The Problem of Relations

Are relations real? There are reasons to think not, even though properties are agreed to be real. That would yield a metaphysics in which relations are regarded as mental constructions projected onto the world, while properties (or most of them) are treated as objective constituents of reality. That is, we embrace idealism about relations and realism about properties contrary to a standing tradition that treats them identically. Relations are reified fictions, while properties are found realities. What reasons might justify such a divided position?[1]

Here is one argument. Consider the relations expressed by “father of” and “son of”, and suppose that a is the father of b: is the fact stated by “a is the father of b” the same fact as that stated by “b is the son of a”? Apparently it is: the state of affairs that makes both propositions true is identical. But the relations in question are different, so the complex consisting of a, b, and these relations are different. Therefore relations are not constituents of facts. It is, intuitively, the same state of the world that corresponds to both propositions, but the relations expressed are not the same relations, so the relations are not objective features of the world. We have different relational concepts, but they don’t denote different objective traits of reality.

Here is another argument: we don’t have impressions of relations in the way we have impressions of properties. I see the properties of being red and square—they form distinct constituents of my visual field—but I don’t see the relation of being next-to or on. I see objects standing in these relations, but I don’t see the relations themselves. I have no sense datum of these relations, no phenomenal element corresponding to them. Rather, I infer their presence from what I see of the properties of things. Hume famously argued that we don’t see the causal relation; well, we don’t actually see any relation, even simple spatial relations. That is why relations strike us as abstract and curiously attenuated: they don’t produce sensory effects comparable to those produced by properties. And a fortiori for such relations as fatherhood or being-brighter-than or identity: these correspond to no distinguishable sensory content.

We can imagine someone who is “relation-blind” but not someone who is “property-blind”.  This individual has no sense of relations between things but sees shapes and colors: she never describes anything as next to something or related in any way, sticking to monadic predications. There is no perceptual awareness of relations and no cognitive competence in relation concepts. But it is not possible to be aware solely of relations without any awareness of properties: for that would preclude awareness of objects altogether. Relations are added to perception of objects, but properties are constitutive of it. You can be color-blind and still see, and you can be relation-blind and still see; but you can’t be property-blind and still see.

Relations never constitute the nature of an object (they are always “external”), but properties do. Objects can have natures without relations existing, but not so for properties. Relations are extrinsic to the nature of an object. Thought about objects can thus dispense with relations. Describing the nature of a thing never involves specifying its relations.[2]

It is notable that no one ever cites relations as paradigms of universals: they don’t strike us as ontologically robust in the way properties do. Plato never talks about the form of left-ness, say. It is easier to be a nominalist about relations than about properties because relations seem wispy and word-like.[3] What causal powers do they possess? Can we form mental images of them? If you ask me to form an image of red, I can do so; but if you ask me to form an image of adjacency, the best I can do is picture a pair of adjacent objects. This is why it seems intuitively natural to conceive of relations as sets of ordered pairs (or triples in some cases): we have no solid conception of them as existing over and above their extensions. Relations have domains and ranges, and these seem to exhaust their nature; but we don’t likewise fall in with the idea that properties are identical with their extensions—that there is nothing more to redness, say, than a set of objects falling under the predicate “red”. We are natural realists about properties, but not about relations.[4]

Relations provide principles of grouping—they bring separate objects together. This is made vivid by Gestalt figures in which it is clear that perceived relations act to create visual totalities. This suggests a functional basis for the perception of relations: we perceive (or impute) relations because it is useful to do so. Thus relational cognition is an interest-relative phenomenon: it is useful to know that the computer is on the table when you are looking for the computer, or that this person is the father of that person. We would traffic in relations even if the world objectively contained none. A social species needs to be sensitive to family relations, say, regardless of the metaphysics of relations.[5] Reifying relations is biologically advantageous. Relational cognition is a useful heuristic whether or not relations are objectively real. It operates like a grid we place over things in order to aid action. Its origin is our needs not pre-existing reality.

