compacted relations between particles composing atoms. We underestimate how relational things really are in nature. We are prone to anti-relationalism. Everything may not be relative, but it is relational.