Relation

Plato, like the ancients generally, discusses relative terms rather than relations considered in themselves, and he employs no technical word for relation as such. The late dialogue Sophist nevertheless raises the question in a form that governs much of what follows. The Eleatic Stranger argues that Being, Sameness, Difference, Motion, and Rest cannot each stand alone. Motion is, and so partakes of Being; it is the same as itself, and so partakes of Sameness; it is other than Rest, and so partakes of Difference. To deny that the greatest kinds can blend with one another would be, on this argument, to destroy the possibility of significant speech, since every statement joins one form to another. The communion of the kinds is thus presented not as an addition to the theory of forms but as a condition of any discourse whatever.

A second line of consideration appears where Plato takes up comparative terms. Comparatives such as the hotter and the colder, he writes, are to be ranked in the class of the infinite. A thing is hotter only by comparison with something colder, and colder only by comparison with something hotter, so that neither term admits of measure or definition when taken by itself. Terms of this kind have the appearance of quantities, though what they report seems rather to be the outcome of an act of comparing; the measurement of magnitude proper is treated under the idea of Quantity. In the Charmides, Socrates raises a further difficulty about relations of things to themselves, questioning whether sight can see itself or knowledge be knowledge of knowledge. Whether such reflexive relations are admissible remains a question for the later tradition.

The argument of the Sophist also bears on the problem of negation. If each form were simply itself and nothing else, no form could be predicated of another, and the discourse of philosophy would fall silent. By showing that Difference pervades every form, Plato makes negative statement intelligible: to say that Motion is not Rest is not to invoke sheer non-being but to invoke otherness. Non-being, so rehabilitated, becomes a legitimate object of thought, and the weaving together of forms which Plato identifies with dialectic acquires an ontological ground. It follows that knowledge of any single form requires knowing how it stands to others, so that what is known is a structure rather than an isolated item. The relation of sameness and otherness is considered further under the idea of Same and Other.

The communion of forms set the terms of much later dispute about relation. Aristotle takes up the analysis of correlative terms and assigns relation a place among the categories, where it is counted the least substantial of them. The Neoplatonists move in the opposite direction, treating the mutual dependence of the intelligibles as a doctrine of procession and return. Plotinus, in questioning whether right and left or double and half have any actuality apart from our conception of their juxtaposition, is addressing a question which the Sophist had already made unavoidable: whether the order among things belongs to the things themselves or to the mind that compares them.

Aristotle takes the Platonic observation that the kinds commune with one another and gives it a categorical treatment. In the Categories, relation is listed among the ten categories of being, alongside substance, quantity, quality, and the rest. Relatives are those things which are said to be what they are of other things, or which in some other way involve a reference to something else. The double is double of a half, the master master of a slave, knowledge knowledge of the knowable. In each instance the term cannot be understood or defined without reference to its correlative, and since the correlative in turn draws its meaning from the first, each member of the pair borrows from the other. This reciprocity, rather than any independent nature, is what marks the category off from the others.

The doctrine of correlatives leads Aristotle to two further considerations. The first concerns the naming of relatives. Where reciprocity of correlation does not appear to hold, he suggests that the fault may lie with our use of words rather than with the things. The correlative of rudder cannot be boat, since there are boats which have no rudders, and it would be more accurate to coin some word such as ruddered; so too the correlative of slave is not man taken in any sense whatever, but man understood as master. The second concerns coexistence. Things designated by a pair of reciprocally relative terms must, he holds, exist together: no man is called a master unless another exists who can be called his slave. The apparent exception of knowledge and the knowable, since the knowable seems able to exist before anyone knows it, may again be a matter of improper naming, for knowledge and the known do come to be simultaneously.

Aristotle also holds relation to be the least substantial of the accidents. A sign that the relative is least of all a substance and a real thing, he writes, is that it alone has no proper generation, destruction, or movement. In respect of quantity there is increase and diminution, in respect of quality alteration, in respect of place locomotion; but a thing may become now greater and now less without itself changing at all, if that with which it is compared has changed in quantity. Relations, on this account, presuppose the substances they relate and add nothing to their being. Whether this subordination can be maintained is the question the later tradition returns to, most sharply where the relations of equality and inequality are considered under the idea of Quantity, and where cause and effect are considered under the idea of Cause.