And here we reach the nub: there is something like a relation of supervenience between monadic facts and relational propositions. Relations are not part of the ultimate fabric of reality; they depend upon more basic features. For example, we say that the computer is on the table—that these objects stand in the relation so expressed—but the hard facts are that the computer is at a certain place and the table at another place. We could specify the spatial coordinates of these objects and never mention the relation in question. That relation indeed follows from these more basic facts, but they can be specified without invoking the relation. Or consider the parenting relation: the hard facts are that certain copulation activity takes place, a process of gestation occurs, and offspring are born. These facts are sufficient to ensure that the relation expressed by “parent of” holds, but they can be specified without employing that relational notion. This is something we add to the basic facts—a useful heuristic, a convenient fiction. The hard-line anti-relational metaphysician will insist that objective reality consists of nothing but non-relational facts that we dress up as relations to serve our own purposes. This austere theorist countenances only monadic propositions at the basic level, with relational propositions allowed only as supervenient on these. The picture is that the world consists of objects with monadic properties, each endowed with an intrinsic nature, and that any talk of relations between them is imposed by us. It is not false to say that objects stand in relations, but they do so only in the sense that objects have colors—both are essentially mind-dependent aspects of things. Neither colors nor relations belong in the “absolute conception”. They are phenomenal not noumenal, subjective not objective. This is why philosophers don’t traditionally list relations as among the primary qualities of things: they don’t carry the same weight of objectivity. They are not constitutive of the substance of things.

We operate with the idea of natural kinds according to which we discover real essences not expressed in our ordinary words for the kind. These are cases in which properties possess hidden depths. But relations never seem to qualify for this status: we don’t pick out a relation by ostensive pointing (“that relation”) and then discover its hidden essence. There is no illuminating empirical theory of what constitutes (say) being-on-top-of or being-the-father-of comparable to the theory that water is H2O or heat is molecular motion. This suggests that we are not dealing with objective kinds found in nature but with classifications manufactured by the mind for its own ends. Not every part of our conceptual scheme is geared to reflecting antecedent facts of nature, and it looks as if relational concepts have another raison d’etre more akin to our ideas of secondary qualities. It is true that the relational scheme is closely tied to the underlying monadic facts, but it is something superadded, imposed from without.

Here is another point, intuitively suggestive though hard to convert into an actual argument. There are just too many relations in the universe; they come too cheaply. Every single grain of sand has endless spatial relations to other physical objects in the universe, some millions of light-years away—not to speak of such odd relations as “being part of a beach I am particularly fond of”. Why would nature create such pointless plenty? What purpose do these multitudes of relations serve? They seem gratuitous, de trop. If God created the world, why did he so stuff it with reams of redundant and tedious relations? But if relations are essentially fictional, we avoid this supernumerary abundance—as we avoid populating the world with the endless armies and mythical beasts of fiction. When we are first told of the profligacy of relations we react with surprise—“I never thought of that, but I suppose it must be so”—but in fact our initial instincts are sound: it is all projection and fancy. We pick out (or invent) the relations that matter to us; the rest we ignore—there is no point in imposing them. They are like a mist into which we decline to gaze: that is, their endless plurality is an indication of insubstantiality. The grain of sand has its hard inner nature, but its limitless penumbra of relations is so much airy nothingness.

We can conceptualize the anti-realist position about relations by using the familiar apparatus of skeptical problems and skeptical solutions in the manner of Hume.[6] Relations are not perceptible facts like properties—they are not part of the primitive data of experience. Nor are they reducible to anything else more palpable. All we ever see of the world is objects having monadic properties; we never see relations naked, so to speak (cf. causal necessity). They are neither physical nor mental. They are not things. Yet we talk about them, and this talk seems useful. Why do we do this if relations don’t objectively exist? Because they serve a biological purpose: they allow us to group things, finding collections in addition to individuals. We then project them onto the world—we reify them. We treat them as more real than they are. In this we are encouraged by language, since there are relational predicates as well as monadic ones. We have relational concepts, but they don’t correspond to objective traits of the universe—they don’t refer to anything that exists independently of the human standpoint. Or more cautiously, the way we tend to conceive of relations has no objective counterpart—though they do supervene on the genuinely objective. We thus misconstrue our relational concepts, treating them as if they are just like our property concepts, which do mirror an antecedent reality. This is the skeptical solution to the skeptical problem. We could even put it as the thesis that relation words have assertion conditions but not truth conditions—criteria of use but not correspondence to fact. We have an “intuition of impalpability” with regard to relations and this reflects their lack of objective existence, but relation talk has its own interest-relative rationale. Accordingly, strict ontology forbids their inclusion in the basic furniture of the world, but we need not dispense with them altogether. We must recognize their true status and not succumb to the perils of reification. Only philosophical confusion can come from regarding our talk of relations as a reflection of objectively real facts, as if further knowledge of their nature could vouchsafe important information about reality. Realism about relations is to be shunned, difficult as that may be given our mental make-up.

