Space

Plato treats space not as a topic of geometry but as a cosmological necessity. In the Timaeus, the account of the production of the universe distinguishes three principles: the eternal Forms, the visible copies patterned after them, and a third kind that is neither intelligible as the Forms are nor sensible as their copies are. This third kind is the receptacle, the medium in which becoming takes place. It has no character of its own. It receives all impressions without retaining any form, as gold may be endlessly reshaped yet remain gold. Plato calls it the nurse of all becoming, and he admits that it is grasped only by a kind of bastard or spurious reasoning, neither by intellect nor by sense.

The receptacle is not empty space in the later atomist sense. It is not a void between solid bodies, nor a coordinate grid independent of matter. It is closer to a formless substratum, a featureless this that underlies every sensible thing. The elemental bodies (earth, water, air, fire) are geometrical structures, triangles assembled into regular solids, that take their places within the receptacle. Before the Demiurge imposes order, the receptacle shakes and sifts these elements chaotically, like grain in a winnowing basket. Space, on this account, precedes cosmos; it is the condition for any physical arrangement at all. Whether the receptacle is more properly called space or prime matter is a question the Timaeus leaves open, and one that later readers, including Augustine and Aquinas, will take up in connection with the idea of Matter.

The difficulty is deliberate. Plato marks a limit of rational discourse: the receptacle cannot be defined as a Form is defined, yet it cannot be dismissed as mere nothing. It occupies an ontological middle ground that resists clean classification. That ambiguity will lead Aristotle to replace the shadowy third kind with a more precise concept of place, and will keep open the question whether space is an independent container or only the formless condition of becoming.

Plato's receptacle sets much of the later agenda. Thinkers who ask whether space is substance, property, or relation, or whether it is identical with matter devoid of form, are in one way or another responding to the third kind he introduced and left unfinished.

Aristotle replaces Plato's shadowy receptacle with a more rigorous concept: place (topos). He begins Book IV of the Physics by listing the reasons men believe in place (things can be displaced; the elements have natural places they seek) and the puzzles that make place hard to define (whether it is a body, a boundary, a form, or something else). After eliminating alternatives, he settles on a definition: the place of a thing is the innermost motionless boundary of the body that contains it. Place is therefore a relation between a body and what surrounds it. It is not itself a substance, nor an independent container in which bodies move as actors on a stage.

This definition rules out empty space. If place is always the boundary of a containing body, then there can be no place where nothing is contained. Aristotle devotes several chapters to refuting the void. He argues that motion in a void would be impossible, or at least unintelligible, because natural motion requires a direction (up, down) that only makes sense relative to a surrounding plenum. In a true void, no body could be heavier or lighter, faster or slower, for there would be nothing to differentiate one region from another. The universe is finite, spherical, and full; beyond the outermost sphere there is not empty space but nothing at all. The world as a whole has no place, since there is no containing body outside it by which it could be bounded.

The consequences extend beyond physics. A cosmos without void is a cosmos of continuous contact, in which every motion is transmitted through the plenum. It also implies a natural center and periphery, a hierarchy of place that later writers will connect with the hierarchy of being, and that theological writers will relate to the spiritual significance of position treated under the idea of Angel and under Heaven and Earth. Aristotle's view of the world as a material plenum stands in direct opposition to the atomists, for whom the whole of matter is discontinuous and the void indispensable.

Aristotle's denial of the void becomes the orthodox position of much medieval natural philosophy. When early modern thinkers begin to accept empty space, they must first meet his arguments, and the debate over absolute and relative space in Newton and Leibniz still turns in part on whether place can be understood without a containing body.

Lucretius, transmitting the atomism of Epicurus, opens De Rerum Natura with a challenge to the Aristotelian plenum. The universe, he maintains, consists of exactly two things: solid bodies and empty space. There is nothing else. Every compound phenomenon, from fire to thought, reduces to atoms moving through void. The argument is presented as a deduction rather than a mere hypothesis: if there were no void, nothing could move, because there would be no room for any body to go; things do move; therefore the void exists. Wherever space lies empty, body is not there; wherever body has its station, there is no empty void.

The argument extends to the invisibly small. Bodies appear solid, yet they break, wear down, and absorb liquid. Water seeps through rock; food nourishes the body; sound passes through walls. None of this is possible, on Lucretius's view, unless the apparently continuous surfaces of things are riddled with tiny gaps. The void penetrates matter at every scale. Against the claim that nature abhors a vacuum, he replies that nature requires one. Without void, the atoms could never have separated from one another, and no differentiation of matter would exist. The indivisibility of the simple bodies consists in their absolute solidity and lack of void; the divisibility of composite bodies derives from their being constituted by both atoms and void. The issue of the void is thus inseparable from the idea of Matter and from the problem of the continuum.

