One and Many

The Eleatic doctrine that being is one, indivisible, and unchanging, the many things of experience being dismissed as illusion, comes to Plato as an inheritance rather than a discovery. In the dialogue named for Parmenides, the old master is made to examine his own thesis. If the One is strictly one, it may be asked whether it can be said to be at all; for to be is to partake of being, and so to be two, one and being. The hypothesis is carried through in eight directions, and no simple answer survives the exercise. Unity, if it is anything, appears obliged to contain multiplicity, and multiplicity, if it is anything, appears obliged to be unified in some manner.

In the Sophist and the Philebus the difficulty is converted into a method. Plato weaves the great kinds, Being, Sameness, Difference, Motion, and Rest, so that each form is one in itself while communing with the others; the manner of that communion is treated more fully under the idea of Same and Other. In the Philebus the procedure is called a gift of the gods: whatever is said to be consists of a one and a many and has in its nature a conjunction of limit with the unlimited, and the philosopher is charged with counting the definite many which lie between the bare one and the indefinite many. Those who pass at once from unity to infinity are said by Socrates to practice disputation rather than dialectic.

The doctrine of forms is drawn into the same difficulty. A form must be one, justice itself or beauty itself, yet it is shared by many particulars, and the forms taken together compose a structured plurality in which the form of the one is one form among many. The Parmenides asks how a single form can be present in many things at once, whether as a whole or in part, and no resolution is offered there. The same pair of terms governs Plato's political and psychological inquiries. The city of the Republic is a multitude which is to be made one so far as possible, and the soul is a single thing having parts whose agreement constitutes justice, questions pursued under the ideas of Justice and Soul.

The question Plato leaves open is how one form can be present in many particulars without being divided among them. Aristotle holds that the difficulty arises from separating the forms from the things which have them, and that it loses its force once the several senses of unity are distinguished. Plotinus holds instead that no account of unity is adequate which does not place the One prior even to being. Both replies begin from questions the Parmenides declines to close.

Aristotle's reply to the Eleatics is a reply by distinction. Parmenides and Zeno erred, he says in the Physics, by taking "one" and "being" univocally, so that to argue with them is like refuting a position maintained for the sake of argument. Being is said in many ways, of substance, quality, quantity, and relation, and unity is said in as many ways. A thing may be one in number, one in species, one in genus, one by proportion, or one as a continuous quantity is one. When these distinctions are drawn the paradoxes lose their force, and the question which remains is what kind of unity belongs to what kind of thing. The method of separating the senses of a term is considered under the idea of Definition.

The answer is sought in substance. Every natural substance, this man or this horse or this oak, is one essentially, being a composite of matter and form whose unity is not added to it but constitutes what it is. A machine or a heap is one only accidentally, its unity imposed from without upon pieces which remain, each of them, substances in their own right. A living thing is one because its form organizes its matter into a single nature having a single activity, and it remains one only so long as its matter and form are not separated, just as it remains one quantitatively only so long as it is not divided. Being and unity, Aristotle writes in Metaphysics IV, are implied in one another as principle and cause are implied in one another. Whatever is, is one in the manner proper to its kind.

Since each substance possesses its own unity, the world cannot itself be a single substance. It is an aggregation of substances whose unity lies in the order and connection among them, and that order derives largely from the ways in which distinct substances act upon one another. Because causality on this account admits contingency and chance, a matter examined under the idea of Necessity and Contingency, the interdependence of substances does not lock them together into a solid block. In Book X the analysis is extended to opposition itself: all contraries, Aristotle holds, are reducible to being and non-being and to unity and plurality, rest belonging to unity and motion to plurality. Whether the same pair governs the unity of the city, a multitude made one for a common life, is raised in the Politics against Plato.

The pluralism of substances leaves a question which later writers press. If each substance is a unity in itself, it may be asked what unity belongs to the whole beyond the order of its parts. Plotinus answers that an adequate account of unity must ascend to a principle prior to all multiplicity. Aquinas retains the Aristotelian substance while making unity convertible with being, and finds that principle in the simple being of God. Leibniz, holding that only the simple is truly one, finds the composite substances of the Metaphysics insufficiently unified.