The Aristotelian analysis furnished the framework within which the question of relation was argued for a long time afterward. Aquinas adopts its apparatus and extends it to the doctrine of the Trinity, where relation is required to bear a weight the Categories had not assigned it. Hobbes and Locke press the other side, treating relations as products of comparison performed by the mind. Modern logicians raise a different objection: Russell holds that a logic recognizing only the ascription of a predicate to a subject is unable to admit the reality of relations, and must reduce them to properties of the terms apparently related. Whether the relational logic thus proposed is more general than the subject-predicate logic traditionally called Aristotelian, or whether the two belong to different enterprises altogether, is discussed under the ideas of Logic and Judgment.

Aquinas begins from the Aristotelian category and first settles the question whether relations are anything at all. Some, he observes, have said that relation is not a reality but only an idea, and this he takes to be plainly false from the very fact that things themselves have a mutual order and relation. Not every relation is real, however. Those which result in the things understood from the operation of the intellect alone are logical relations only, inasmuch as reason observes them as existing between two things understood. The relation of a thing to itself is of this sort, since reason, by apprehending one thing twice, regards it as two; so also are the relations of genus and species, which follow upon an act of reason. Real relations, by contrast, are those which have a foundation in both extremes, as with great and small or double and half, where there is quantity in either term.

Between these two classes Aquinas admits an intermediate case, in which a relation is a reality in one extreme and only an idea in the other. This happens whenever the two extremes are not of one order. Since God stands outside the whole order of creation, and creatures are ordered to Him and not conversely, creatures are really related to God, whereas in God there is no real relation to creatures but a relation only in idea. The doctrine preserves the divine simplicity while allowing that the world genuinely depends on its maker. Whether a relation can be real at one end and logical at the other has been questioned by later writers, and the wider issue of divine transcendence and immanence is treated under the idea of God.

The most demanding use to which Aquinas puts the category is the doctrine of the Trinity. Orthodoxy requires that Father, Son, and Holy Spirit be really distinct from one another and yet identical with the one divine essence, and any distinction drawn from something absolute would divide the Godhead. The persons are therefore distinguished by their relations of origin alone: paternity, filiation, spiration, and procession. Relation in God, Aquinas writes, is not as an accident in a subject but is the divine essence itself, and so it is subsistent. He considers two principles of difference among the divine persons, origin and relation, and judges it better to say that they are distinguished by relations; for when a relation is an accident it presupposes the distinction of subjects, whereas when it is subsistent it does not presuppose but brings about distinction. Descartes, denying that any real distinction in respect of the divine essence can be discerned between them, likewise leaves open a distinction in respect of their relation to one another.

It would seem to follow that, except in God, relations are not subsistent. The matter and form which constitute a physical thing are united rather than related, and though they are really distinct principles, their distinction does not make them relations or place them in relation to one another. What Aquinas thus leaves standing is an asymmetry: in the divine case relation carries the whole weight of personal distinction, while in creatures it remains an accident of substances already constituted. Leibniz rejects the framework but not the question, and Hegel presses the point in the opposite direction, asking whether anything at all can be what it is apart from its relation to another. The types of order which relation makes possible, in nature, in the soul, and in the state, are considered under the ideas of Nature, Soul, and State.

Hobbes departs from the Aristotelian and scholastic account by denying that relations have any standing outside the mind. In De Corpore and in the opening chapters of Leviathan he sets out a nominalist theory of language and thought in which all reasoning is a kind of computation, the adding and subtracting of names. To say that one thing is greater than another, or the cause of another, is on this view not to report a link obtaining between bodies but to describe an act of comparison performed by someone who thinks. Bodies exist and their motions exist; the relations predicated of them belong to discourse rather than to nature. What Aristotle had treated as a category of being Hobbes treats as an artifact of naming, and the scholastic disputes over real and logical relations accordingly lose their subject matter.

The position follows from the materialism. If whatever exists is body in motion, there is no room in nature for a third thing standing between two bodies and joining them. Two bodies may collide, and the collision is a real event involving real motions; but cause and effect are names assigned to the bodies before and after, not threads running invisibly between them. So too father and son name two bodies standing in a sequence of generation, while paternity is the way that sequence is ordered in thought. Hobbes does not propose to dispense with relative terms, which he takes to be indispensable to reasoning of any kind. He insists only that their signification is to be found in the operations of the mind and in the settled use of words, not in a structure discovered among things.

