Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology, epistemology, and character of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a central aspect of early analytic philosophy. The subject focuses on a number of basic issues, including whether time and space exist in- dependently of the mind, whether they exist independently of one an- other, what accounts for time's apparently unidirectional flow, whether times other than the present moment exist, and questions about the na- ture of identity.

The earliest recorded Western philosophy of time was expounded by the ancient Egyptian thinker Ptahhotep, who said, "Do not lessen the time of following desire, for the wasting of time is an abomination to the spirit." The Vedas, the earliest texts on Indian philosophy and Hindu philosophy, dating back to the late 2nd millennium BC, describe ancient Hindu cosmology, in which the universe goes through repeated cycles of creation, destruction, and rebirth, with each cycle lasting 4,320,000 years. Ancient Greek philosophers, including Parmenides and Heracli- tus, wrote essays on the nature of time. Plato, in the Timaeus, identified time with the period of motion of the heavenly bodies, and space as that in which things come to be. Aristotle, in Book IV of his Physics, defined time as the number of changes with respect to before and after, and the place of an object as the innermost motionless boundary of that which surrounds it.

In Book 11 of St. Augustine's Confessions, he ruminates on the na- ture of time, asking, "What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not." He goes on to com- ment on the difficulty of thinking about time, pointing out the inaccura- cy of common speech: "For but few things are there of which we speak properly; of most things we speak improperly, still the things intended are understood." But Augustine presented the first philosophical argu- ment for the reality of Creation in the context of his discussion of time, saying that knowledge of time depends on the knowledge of the move- ment of things, and therefore time cannot be where there are no crea- tures to measure its passing. In contrast to ancient Greek philosophers who believed that the universe had an infinite past with no beginning, medieval philosophers and theologians developed the concept of the universe having a finite past with a beginning, now known as Temporal finitism.

A traditional realist position in ontology is that time and space have existence apart from the human mind. Idealists, by contrast, deny or doubt the existence of objects independent of the mind. Some anti- realists, whose ontological position is that objects outside the mind do exist, nevertheless doubt the independent existence of time and space.

In 1781, Immanuel Kant published the Critique of Pure Reason, one of the most influential works in the history of the philosophy of space and time. He describes time as an a priori notion that, together with oth- er a priori notions such as space, allows us to comprehend sense experi- ence. Kant denies that either space or time are substance, entities in themselves, or learned by experience; he holds, rather, that both are el- ements of a systematic framework we use to structure our experience. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantitatively compare the interval between events. Although space and time are held to be transcendentally ideal in this sense, they are also empirically real – that is, not mere illu- sions.

Idealist writers, such as J. M. E. McTaggart in The Unreality of Time, have argued that time is an illusion.The writers discussed here are for the most part realists in this regard; for instance, Gottfried Leib- niz held that his monads existed, at least independently of the mind of the observer. The great debate between defining notions of space and time as real objects themselves (absolute), or mere orderings upon actu-

al objects, began between physicists Isaac Newton and Gottfried Leibniz in the papers of the Leibniz – Clarke correspondence.

Arguing against the absolutist position, Leibniz offers a number of thought experiments with the purpose of showing that there is contradic- tion in assuming the existence of facts such as absolute location and ve- locity. These arguments trade heavily on two principles central to his philosophy: the principle of sufficient reason and the identity of indis- cernibles. The principle of sufficient reason holds that for every fact, there is a reason that is sufficient to explain what and why it is the way it is and not otherwise. The identity of indiscernibles states that if there is no way of telling two entities apart, then they are one and the same thing.

The example Leibniz uses involves two proposed universes situated in absolute space. The only discernible difference between them is that the latter is positioned five feet to the left of the first. The example is only possible if such a thing as absolute space exists. Such a situation, however, is not possible, according to Leibniz, for if it were, a universe's position in absolute space would have no sufficient reason, as it might very well have been anywhere else. Therefore, it contradicts the princi- ple of sufficient reason, and there could exist two distinct universes that were in all ways indiscernible, thus contradicting the identity of indis- cernibles.

Standing out in Clarke's response to Leibniz's arguments is the bucket argument: Water in a bucket, hung from a rope and set to spin, will start with a flat surface. As the water begins to spin in the bucket, the surface of the water will become concave. If the bucket is stopped, the water will continue to spin, and while the spin continues, the surface will remain concave. The concave surface is apparently not the result of the interaction of the bucket and the water, since the surface is flat when the bucket first starts to spin, it becomes concave as the wa- ter starts to spin, and it remains concave as the bucket stops.

In this response, Clarke argues for the necessity of the existence of absolute space to account for phenomena like rotation and acceleration that cannot be accounted for on a purely relationalist account. Clarke argues that since the curvature of the water occurs in the rotating bucket as well as in the stationary bucket containing spinning water, it can only be explained by stating that the water is rotating in relation to the pres- ence of some third thing – absolute space.

Leibniz describes a space that exists only as a relation between ob- jects, and which has no existence apart from the existence of those ob- jects. Motion exists only as a relation between those objects. Newtonian space provided the absolute frame of reference within which objects can have motion. In Newton's system, the frame of reference exists inde- pendently of the objects contained within it. These objects can be de- scribed as moving in relation to space itself. For many centuries, the evidence of a concave water surface held authority.