Plotinus carries the Platonic question a step further. If whatever is, is already one and many, then the ground of all things must be prior to that duality: sheer One, without parts, without otherness, without even the distinction of thinker and thought. The One is not a being among beings, nor is it Being itself, but the source above being; and it stands above intelligence as well, since knowing requires an object, and the relation of knower to known would fracture its simplicity. "What stands above Being stands above intellection," he writes, "it is no weakness in it not to know itself, since as pure unity it contains nothing which it needs to explore." He finds a warrant for the doctrine in Plato's Parmenides, where he distinguishes a primal One, a secondary one-many, and a third which is one-and-many.

The many proceed from the One by emanation rather than by making. The One, seeking nothing and lacking nothing, overflows; what overflows turns back toward its begetter, and in that turning becomes the Intellectual-Principle. This second hypostasis is a one-many, because in striving to grasp its prior as pure unity it goes forth amassing successive impressions, so that its object becomes multiple. From Intellect proceeds Soul, which is the idea and act of the Intellectual-Principle, taking its fullness by looking toward its source and generating its image by a downward movement into sense and the vegetal order. Each level is less one and more many than the level above it, and nothing, Plotinus says, is completely severed from its prior. How such dependence differs from causing and being caused is treated under the ideas of Cause and Nature.

Since everything except the One is a one-many, unity admits of degree, and the degree of a thing's unity measures its nearness to the source. Had a thing not attained such unity as is consistent with being made up of multiplicity, its existence could not be affirmed at all. The doctrine bears upon knowledge and upon conduct alike. Discursive reason, being itself a thing of multiplicity, cannot fully grasp what is simple, so that the ascent toward the One passes beyond argument into contemplation, a matter considered under the idea of Wisdom. Purification, by which the soul is drawn back from dispersion among many goods, is the practical side of the same ascent.

The hierarchy of unities constructed in the Enneads passes into Christian thought through Augustine, who takes over the ascent while identifying the One with the God of Scripture and putting creation in the place of emanation. Aquinas retains the graded simplicity, ranking bodies below angels and angels below God, while holding that the many are willed rather than overflowed. Writers in the mystical tradition of both East and West continue to describe the return in terms Plotinus supplied.

In Augustine the Neoplatonic hierarchy is restated as Christian doctrine, and is altered in the restatement. The One of Plotinus becomes the God of Scripture, simple, eternal, and self-sufficient, but no longer above being, since God is being itself: ego sum qui sum. And because God creates rather than overflows, the many of creation stands outside the divine substance. It is not a diminished emanation but a distinct order of things called out of nothing, related to its maker as an effect to its cause and not as an aspect to that of which it is an aspect. The difference between these two accounts of dependence is treated more fully under the ideas of God and World.

The doctrine of the Trinity requires a grammar of unity finer than the pagan philosophers had needed. Against the Arians, Augustine defends the confession expressed in the Nicene Creed, that Father, Son, and Spirit are not three substances but three persons of one substance. In On the Trinity he looks for likenesses within the soul, memory with understanding and will, or the lover with the beloved and the love between them, each a single mind having a real internal threefoldness. The unity affirmed is neither numerical sameness nor the unity of a collection, but one simple essence subsisting in a trinity of relations. Since the divine simplicity excludes composition of every sort, the persons are distinguished by relation alone.

Creation being a many by God's will, every creature bears in its being, its unity, and its goodness a trace of the one who made it, and Augustine reads such vestiges throughout nature. Evil, on this account, is nothing positive. It is privation, a defect of the unity and order which a thing ought to have, so that corruption consists in a tendency toward dispersion, a position examined under the idea of Good and Evil. The same analysis governs his account of the soul and of the city. The will is scattered among many goods until it is gathered into the love of one, and the earthly city is a multitude held together by love of self while the heavenly city is a multitude made one by love of God.

Augustine's formulations supply the terms in which Western theology afterward states the question. Creation is distinct from God and yet wholly dependent upon Him; the Trinity is a unity which does not suppress distinction; the health of the soul consists in the gathering of its scattered many into one love. Aquinas takes over each of these positions and gives unity a technical place among the properties convertible with being. The Reformers dispute much else while leaving the Augustinian account of unity largely as they found it.

Aquinas brings the Aristotelian and the Augustinian analyses under a single architecture. Unity, he argues in the eleventh question of the first part of the Summa, adds no reality to being; it adds only the negation of division, so that whatever is, is one insofar as it is undivided in itself and divided from everything else. Ens et unum convertuntur. What is asserted here is neither the numerical one of the arithmetician alone nor the One which Plotinus set above being, but a property belonging to being as such and belonging to each thing in whatever manner that thing exists. That being is said analogically rather than univocally is presupposed throughout, and is examined under the idea of Being.