I now want to switch gears and consider the bearing of the foregoing on a seemingly unrelated question, namely the nature and origin of philosophical problems. And at this point we are about to get even more radical, not to say shocking: for the question is whether a false view of relations is at the heart of many, if not all, philosophical problems. Be warned, then: things are going to get gnarly. The first and paramount point to note is that a great many philosophical problems are overtly concerned with understanding certain allegedly problematic relations. Here is a list: the relation of mind to body (or brain); the relation between knowledge and reality; the relation of intentionality; the relation of reference; the relation between an object and its properties; the relation of personal identity; the relation between desire and free action; the relation between perceptual experience and external objects; the relation between God and the world; the causal relation; the relation between psychology and physics; the relation between ethical principles and human motivation; the relation between subjective states and aesthetic value; the relation between language and necessity; the relation of numerical identity. We think there is a relation between the paired items listed, but we find it hard to determine the nature of this relation; the relation seems inscrutable, open to different theories, essentially contestable. We try to peer into the relation, as if into a murky pool. We assume that there is a relation and that it has a determinate constitution; we don’t think the idea of such relations is a fiction, a mere useful cognitive heuristic. Philosophy is understood as the investigation of these real relations—for example, it investigates the nature of the emergence relation between brain and mind, or how desire relates to action in cases of free will, or how acts of reference relate to objects in the world. On the one hand, there is this; on the other hand, there is that; the question is how exactly the two are related. Is the relation in question causal (but what is that relation?) or a kind of isomorphism or identity or supervenience or analytic reduction or part-whole composition or complete independence? If we could just see more clearly into the relation, it would solve our philosophical problems! But the relation remains elusive.

But all this presupposes that relations are real—that they have an objective nature, discoverable or not. It all reifies relations, treating them as analogous to properties with an objective essence. What if relations are unreal, merely useful fictions for grouping things? What if relations simply don’t exist? Then there is no such thing as the relation of emergence or the reference relation or the relation between knowledge and reality or the relation of reduction or any of the other relations listed. So there is nothing that the philosophy of these relations is trying to discover the nature of. Philosophy reifies relations, just as we are prone to more generally, thus generating problems that don’t exist but for this reification. It attempts to do the impossible: reveal the nature of relations that have no nature because there are no such relations, just relational words and concepts—classificatory heuristics that have no corresponding real essence. If we could stop reifying the relational concepts that philosophy thrives upon, we could rid ourselves of its problems. In short, philosophical problems arise from the false reification of relations; there simply are no such relations to get philosophically perplexed about. For instance, there are mental states and there are brain states, and they co-evolve in certain ways; but there is no relation between them—specifically, no generative relation. Why? Because there is no relation between anything—not really, not objectively. We can study properties, either scientifically or philosophically, because properties are real and have a nature; but we can’t study relations in this way—and philosophy is up to its ears in relations. The form of a philosophical problem is, “How is x related to y?”: but then it is engaged on an impossible enterprise, destined for frustration and failure. We can ask how we relate one thing to another, as a cognitive act, but there is no such thing as how things are objectively related—not in the sense that philosophy presupposes and requires. Talk of relations has its roots in our practices of grouping, not in mind-independent reality, so we cannot set out to analyze relations as if they had a basis in the objective world. Given that there are no relations in reality sub specie aeternitatus, philosophy has to be wrong in trying to ascertain the objective nature of relations; at best it can enquire into our relational concepts, which are thin and interest-relative. Philosophy reifies relations and then finds that it can say nothing clear and convincing about their putative nature. So, at least, it may be maintained.