Another important figure in this debate is 19th-century physi- cist Ernst Mach. While he did not deny the existence of phenomena like that seen in the bucket argument, he still denied the absolutist conclu- sion by offering a different answer as to what the bucket was rotating in relation to: the fixed stars. Mach suggested that thought experiments like the bucket argument are problematic. If we were to imagine a uni- verse that only contains a bucket, on Newton's account, this bucket could be set to spin relative to absolute space, and the water it contained would form the characteristic concave surface. But in the absence of anything else in the universe, it would be difficult to confirm that the bucket was indeed spinning. It seems equally possible that the surface of the water in the bucket would remain flat.

Mach argued that, in effect, the water experiment in an otherwise empty universe would remain flat. But if another object were introduced into this universe, perhaps a distant star, there would now be something relative to which the bucket could be seen as rotating. The water inside the bucket could possibly have a slight curve. To account for the curve that we observe, an increase in the number of objects in the universe also increases the curvature in the water. Mach argued that the momen- tum of an object, whether angular or linear, exists as a result of the sum of the effects of other objects in the universe.

Albert Einstein proposed that the laws of physics should be based on the principle of relativity. This principle holds that the rules of physics must be the same for all observers, regardless of the frame of reference that is used, and that light propagates at the same speed in all reference frames. This theory was motivated by Maxwell's equations, which show that electromagnetic waves propagate in a vacuum at the speed of light. However, Maxwell's equations give no indication of what this speed is relative to. Prior to Einstein, it was thought that this speed was relative to a fixed medium, called the luminiferous ether. In contrast, the theory

of special relativity postulates that light propagates at the speed of light in all inertial frames, and examines the implications of this postulate.

All attempts to measure any speed relative to this ether failed, which can be seen as a confirmation of Einstein's postulate that light propa- gates at the same speed in all reference frames. Special relativity is a formalization of the principle of relativity that does not contain a privi- leged inertial frame of reference, such as the luminiferous ether or abso- lute space, from which Einstein inferred that no such frame exists.

Einstein generalized relativity to frames of reference that were non- inertial. He achieved this by positing the Equivalence Principle, which states that the force felt by an observer in a given gravitational field and that felt by an observer in an accelerating frame of reference are indis- tinguishable. This led to the conclusion that the mass of an object warps the geometry of the space-time surrounding it, as described in Einstein's field equations.

In classical physics, an inertial reference frame is one in which an object that experiences no forces does not accelerate. In general relativi- ty, an inertial frame of reference is one that is following a geodesic of space-time. An object that moves against a geodesic experiences a force. An object in free fall does not experience a force, because it is following a geodesic. An object standing on the earth, however, will experience a force, as it is being held against the geodesic by the surface of the plan- et. In light of this, the bucket of water rotating in empty space will expe- rience a force because it rotates with respect to the geodesic. The water will become concave, not because it is rotating with respect to the dis- tant stars, but because it is rotating with respect to the geodesic.

Einstein partially advocates Mach's principle in that distant stars ex- plain inertia because they provide the gravitational field against which acceleration and inertia occur. But contrary to Leibniz's account, this warped space-time is as integral a part of an object as are its other defin- ing characteristics, such as volume and mass. If one holds, contrary to idealist beliefs, that objects exist independently of the mind, it seems that relativistics commits them to also hold that space and temporality have exactly the same type of independent existence.

The position of conventionalism states that there is no fact of the matter as to the geometry of space and time, but that it is decided by convention. The first proponent of such a view, Henri Poincaré, reacting to the creation of the new non-Euclidean geometry, argued that which geometry applied to a space was decided by convention, since different

geometries will describe a set of objects equally well, based on consid- erations from his sphere-world. This view was developed and updated to include considerations from relativistic physics by Hans Reichenbach. Reichenbach's conventionalism, applying to space and time, focuses around the idea of coordinative definition.

Coordinative definition has two major features. The first has to do with coordinating units of length with certain physical objects. This is motivated by the fact that we can never directly apprehend length. In- stead we must choose some physical object, say the Standard Metre at the Bureau International des Poids et Mesures, or the wavelength of cadmium to stand in as our unit of length. The second feature deals with separated objects. Although we can, presumably, directly test the equali- ty of length of two measuring rods when they are next to one another, we can not find out as much for two rods distant from one another. Even supposing that two rods, whenever brought near to one another are seen to be equal in length, we are not justified in stating that they are always equal in length. This impossibility undermines our ability to decide the equality of length of two distant objects. Sameness of length, to the con- trary, must be set by definition.

Such a use of coordinative definition is in effect, on Reichenbach's conventionalism, in the General Theory of Relativity where light is as- sumed, i.e. not discovered, to mark out equal distances in equal times. After this setting of coordinative definition, however, the geometry of spacetime is set. As in the absolutism/relationalism debate, contempo- rary philosophy is still in disagreement as to the correctness of the con- ventionalist doctrine. While conventionalism still holds many propo- nents, cutting criticisms concerning the coherence of Reichenbach's doc- trine of coordinative definition have led many to see the conventionalist view as untenable.