Lucretius also argues that space is infinite. If the universe had an edge, one could stand at the boundary and throw a spear; either it passes through, proving there is space beyond, or something stops it, proving there is body beyond. In either case the boundary is not final. The whole universe, he concludes, is bounded in no direction. The argument recurs, in various forms, in Locke's thought experiment of a man stretching his hand beyond the extremity of corporeal beings, and in the modern controversy over absolute space.

Lucretius ensures that the atomist alternative survives into the Renaissance, where it supplies Gassendi, Boyle, and Newton with materials for a physics that accepts empty intervals between bodies and rejects the necessity of a universal plenum.

Aquinas inherits Aristotle's definition of place and refines it within a theological framework. In his Commentary on the Physics, he defends the core thesis: place is the boundary of the containing body, not a self-subsisting container. He agrees that the void is impossible and that the universe is a finite plenum. Christian doctrine, however, introduces questions Aristotle never faced. Where is God? Where are the angels? What, if anything, is outside the created world? These questions belong as much to the idea of Angel and of God as to the physics of place.

For angels, Aquinas distinguishes between corporeal and spiritual modes of being in place. A body occupies place by being contained within the boundaries of what surrounds it. An angel, having no body, is not contained at all. Instead, an angel is said to be in a place by the application of its power to that place: it acts there, and so it is there. Aquinas is extending the concept of place beyond Aristotle's physical definition. It allows him to say that an angel can be in one place, or move from place to place, without admitting that incorporeal substances are spatially extended. At a given time an angel is not everywhere, nor in several places, but in only one place; and, according to the manner of its presence, there can be only one angel in one place at a time.

God presents a different case. God is not in place at all, because nothing contains him. Yet he is present to every place by his essence, power, and presence. The universe as a whole has no place outside itself. There is no empty space beyond the outermost heaven, because beyond presupposes spatial extension, and extension is a property of created body. In commenting on Augustine's reading of formless matter in Genesis, Aquinas also connects Plato's receptacle with prime matter, noting that formlessness is why the earth is said to be void and empty, and why Plato says matter is place. Space, place, and matter thus remain closely linked in the scholastic synthesis.

Aquinas shows that the Aristotelian framework can absorb theological demands, but only by stretching the concept of place past its original physical meaning. Later writers who separate space from body, or who treat infinite space as somehow related to divine omnipresence, will work in a different register from this careful extension of topos.

Descartes breaks with Aristotle's definition of place but preserves his conclusion that there is no void. The central move is to identify the essence of body with extension. A body is nothing other than a region of space with certain modes (shape, size, motion). Strip away color, hardness, weight, and every other sensory quality, and what remains is pure extension in three dimensions. But if body just is extension, then extension without body is a contradiction. So-called empty space would be extension that is not extended, which is incoherent. In the Principles of Philosophy, Descartes states that the nature of matter or body, in its universal aspect, consists solely in being a substance extended in length, breadth, and depth.

This identification transforms the ontology of space. For Aristotle, place was a boundary; for Descartes, space is the substance itself. The entire physical world is one continuous extended substance, differentiated only by the motions of its parts. Where we think we see a void (a sealed container with the air pumped out), there is in fact subtle matter, an imperceptible fluid that fills every apparent gap. Descartes builds his physics on this foundation: vortices of subtle matter carry the planets; light is pressure transmitted through the plenum; there is no action at a distance because there is no distance empty of matter. He does distinguish space as the extension of body from place as the position one body occupies relative to another, and he objects to those who, like Aristotle, mean by place the surrounding surface of a body. Local motion, he argues, is a change in relative position, not a change in the surrounding surface.

The claim leaves certain difficulties. If space and body are identical, then the concept of how much body is in a given space becomes hard to formulate, and density becomes difficult to explain. The whole picture depends on the assumption that extension is the only essential property of matter, an assumption that Newton and Locke will reject when they treat space as distinct from body and admit the possibility of vacuum. The problem of action through empty space, and of the ether as a medium, will later reopen the question whether filled space is required for physical influence.

Descartes gives seventeenth-century physics a thesis that identifies extension with body without remainder. Newton's absolute space will be defined partly in opposition to that identity, and the void that Descartes excludes will reenter natural philosophy as a working assumption.

Newton opens the Principia with a distinction Descartes could not make: between absolute and relative space. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of absolute space, which our senses determine by its position with respect to bodies. The distinction is not idle metaphysics. Newton needs absolute space to define absolute motion, which his laws of mechanics require. The rotating bucket experiment is offered as evidence: water in a spinning bucket climbs the sides even after the bucket and water rotate together, so the centrifugal effect cannot be explained by motion relative to the bucket alone. It must, on this view, be motion relative to absolute space itself.