As promised, this is surprising and shocking. The shape of the position resembles Wittgenstein’s equally surprising and shocking contention that philosophy arises from reifying the forms of language (as I would loosely paraphrase his position)—also a type of misunderstanding. Both positions detect misconceptions of the real: taking relations to be like properties, and taking the forms of language to mirror reality. The question for Wittgenstein is whether philosophical problems really do arise in the way he suggests, and the question for the proponent of the anti-relational conception of philosophical problems is whether they really arise from the fallacious assimilation in question. Let us accept that relations are unreal and that philosophy is characteristically concerned with problematic-seeming relations; the question is whether it must take that form. Is it possible to formulate the standard philosophical problems without assuming that they concern the nature of real relations? Maybe this will work for some problems (e.g., the free will problem) but not for others (e.g., the mind-body problem); in any case, the question is not trivial. I really don’t know the answer to this question and will not pursue it here; what is clear is that traditionally that is the way philosophical problems have presented themselves—as puzzles about relations of certain kinds. For instance, we have the practice of predication, so we ask how what is predicated (a property) relates to the thing we predicate the property of (an object). Thus we conjure up the relation of instantiation and picture it as linking one kind of entity to another, perhaps as a kind of gripping relation. The question then becomes whether the instantiated entities are platonic universals or expressions of language or ideas in the mind; and whether the object is nothing but the properties it instantiates or somehow stands apart from them. It is difficult to see how we could formulate the problems that arise here without invoking the notion of an objective relation: that is the matrix through which we view the problem. We find it hard to imagine what it would be to think without this matrix and its reifying tendencies; our minds are suffused with relational concepts. But if we take seriously the anti-realist arguments against relations, we have to admit that the old way doing things has to be wrong. To a being not in the grip of relational thought, seeing reality for the totality of monadic facts that it is, these philosophical problems would seem artificial and misguided. Once the monadic facts have been listed and explained there is nothing more to say, no more questions to ask. There simply are no meaningful philosophical puzzles of the form “How is x related to y?” We can sensibly ask how we relate x to y, and for what purpose, but there is no sense in asking how the things are related, if that means asking after the real nature of the objective relations our grouping practices reflect. Relations, to repeat, are not constituents of facts (see the first argument above): facts are not made of pairs of objects and a further entity that links them, viz. the relation. When x loves y there isn’t x, y, and the loving relation, as an extra ingredient of reality, forming a complex entity of which the relation is one component; rather, x has various emotions and beliefs with a certain content, these being monadic properties of x. There is nothing more to the fact than these properties; speaking of a relation of loving between x and y is derivative talk, capable of misleading us into false reification. Relations resolve into a congeries of properties, or else are mental projections or mere words. Our language and thought play a trick on us: we perceive objects with properties laid out in a certain way and we proceed to group them according to predilection—but then we project the patterns of grouping and invest reality with objective relations. This is how we come to conceive of family relations when really the hard facts are just copulations and births arranged in time. Even spatial relations are just objects having properties at specific locations, objectively speaking; anything extra is human imposition. Thus anti-relational metaphysics cuts at the heart of traditional philosophy. Reality doesn’t have the relational form that philosophical questions presuppose. Maybe we can’t stop thinking in these terms, so that philosophical problems will always grip us; but that doesn’t mean that these problems have any basis in the objective nature of the world. They arise from our self-produced concepts not from reality as such.[7]


[1] I wish I could cite an obscure philosopher (Hegel maybe) whose writings suggested the position developed in this paper: not as an interpretation of that philosopher, and not as my own view, but as what occurred to me upon reading said obscure philosopher. I certainly find the view extraordinary and literally incredible, but I also think a case can be made for it (as well as against it). Let me say that the ideas occurred to me in a dream, on which I drowsily made notes in the middle of the night, and in the morning tried to decipher those notes, coming up with what follows. So this is an essay in philosophical dream interpretation directed at myself.

[2] Hegel’s idea that all relations are really “internal” might be seen as a tacit recognition that only properties are real, i.e. only what contributes to the nature of an object can be true of it. This naturally gives rise to a general monism. The alternative is to deny that relations are real; then objects can have natures constituted only by their monadic properties. The essence of reality is to be unrelated: it is we who imbue reality with relations; in itself reality consists of self-standing objects mutually ignoring each other.

[3] Here is a passage from Russell’s The Problems of Philosophy that expresses the kind of position I am articulating (not endorsing): “Suppose, for instance, that I am in my room. I exist, and my room exists; but does ‘in’ exist? Yet obviously the word ‘in’ has a meaning; it denotes a relation between me and my room. This relation is something, although we cannot say that it exists in the same sense in which I and my room exist. The relation ‘in’ is something which we can think about and understand, for, if we could not understand it, we could not understand the sentence ‘I am in my room’. Many philosophers, following Kant, have maintained that relations are the work of the mind, that things in themselves have no relations, but that the mind brings them together in one act of thought and thus produces the relations which it judges them to have.”

[4] Relations are typically expressed by verbs and prepositions (e.g. “at”), but it is a stretch to take these as referring to objective traits of the world—as if they are names of a certain kind of entity. In the case of nouns, this is far more natural (“red”, “man”). The idea that “at” denotes something seems fanciful, though it certainly has a meaning. Thus relation words are more like connectives such as “and” and “or”.

[5] We have a strong tendency to insist on social groupings of one kind or another, plausibly driven by genetic considerations, but for the anti-relational metaphysician this is just a matter of biological necessity not objective existence. Thus the reification of relational concepts is only to be expected: the concept of a family is likely to be elevated above what the objective facts warrant, as if written deep into the nature of things. But the only hard facts here are certain patterns of genetic transmission.