From this principle a hierarchy of unities follows. Material things are composed of matter and form, of substance and accident, and of essence and existence, so that their unity, though real, is not absolute. Angels are simpler, being forms without matter, yet even in them essence and existence are not the same. God alone is simple without qualification: in Him essence is existence, and there is no composition of any kind. His unity is therefore not that of a first member in a series but that of the sole being whose nature is to be. Whether and how such a being can be named by a finite intellect is a question taken up under the idea of God.

Because God is simple He cannot be many substances, and because He creates rather than emanates, the world is a genuine many, a plurality of distinct substances each having its own received act of being. Against Avicenna and others who derive the many from the one by a necessary series of intermediaries, Aquinas holds in question 47 that the distinction and multitude of things proceeds from the intention of the first agent. The divine goodness, which no single creature could represent, is represented by the whole order of creatures taken together. Plurality is thus ordered to unity rather than opposed to it, and the unity of the universe consists in the relation of its parts to one another and to their first cause.

The scholastic account rests on two propositions which later philosophy separates. The world is many because God willed a likeness of His goodness which no one creature could bear, and it is one because every creature is held in being by the simple act of the first cause. Spinoza retains the definition of substance and denies that there can be more than one substance. Leibniz retains the plurality and denies that anything composite is a substance at all. Both proceed from distinctions which the schoolmen had drawn.

Spinoza begins from the definition of substance which the schools had transmitted, that which exists in itself and is conceived through itself, and draws from it a consequence the schools had not drawn. Two substances sharing an attribute would be distinguishable only by their modifications and not in themselves; therefore no two substances can share an attribute. What exists in and through itself is self-caused, necessary, and infinite; and beside an infinite being nothing of the same nature can exist. There is, and there can be, only one substance, which he calls God, or Nature. Those who suppose the finite many to be substances have not, he says, observed a proper order of philosophic study, beginning as they do with the objects of sense, which have least reality, and coming last to the divine nature, which ought to be studied first.

Whatever is not the one substance is a mode, a modification of substance under one of its infinite attributes, of which the human mind knows two, thought and extension. This man, this stone, this motion, this idea: none of these exists in itself. God is the immanent and not the transitive cause of things, so that the world is not an effect standing outside its cause but is in God as an aspect is in that of which it is an aspect. The distinction between natura naturans and natura naturata, discussed under the idea of Nature, permits Spinoza to separate the infinite from the finite without dividing God from the world. The one substance, being indivisible, is not a whole whose parts might exist apart from it.

Consequences follow for questions far removed from the definition of substance. Since the one substance acts from the necessity of its own nature, nothing is contingent and nothing could have been otherwise, a position examined under the idea of Necessity and Contingency. Freedom is accordingly not a power of having acted otherwise but an adequate understanding of one's place within the whole, and the passions lose their hold as their causes are understood. The highest activity of the mind is the intellectual love of God, which is the knowledge of finite things under the aspect of eternity. That the primacy of the one thus reaches into ethics shows the doctrine to be more than a matter of emphasis in metaphysics.

Later writers tend to define their positions by their answer to Spinoza. Leibniz accepts that only what is truly one is truly a being, and concludes for an infinity of simple substances rather than a single infinite one. Hegel objects that in such a unity determination is lost, and requires that substance become subject. William James, describing what he calls the block universe, has Hegel's Absolute more often in view than Spinoza's God, though the picture he draws belongs to both.

Leibniz proceeds from a premise Spinoza would have granted and arrives at the contrary conclusion. What is not truly one being, he writes to Arnauld, is not truly a being either; but where Spinoza infers that only the infinite can be truly one, Leibniz infers that only the simple can. Whatever has parts is an aggregate, and an aggregate is one by the mind's regard rather than in itself. The real things of the world must therefore be indivisible unities without extension and without parts: monads, each a simple substance and each a perceiving point of view upon the whole. The Aristotelian composite of matter and form is set aside on the same ground, since matter, being divisible without end, can supply no unity of its own.