For Descartes, space was identical with matter. Newton separates them completely. Space is the stage; matter is what moves upon it. Space can exist empty, and Newton has no objection to the void. The success of his gravitational theory is often taken to depend on action at a distance across empty space, the very thing Cartesian physics declared impossible. Yet Newton himself, in a letter to Bentley later cited by Faraday, recoils from the idea that gravity should be innate in matter so that one body may act on another through a vacuum without any mediating agency. In the Optics and related writings he entertains an ethereal medium more subtle than air, and he also suggests that absolute space may be related to the sensorium of God, the medium through which God perceives and acts upon creation. Space thus takes on, in his more speculative moments, something of a divine character: infinite, eternal, and uncreated. The relation of space to divine omnipresence connects this discussion with the idea of God and with questions of quantity and infinity treated under Infinity.

Difficulties remain. Newton posits an entity that is neither substance nor property in the ordinary sense, neither body nor mind, yet real and infinite. It cannot be perceived directly; only its effects (absolute acceleration, centrifugal forces) are said to reveal it. Critics will ask whether such an entity is truly intelligible or whether it functions mainly as a postulate required by the laws of motion. Place, for Newton, is a part of space which a body takes up, and is absolute or relative according to the space; he rejects Aristotle's identification of place with the surrounding surface of a body.

Newton's absolute space becomes the default assumption of classical physics for a long period. Leibniz mounts the first sustained philosophical challenge, and Kant later proposes a resolution that treats space as a form of intuition rather than as either absolute container or mere relation among bodies.

Leibniz opposes Newton's absolute space in a correspondence with Samuel Clarke that remains one of the clearest debates in the metaphysics of space. His principal argument turns on the principle of sufficient reason. If absolute space existed, then God, in creating the world, would have had to choose where in that infinite, homogeneous container to place matter. But every point of absolute space is identical to every other. There could be no reason for God to place the universe here rather than three feet to the left. Since God does nothing without a reason, absolute space, Leibniz concludes, is impossible. The same principle, applied to time, yields a parallel argument against absolute time, so that the relational account of space is of a piece with his treatment of time and with the idea of Relation more generally.

The alternative is that space is nothing but the order of coexisting things. When we say two bodies are a certain distance apart, we are describing a relation between them, not a property of some underlying container. If every body in the universe were moved three feet to the left, nothing would change, because three feet to the left has no meaning apart from the relations among bodies. Space, on this view, is like a family tree: the tree describes relations among people; it is not a thing those people inhabit. Similarly, space is the structure of relations among substances, not a substance itself. Relative place and relative motion are intelligible; absolute place and absolute motion, as Newton defines them, are not.

Leibniz's deeper metaphysics reinforces the point. The Monadology teaches that ultimate reality consists of simple, unextended monads. Extension is phenomenal, a well-founded appearance that emerges from the pre-established harmony of monadic perceptions. Space, as extended, cannot be fundamental. It is an abstraction from the ways monads represent one another. The debate thus joins the problem of space to the problem of substance and of the continuum, and it anticipates later questions about whether spacetime is a substance or a structure of relations.

Leibniz's relational view does not prevail in the physics of his century, where absolute (or at least substantival) space proves more serviceable for mechanics. His arguments, however, remain a standing alternative, later taken up in various forms by Mach, Einstein, and those who treat spacetime as a structure rather than as an independent entity.

Locke approaches space not as a physicist constructing a system of the world but as an empiricist cataloguing the contents of the mind. In Book II of the Essay Concerning Human Understanding, he argues that space is a simple idea, received from both sight and touch. We see distance between objects; we feel the extension of our own bodies. From these basic impressions the mind forms the idea of space. It is not innate; it is not a priori in Kant's later sense. It enters the mind through experience, like every other simple idea. The question how we know space is thus treated under the idea of Experience and of Idea as much as under the physics of place.

Locke's empiricism leads to a conclusion that sits awkwardly with Descartes. We can conceive space without body. Close your eyes and imagine the universe annihilated; you can still think of the empty expanse that remains. This thought experiment suggests that space and body are not identical. Those who assert the impossibility of space existing without matter must, Locke writes, make body infinite; and those who dispute for or against a vacuum thereby confess that they have distinct ideas of vacuum and plenum. Descartes was wrong, on this showing, to reduce body to extension, because we can coherently separate the two in thought. Space, for Locke, is something real and distinct from the bodies that fill it, though he declines to say whether it is a substance, a mode, or something else. He frankly admits that the question exceeds the reach of his method.