Since names are the instruments of reckoning, much depends for Hobbes on their constancy, and here he finds relative terms particularly unreliable. Names of things that please or displease us vary with the affections of the speaker, so that one man calls wisdom what another calls fear, and one cruelty what another calls justice. Such terms are relative in a further sense: what they signify depends on the standpoint from which the comparison is made. This is the source of Hobbes's insistence on definitions at the outset of any inquiry, and it connects his theory of relation with his account of civil order, where the sovereign's determination supplies a common measure that private judgment cannot. The contrast between absolute and relative modes of consideration, in respect of truth and of goodness alike, is treated under the ideas of Truth and Good and Evil.

Hobbes's reduction of relation to computation was not widely accepted, but it altered what defenders of real relations were obliged to argue. After him the reality of relations could not be assumed as evident; it had to be established against a stated alternative. Locke retains the view that relations arise from the mind's comparing while allowing them foundations in the things compared, and Hume carries the analysis further, resolving causation itself into constant conjunction and the habits of the imagination. The line of argument running from Hobbes through Locke to Hume may be described as a sustained inquiry into how much of what we call relation belongs to the structure of thought rather than to the structure of the world.

Locke gives relation four chapters of the Essay and treats it as one of the three sorts of complex idea, the others being modes and substances. Relation consists, he says, in the consideration and comparing of one idea with another. The ideas compared may be simple or complex, but the relation lies between them rather than in them: it is not contained in a simple idea, nor in the compounded ideas of modes and substances, which are combinations and not comparisons. Any idea whatever may occasion the mind to bring two things together, so that any of our ideas may be the foundation of relation; but there must always be, as Locke puts it, two ideas or things, either really separate in themselves or considered as distinct, and then some ground or occasion for their comparison. Relations, in this sense, are the workmanship of the understanding.

The analysis has consequences for the idea of substance. The complex idea of a substance is for Locke a collection of simple ideas of sensible qualities which we find united in the thing called horse or stone, together with the supposition of some common subject supporting them, though of that support we have no clear or distinct idea. Those simple ideas are compounded, not related; relation is therefore excluded from the interior constitution of substances. Locke goes further and makes relations extrinsic to the natures of the things related. Ideas of relation, he observes, may be the same in men who have far different ideas of the things compared, and relations are not contained in the real existence of things but are something extraneous and superinduced. Berkeley and Hume follow him on this point, the one holding that relations are distinct from the ideas or things related, the other that events are conjoined but never connected.

Locke is nevertheless attentive to how relative terms function in speech. Concubine, he remarks, is no less a relative name than wife; but in languages where such words have no correlative term, men are not so apt to take them for relatives, wanting that evident mark of relation which correlatives supply, since these seem to explain one another and to be unable to exist apart. He distinguishes proportional relations of greater, less, and equal, natural relations such as father and brother, instituted or voluntary relations such as general and citizen, and moral relations of the virtuous and the criminal. In the chapters on identity and diversity he argues that personal identity is itself a relation, holding between a present self and a past self through continuity of consciousness, so that what a person is depends on a relational fact rather than on the persistence of a substance. That question is treated more fully under the idea of Same and Other.

Locke's account occupies a middle position between the scholastic doctrine of real relations and the reduction of relation to naming. He keeps the view that comparison is an act of the mind while allowing that the comparison answers to something in the things, and his division of the kinds of relation gives later writers a map of the ground. Hume takes up that division and reduces it to seven philosophical relations, then presses the analysis toward a conclusion Locke does not draw, that causation has no discoverable foundation in objects at all. Leibniz, replying to Locke in the New Essays, objects from the other side that the mind's comparing cannot make relational truths true, and that their reality must come from the supreme reason.

Leibniz approaches the question of relation from a metaphysics which leaves little room for real relations. The monads, which are the true substances, have no parts and no windows through which anything could enter or depart. Each contains within itself from the first a complete series of perceptions mirroring the whole universe from its own point of view, and none acts upon or receives anything from another. If that is so, the connections we observe among things, whether of causality, resemblance, or place, cannot be additional realities interposed between substances. Leibniz calls them ideal. They arise when an intellect compares the states of one monad with those of another, and they add nothing to the being of what is already there. The category which Aristotle counted the least substantial of the accidents is here denied any standing among things at all.