The universe on this account is an infinite plurality of monads, differing in the distinctness of their perceptions, each mirroring the whole from its own situation and each unfolding by an internal law. They do not act upon one another, having, in the phrase of the Monadology, no windows; their perceptions nevertheless agree, because God in creating them established a harmony among their several series. The one and the many are reconciled neither by emanation nor by the reduction of the many to modes, but by a concert of independent unities. Bodies are aggregates of monads, phenomena well founded in them; space and time are orders of coexistence and succession rather than things, a doctrine contested by Newton's followers and examined under the ideas of Space and Time.

Because each monad unfolds its whole history from within, the question of freedom is shifted from the action of external causes to the completeness of the individual notion, and spontaneity is held to belong to simple substance as such. The plurality of monads enters also into Leibniz's account of creation. God considers infinitely many possible worlds, each a different collection of compossible substances, and chooses the one in which the greatest variety is joined to the greatest order. Variety on this view is a perfection rather than a defect, so that the many is not something which the one must overcome. Whether such a world admits any real action of one thing upon another is treated under the idea of Cause.

The Leibnizian pluralism turns on the claim that unity is the mark of substance and that only what is simple is one. Kant, trained in that school, denies that substances so conceived can be known at all, and transfers the unity of the manifold to the conditions of experience. Later doctrines which make reality consist of centers of experience rather than of extended bodies continue to draw upon the same argument, as does the dispute over whether wholes are anything more than their parts.

Hume applies the empirical principle to unity itself and reaches a conclusion which the rationalist systems cannot accommodate. Every perception of the mind is distinct from every other, and the mind, as he says, never perceives any real connection among distinct existences. What experience yields is a many: separate impressions and ideas, each complete in itself. Unity is nowhere given among them. Whatever binds them together is contributed by the mind through habit, custom, and the association of ideas, principles which Hume proposes for the study of human nature as attraction had been proposed for the study of bodies.

The self, accordingly, is not a substance but a bundle. Looking within, Hume finds no impression of a simple and continuing self, only a succession of perceptions; and since every idea must be derived from some impression, no idea of such a self can be had. The identity ascribed to a person through time is a fiction produced by resemblance among the perceptions and by the continuity of memory. Causation receives the same treatment, discussed further under the idea of Cause: no tie between cause and effect is ever observed, only constant conjunction and the expectation which follows upon it, so that what makes many events into one connected series is a determination of the mind rather than a bond among things.

The reasoning extends to bodies and to the world at large. The continued and distinct existence of objects is supposed rather than perceived, the imagination supplying continuity where the senses give interrupted appearances. Aristotle's individual substances, Spinoza's one substance, and Leibniz's monads alike claim more than the evidence allows, since each asserts a unity which no impression presents. Hume does not expect that we shall cease believing in selves, bodies, and causes; belief of that kind, he holds, is not produced by argument and cannot be destroyed by it. What philosophy can do is describe the manifold given in experience and the customary transitions the imagination makes among its parts, a task considered under the idea of Experience.

The problem of the one and the many is thus transferred from the constitution of things to the constitution of the mind. Kant accepts the transfer while denying that habit can account for the result, and puts the unity of apperception in the place Hume had given to association. Later empiricists return to the Humean manifold, though William James, among others, holds that relations are themselves given in experience rather than added to it by the knower.

Kant takes over Hume's problem and alters its terms. Sensibility, he agrees, yields only a manifold: a many of intuitions in space and time having no unity of its own. But a manifold could not be represented even as a manifold unless its members were held together in a single consciousness. The I think, he writes, must be able to accompany all my representations. The combination which makes many representations into one object is not found among the data given to sense, nor is it, as Hume supposed, produced by association; it is an act of the understanding, exercising a priori the functions Kant calls categories.

This unity of apperception is the ground of every other unity we think, and the categories, among them substance, causality, and community, are the rules by which the manifold is combined into a single connected order of nature. Without them experience would fall apart into a succession of impressions belonging to no one; with them the plurality of sense becomes the one nature which physics describes. Unity in this sense is neither discovered among things nor invented by custom, but is a condition of the possibility of objects of experience at all. What the mind contributes and what is given to it are distinguished further under the ideas of Experience and Knowledge.