[6] See also Kripke’s development of this apparatus in Wittgenstein on Rules and Private Language (1982).

[7] Let me emphasize that I am not advocating this position as true; I am rather articulating a line of argument that strikes me as worth pondering. It is certainly startling in its originality and sweep. I am in the grip of relational thinking as much as anyone, and not naturally inclined to suppose that philosophical problems are really pseudo-problems. On the other hand, the position has a certain grim appeal.

7 replies
  1. Oliver S.
    Oliver S. says:

    Nonreductive realists about polyadic attributes argue that…

    “Relations are the sine qua non of a plural universe, of connectedness, structure, order, and form.”

    (Mertz, D. W. Moderate Realism and Its Logic. New Haven: Yale University Press, 1996. p. 25)

    I’m skeptical about the existence of relations (as entities sui generis), but I cannot help conceding that the realistic view is not without plausibility:

    “Without a category of entities whose natures are to outwardly bridge ‘ontological distance’ and ‘hold themselves together with’ things with which they share no composing being, i.e., without entities that are /ontoglial/ (Greek: ‘glue of being’), discrete entities would each remain absolutely isolated from every other. Every entity would exist as a radically segregated atom, an extreme ‘monad’ completely devoid of inter-connections—physical, cognitive (e.g., associations), etc., with any others—and with any such entity, because of this total mutual isolation, no mind (assuming per impossibile there are minds, what necessarily are dynamically functioning structures) would have epistemic access since this would require real epistemic relationships linking knower and known-other.”

    Without real relations and connections “the ontic possibilities are the extremes of either the radically discrete in a vacuum of absolute mutual isolation, or a divisionless One in which all differentiating identities are obliterated in a homogeneous blend, both extremes in the end unknowable and ineffable.”

    (Mertz, D. W. On the Elements of Ontology: Attribute Instances and Structure. Berlin: De Gruyter, 2016. pp. 188+195)

  2. says:

    Damn, I wish I had said that. On the other hand, we have a possibility proof, in defense of “..a divisionless One in which all differentiating identities are obliterated in a homogeneous blend”. It’s called The Fox News channel..The impeachment proceedings both repel and compel. Talk about a “grim appeal”. Politics aside, I believe both Chomsky and Carlo Rovelli would find this latest Post of your’s a good deal congenial.

  3. Giulio Katis
    Giulio Katis says:

    Is not a (binary) relation just a property on (ordered) pairs of ‘things’? From this perspective, perhaps the question you are asking is whether every relation between two things can be understood as a property of one thing that spans the two things and the identified relation between them. Even if this (empirically sounding) question were true, I don’t think we can dispense with relations, for the same reason we can’t dispense with speaking in terms of both parts and whole.

    I wonder if somewhere there is conscious intelligent life very different from ours that evolved in a fluid environment, made of fluid rhythmic material – a musical life form, let’s say – that sees relations directly, but not ‘things’. So things are like fairy dust to them and impermanent. They might question whether these ‘things’ their philosophers speak of are real at all.

  4. Oliver S.
    Oliver S. says:

    “There are certainly relational truths, but there may well be no relational /truthmakers/.”

    (Lowe, Jonathan E. “There Are (Probably) No Relations.” In The Metaphysics of Relations, edited by Anna Marmodoro and David Yates, 100-112. Oxford: Oxford University Press, 2016. p. 100)

    Arguably, our relational concepts or predicates are irreplaceable by nonrelational ones, and our relation talk is indispensable and inevitable. However, the crucial ontological question is whether relational propositions depend for their truth on the existence of relations qua polyadic attributes.
    Note that “relation” isn’t synonymous with “polyadic attribute”, because reductive realists about relations don’t deny their existence but identify them either with (pairs or groups of) nonrelational monadic attributes (properties) or with (pairs or groups of) relational monadic attributes (properties) as a kind of monadic attributes sui generis.

    By the way, interestingly, Fraser MacBride draws a distinction between truthmaking and ontological commitment, and argues that we may still be ontologically committed to (internal) relations even if they aren’t required as truthmakers for relational propositions:

  5. says:

    Talk of relations, “bottoms out”, as it were, with respect to life-forms and their environments. All else is idle. There’s no escaping a creature’s evolved perceptual or conceptual profile. One creature’s relation is another’s property. The world is as it is, was as it was, and will be as it will be—irrespective of any human (or non- human) complication.


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