This does not make relations arbitrary or dispensable. Every truth concerning a substance is for Leibniz grounded in the predicates contained in its complete concept. If Paris loves Helen, there is something in the concept of Paris which grounds his being a lover of Helen, and something in the concept of Helen which grounds her being beloved; the relation supervenes upon these intrinsic facts. God, in choosing this world, established a harmony among all monads such that their inner states correspond as if they acted on one another. The appearance of relation is thus well founded, and Leibniz says of relations and orderings that though they are in some measure beings of reason, they have their foundations in things, their reality coming, like that of the eternal truths, from the supreme reason. Against Locke he insists that the mind's act of comparing discovers relational truths without making them.

The doctrine bears on the order of nature as well as on the analysis of substance. Space and time, on Leibniz's account, are not containers but orders, the one of coexistences and the other of successions, and they are therefore relative rather than absolute; the dispute with Newton on this head is treated under the ideas of Space and Time. The same tendency appears in his treatment of the hierarchy of created things, where each monad differs from every other in the degree and distinctness of its perceptions, and where the continuity of the scale is itself a relational fact about the whole rather than a property of any member. Whether an order of this kind can be established among substances that do not touch is the difficulty his critics press.

The ideality of relations left later metaphysics with a question it could not set aside. If what is ultimately real consists of self-contained substances, then relation is always secondary, something the intellect adds to a world of interiors. Kant retains the view that relations do not belong to things as they are in themselves, but he transfers them from the divine understanding to the human, making them conditions under which any experience of an ordered world is possible. Hegel takes the opposite course, denying that the terms are prior to the relations at all. The larger issue, whether the universe is a whole of internally related parts or a set of externally related wholes, recurs wherever the order of nature is discussed, and is considered under the ideas of Nature and World.

Hume takes up Locke's division of the kinds of relation and reduces it to an enumeration. Seven philosophical relations are distinguished in the Treatise, these being the ways in which the mind may compare ideas: resemblance, identity, relations of time and place, proportion in quantity or number, degrees in any quality, contrariety, and causation. Four of them can be known by inspecting the ideas compared, since they depend on nothing beyond those ideas. Causation is unlike the rest in carrying us past what is given, for it alone allows us to infer the existence of something not presently perceived. On this account causation becomes the support of all reasoning about matters of fact, and for that reason the relation which most requires examination.

Alongside the philosophical relations Hume sets the natural relations, the principles by which one idea introduces another in the imagination. Nature, he writes, has established connections among particular ideas, so that no sooner does one idea occur to our thoughts than it introduces its correlative. These principles of connection are three: resemblance, contiguity in time or place, and cause or effect. Experience, so conceived, is a series of events joined by association, and it would be what it is whether or not there were enduring things or substances beneath the succession. Relations of one sort or another, rather than substances and their attributes, thus become the constituents both of nature as we know it and of knowledge itself. How far the notion of substance can be dispensed with is treated under that idea.

The examination of causation yields a result which bears on the whole question of relation. In any particular instance Hume finds only that the cause is contiguous to the effect, that it is prior in time, and that like causes have been constantly conjoined with like effects in past experience. No necessary connection is perceived. All events, he says, seem entirely loose and separate; one event follows another, but we never observe any tie between them, and they seem conjoined but never connected. The idea of necessary connection is traced not to the objects but to the mind's habit of passing from the impression of one to the idea of the other after repeated experience. Causation considered as a philosophical relation is one thing, and causation considered as a natural relation, a felt transition of the imagination, is another. The analysis of cause is carried further under that idea.

Hume's account of causation obliged those who came after him to declare themselves on whether relations are found or made. Since the relation on which all our reasoning about existence depends is traced to habit rather than to anything in the objects, a realism about relations cannot be assumed without argument. Hume does not deny that causal reasoning is unavoidable; he holds that its necessity is of the mind rather than of things. Kant's reply, that the categories of relation are conditions of experience supplied a priori by the understanding, was framed to answer this argument, though it grants the Humean premise that we do not find such connections lying ready in nature.

Kant classifies judgments in a fourfold way, according to their quantity, quality, relation, and modality. Under the head of relation he distinguishes the categorical, the hypothetical, and the disjunctive, corresponding to the relation of the predicate to the subject, of the cause to its effect, and of subdivided knowledge and the collected members of the subdivision to each other. These, he says, are all the relations of thought in judgments. Borrowing the term from Aristotle, he then calls the pure concepts of the understanding categories and constructs a table of categories running parallel to the table of judgments, on the ground that the same function which gives unity to representations in a judgment gives unity likewise to the synthesis of representations in an intuition. Relation forms one of the four groups, comprising inherence and subsistence, causality and dependence, and community or reciprocity between the active and the passive.