The same doctrine limits what may be said of the unconditioned. Categories employed beyond possible experience yield no knowledge, and when reason attempts to think the absolute one, whether as the simple soul, or as a world finite or infinite in extent, or as a necessary being, it falls into the paralogisms and antinomies of the Dialectic. Monism and pluralism, taken as doctrines about things in themselves, are on this account equally incapable of proof and of refutation. Kant nevertheless allows the idea of a systematic unity of nature a regulative use: inquiry may proceed as though nature formed one ordered whole, without asserting that it does.

The unity of the world is thus made an achievement of mind rather than a property of being, and the question of the one and the many becomes a question about the conditions of thought. Fichte, Schelling, and Hegel refuse the restriction of knowledge to appearances and treat the unity of self-consciousness as the unity of what is. Those who accept the restriction find in the antinomies a reason for setting the ancient question aside as one which admits of no answer.

Hegel declines the Kantian restriction. What Kant called the unity of apperception is for him the self-articulation of being and thought together, and nothing stands behind the categories to be left unknown. In the Science of Logic the concept of unity is shown to generate plurality out of itself. Pure being passes into nothing, and both into becoming; determinate being becomes something; and the something, posited as self-identical and excluding what it is not, becomes the One. But the One, in excluding others, posits them, and so posits the many. Repulsion and attraction, plurality and unity, pass into one another as moments of a single movement.

The Spinozist absolute, on this account, is a unity in which determination disappears, since the finite modes are negated in it rather than preserved. Substance must become subject. The true one is not that which stands over against the many and excludes them, but that which differentiates itself internally and holds its differences within itself; and the infinite which merely excludes the finite is for Hegel a bad infinite, being limited by what it excludes. The whole is prior to its parts and the parts have their truth only within it, a doctrine of internal relations examined under the idea of Relation.

The same movement is traced in nature, in history, and in the life of spirit. Identity gives rise to difference, difference demands reconciliation, and what reconciles them contains more than either pole taken alone. The state, on this view, is neither an aggregate of individuals held together by contract nor a unity in which individuality is dissolved, but a whole in which particular interests are preserved while being subordinated, a position considered under the ideas of State and Liberty. What is negated at each stage is also retained and raised up, and the Absolute Idea is accordingly not a One above the world but the completed whole within which the many have their place.

The one and the many are thus presented as moments of a single self-developing whole rather than as rival first principles. British and American idealists of the following century take up the doctrine of internal relations which follows from this, holding that nothing is what it is apart from its place in the whole. William James contests that doctrine, arguing that the parts of reality may be externally related, and takes the Hegelian Absolute as the clearest instance of what he calls the block universe.

James puts the question first and states it as a quarrel of doctrines. The problem of being one or many he calls in Pragmatism the most central of philosophic problems, central because so pregnant, and he uses it as a test of temperament as much as of argument, aligning monism with rationalism and idealism in the column he heads tender-minded and pluralism with empiricism and materialism in the column he heads tough-minded. As his own account shows, terms of this sort tend to oversimplify. Whoever emphasizes the oneness of the world may also acknowledge its manyness, and whoever finds multiplicity the primary fact may still find unity in the order and connection of things.

The test he proposes is pragmatic. Rather than ask whether the world is one, James asks what difference it makes to say so, and answers that the world is one in many partial ways: spatially, causally, by kinds, by continuity of narrative, and through the systems of exchange and communication which link its parts. What he denies is that these partial unities amount to a single absolute unity in which everything is internally related to everything else. Experience taken as it comes presents things which are with one another rather than things absorbed into one another, and the connections it displays are of the sort he calls concatenated: a loosely knit universe, an each-form rather than an all-form.

The dispute, on his view, is not confined to metaphysics. A block universe leaves no place for novelty, for chance, for evils which might have been otherwise, or for effort which makes a difference to the outcome, and James counts the moral and religious consequences of a doctrine among the evidence bearing upon it, a manner of argument considered under the idea of Truth. Pluralism as he states it permits a finite God, a future not yet settled, and a world still in the making. He does not claim that the many is final, but only that unity, so far as the world has it, is achieved piecemeal and is nowhere complete.

James restates an ancient question in terms drawn from experience rather than from substance, and in doing so returns it to something like the form in which Plato had raised it, as a question of how things are one and many at once. The doctrine of external relations which he defends against the idealists passes into the analytic philosophy of the following generation. His image of the block universe, whatever its accuracy as a description of Spinoza or Hegel, remains the figure through which later writers state the case against monism.