Locke also distinguishes space from place and expansion. Place is the relation of a thing to other visible fixed points. Expansion is the idea of distance in any direction. The mind, by repeating and compounding the simple idea of space, arrives at the idea of immensity, of space without limit. Whether infinite space actually exists is a question he approaches cautiously, noting that our inability to conceive a boundary does not by itself prove there is none. Yet he asks whether, if God placed a man at the extremity of corporeal beings, that man could not stretch his hand beyond his body into space without body, an argument that recalls Lucretius's spear and that supports the infinity of empty space if finite body is granted.

Locke contributes not a full system of space but a discipline of inquiry. He insists that metaphysical questions about space be grounded in identifiable ideas derived from experience. Kant will absorb this demand even as he reverses Locke's conclusion that space is empirical rather than a pure form of outer intuition.

Kant treats the Newton-Leibniz dispute as a false dilemma and offers a third option. Space is neither an absolute container independent of bodies (Newton) nor a system of relations among things in themselves (Leibniz). It is the form of outer intuition, the structure the human mind imposes on all sensible experience. We do not discover space in the world as a property of things as they are in themselves; we bring it to the world as a condition of perceiving anything at all. Space is not an empirical concept derived from outer experiences, but a necessary representation a priori that forms the foundation of all external intuitions.

The Transcendental Aesthetic offers several connected arguments. First, space is not abstracted from experience; rather, experience of outer objects presupposes spatial order. One cannot perceive an object without already perceiving it as somewhere. Second, one can think space without objects, but one cannot think objects of outer sense without space. Third, space is a single, infinite given; particular spaces are limitations within the one space, not parts assembled into a whole. Fourth, the synthetic a priori truths of geometry cannot be grounded in mere concepts or in contingent experience alone; they are grounded in the form of intuition itself. The foundations of geometry thus belong to the idea of Mathematics as much as to the metaphysics of space. Kant also formulates a cosmological antinomy in which the thesis that the world is limited with regard to space and the antithesis that it is infinite both seem susceptible of proof, and both violate the conditions of empirical concepts.

On this account, space applies to everything we can experience, but it tells us nothing about things as they are independently of our experience. The spatial world is the phenomenal world, the world as it appears to minds constituted as ours are. What things are in themselves, apart from our forms of intuition, remains unknowable. Newton was right, on Kant's view, that space is more than a relation among bodies, but wrong that it is an absolute reality. Leibniz was right that space is ideal, but wrong to make it merely conceptual rather than intuitive. Space is nothing other than the form of all appearances of outer sense, the subjective condition of sensibility under which alone outer intuition is possible for us.

Kant's resolution makes space both universal and subjective: it governs all possible outer experience yet belongs to the mind as a form of sensibility, not to things in themselves. Subsequent philosophies of space must either accept this framework or explain why the Transcendental Aesthetic fails.

Hegel begins the Philosophy of Nature with space because nature itself begins with the most abstract and empty determination of externality. Space, for Hegel, is not a form of intuition (Kant), nor an absolute container (Newton), nor a set of relations among substances (Leibniz). It is the Idea in its moment of self-externality: pure being-outside-itself, with no qualitative differentiation. Space is the first category of nature precisely because it is the most impoverished. It has extension but no internal difference, continuity but no individuality. It is, in dialectical terms, the immediate and abstract form of nature's existence. The discussion belongs as much to the idea of Nature and of Being as to the narrower physical problem of place.

The dialectical movement carries space into time. Space, as pure externality, is indifferent to its own parts; every point is identical to every other. But this very indifference is a kind of negativity, a restless non-differentiation that demands resolution. Space passes over into time, which introduces succession and negation. Then space and time together are sublated into matter and motion, where real physical process begins. Space is not destroyed in this transition; it is preserved as a moment within the fuller determination of material nature. The truth of space, Hegel says, is time, just as the truth of time is the concrete unity of both in motion and matter. Questions of quantity, continuity, and the relation of mathematical to physical space reappear here as stages in a logical development rather than as freestanding problems of natural philosophy alone.

Hegel criticizes both Newton and Kant. Newton treats space as something given, independent of the concept; Hegel insists that space must be understood as a moment of the logical development of nature. Kant makes space subjective, a form of human intuition; Hegel argues that this understates nature. Space belongs to the Idea's own self-unfolding, not only to our way of perceiving. Nature is spatial, but its spatiality is the most elementary and abstract thing about it. The spiritual significance of place and position, which earlier writers treat by analogy or theology, is for Hegel absorbed into the systematic order of nature's determinations.

Hegel closes the classical debate by insisting that space is neither subjective nor objective in the older senses but a logical stage in the self-development of reality. Whether this resolution clarifies or obscures the question depends on whether one accepts the dialectical method that produces it.