The contrast with Aristotle's table is instructive. Where for Aristotle substance is the first of the categories and the others signify the accidents of substance, relation having the least reality among them, for Kant relation is one of four coordinate headings, and substance appears within it. What is transcendental is not substance but the relation of substance and accident. The shift is of a piece with a wider tendency in modern thought, evident in the algebra and the theory of functions and series as well as in physics, where, as Cassirer observes, the conceptual revolution consists in displacing substance by function and the interaction of substances by functional relationships and systems of order. Hume's resolution of experience into events connected by resemblance, contiguity, and causation had already pointed in the same direction.

The three Analogies of Experience state what the relational categories accomplish. The first holds that in all change of appearances substance is permanent, since without a persisting substrate change could not be distinguished from replacement. The second holds that every event presupposes something upon which it follows according to a rule, which is Kant's answer to Hume, grounding necessity in the conditions of temporal order rather than in custom. The third holds that substances coexisting in space stand in thoroughgoing reciprocal action. Kant agrees with Leibniz that we cannot know things as they are in themselves, and with Hume that we never perceive a necessary connection among objects; but he concludes that the relational structure of experience belongs neither to things in themselves nor to psychological habit, being rather the set of rules any understanding must employ to have experience at all.

The transcendental treatment of relation concedes to the empiricists that relations are not simply given among objects, while denying that they are therefore merely private. Hegel takes the concession and presses the question which Kant had declined to raise: if relation is constitutive of experience, why should it not be constitutive of what is? The passage from transcendental to absolute idealism turns in good part on whether the relational categories can be released from their restriction to possible experience. The status of the categories themselves, and the question whether the transcendental ones are rightly so called, are treated under the ideas of Judgment and Idea.

Hegel makes relation the governing category of the doctrine of essence. Essence, on his account, is not a self-sufficient ground lying behind appearances but is reflection, and reflection is relational in its own structure, being the movement by which something determines itself only in distinguishing itself from, and referring itself to, what it is not. Identity is accordingly not bare self-sameness; the statement that A is A already invokes the distinction of A from what is not A. Each determination of essence, whether identity and difference, ground and grounded, or inner and outer, proceeds by pairs of correlatives which cannot be understood apart from one another. What Aristotle had noted of relative terms, that each draws its meaning from the other, Hegel extends to the determinations of thought as such.

Relation proper is treated under three headings: whole and parts, force and its expression, inner and outer. Each exhibits the same pattern. The whole is nothing apart from its parts and the parts nothing apart from the whole; force is nothing apart from its expression and the expression nothing apart from the force; the inner is nothing apart from its outward manifestation. In each case what at first presents itself as two independent terms is found to be one self-differentiating movement, the sides being constituted by their mutual reference rather than given separately and afterward joined. The relation of part and whole, and of one part to another in an organic whole, has commonly been taken as the chief instance of internal relationship, and something like it appears in Spinoza's account of the one substance in and through which everything else both is and is conceived.

On this footing the received order of substance and relation is reversed. From Aristotle to Leibniz the assumption had been that substances come first and relations follow upon them; Hegel holds that substance, rightly understood, is already the relation of its attributes, powers, and expressions, a self-determining activity rather than a simple unrelated thing. The claim is not that individual things do not exist but that nothing can be what it is in isolation from everything else. Doctrines of this kind carry consequences well beyond logic. As the standing of each thing in nature depends on whether the universe is conceived as a whole of internally related parts or as a set of externally related wholes, so the standing of the individual in society depends on whether the state is conceived as an organic whole or as a political order formed by free association, a question treated under the idea of State.

The doctrine of internal relations has been resisted by every position which takes substance, the atom, or the self-sufficient individual as its starting point. William James, distinguishing the block universe from the concatenated universe, directs his criticism at Hegel and Bradley precisely on this head, holding that things may be joined without being constituted by their joining; the issue as it bears on contingency is discussed under the idea of Chance. Later writers who insist on the priority of relations over the terms related, whether in the analysis of capital or in the philosophies of process, stand on the other side of the same question, which the Sophist had raised at the beginning in asking how the greatest kinds commune with one another.