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Given that space and time constitute the ‘arenas’ in which all that occurs takes place, it is hardly a surprise that the concepts by which we try to grasp the nature of space and time are central to every aspect of our conceptual scheme. Nor is it surprising that questions concerning both the nature of space and time, and concerning our epistemic access to that nature, have been central philosophical issues from the very inception of philosophy. The crucial role played by space and time in the core of our physical theories of the world, and the astonishing revisions in our understanding of the nature of space and time forced upon us by the series of ‘scientific revolutions’ from the seventeenth century through to the present, have complicated the philosophical discussions of the nature of space and time and of our knowledge of it in fascinating and fruitful ways.

One series of problems concerns the alleged radical difference in nature between time and space. Typical of one side of the debate are the arguments of bergson to the effect that the scientific view of space and time as similar ‘manifolds' of being left out the ‘dynamic’ or ‘transient’ or ‘flowing’ aspect of temporality. Another similar argument was that of McTaggart who argued that tensed discourse was essential to describe the temporality of being. McTaggart claimed that facts related in tensed discourse could not be identified with the facts contained in merely locating events as before or after one another in time, as objects are located spatially relative to one another. Of course McTaggartthen went on to argue that tensed discourse was also inconsistent, and to infer from this the ‘unreality’ of time, a conclusion that would not be drawn by Bergson or other exponents of the ‘transience’ of temporality. Related positions are held by those who, like A.N. Prior, maintain that temporal language has an irreducibly propositionally modal character. All of these views have as an essential component the claim that the past and future should be thought of as not being a true realm of being, with true existence reserved to that which presently exists.

Opposed to this view is the one that would take existence to be, in general, a timeless notion. Events, past, present and future, then would bear temporal relations to one another in close analogy with the spatial relations things bear to one another. To the claim that tensed assertions cannot be translated into those of a tenseless language, the most usual current reply is to argue that tensed discourse has an irreducible indexical aspect (see indexicals). To say of an event that it is past is to say that it is earlier than now. ‘Now’ is taken to be a token reflexive referring to the moment of its utterance. Just as in other contexts, then, the indexicality of the one language is taken not to indicate some novel realm of facts expressed by the language, despite the non-translatability of the indexical-tensed discourse into tenseless, non-indexical, language.

None the less the advocate of a radical disanalogy of time with space can still claim that issues of indexicality do not fully exhaust the claims made that past and future have no real existence. Naturally such a view has difficulties in a relativistic context where what is present in time is relative to a frame of motion, but relativistic considerations do not unequivocally refute the view that past and future have no real existence, for ‘real existence’ can itself be relativized to a frame of motion.

Many issues in the epistemology of space and time fall under general epistemological concerns. It remains a deep philosophical problem how to characterize what we take to be the spatiality and temporality of immediate experience and the relations of such ‘perceptual’ space and time to what we take, in both common sense and in physics, to be the space and time of the physical world. For the purposes of the description of immediate visual experience, for example, we seem to need some sort of notion of ‘visual space’ and the arrangement in it of percepts of particular objects. But how we ought correctly to characterize such a ‘subjective’ space of perception, and how relate it to the space of material things, remains far from clear.

Throughout the history of philosophy the status of our knowledge of the general truths about space, that is of geometry, has played a crucial role. How could there be a theory descriptive of the world whose truths could be known by pure logical deduction from first principles whose truth was ‘self evident’ ? For plato and others geometry served as the ideal to which all science ought to aspire. For kant geometry provided the clearest example of a discipline whose propositions were both synthetic and a priori, and, hence, a means to demonstrate the existence of theoretical knowledge of the world grounded in transcendental idealism. The discovery that many geometries are possible for space that are incompatible with Euclideanmetric geometry, and the application of such geometries to the world in contemporary physics has led, naturally, to scepticism with regard to the view that a particular geometry can indeed be known to hold of the world independently of observation and experiment.

The initial response to the plethora of ‘possible’ geometries for the world was to take the structure of space as something to be inferred inductively from observation and experiment. Jules Henri Poincaré (1854–1912) argued, however, that there would always be an infinite variety of geometries compatible with any specified set of a totality of observational facts. This led to the so called doctrine of ‘conventionalism’ with regard to geometry. While a variety of claims about the indeterminacy of geometry have been called conventionalistic, the dominant strain of conventionalism is some version or other of a Poincare-type thesis. This thesis about geometry is, in turn, an instance of the general claim that theories referring to unobservables are radically ‘underdetermined’ by their sets of observational consequences. In some versions the thesis is one of epistemic scepticism. In other, more radical, stances, such as that of the reductionist, claims are espoused that all geometries with the same observational consequences amount to geometries that are in a deep sense ‘equivalent’ to one another, i. e. that they all say the same thing about the world.

A variety of important questions regarding the epistemology, semantics and metaphysics (ontology) of theories surface very quickly when one explores the question of the alleged conventionality of geometry. In these debates what is observable is usually taken to be local relations of coincidence among material things, non-local features and feature of ‘space itself’ being taken to be in the realm of the only inferrable. Much of the current debate focuses on concrete issues brought to the fore when one considers alternatives to the standard special-and general-relativistic space-time pictures of the world that, allegedly, ‘save the same phenomena’ as the standard theories.

A fundamental metaphysical issue in the field of space and time is one anticipated by the Ancients, but brought to very vigorous life in the debate between leibniz and newton. While Leibniz maintained that space was, essentially, nothing but the family of spatial relationships among material objects (at least in the non-monadological ‘exoteric’ portion of his metaphysics), Newton took space to be something over and above the spatial relations holding among material things. Leibniz is generally taken to be espousing a ‘relationist’ and Newton a ‘substantivalist’ doctrine concerning space (although Newton actually maintained that space was ‘an attribute of the Deity’).

The debate between the relationist and the substantivalist has both a ‘pure’ philosophical aspect and another side in which questions of physics play an essential role. Typical of the purely philosophical side of the debate are such matters as Leibniz's use of the principle of sufficient reason (see rationalism) and of the doctrine of the identity of indiscernibles to prove that substantivalism was a metaphysically unacceptable theory. The core of these arguments is that substantivalism, by allowing for matter to be, as a whole, differently situated in ‘space itself’ generates alleged differences between possible worlds that are non-differences and alleged facts about the actual world that could receive no explanation.

Another set of philosophical debates hinges around the need for the relationist to do justice to the notion of space empty of matter, either empty regions of the actual world or even a possibly totally empty spatial world. To allow for the legitimacy of at least some degree of talk about ‘empty space’, the relationist will frequently resort to talk about possible but non-actual spatial relations among bits of matter, or even possible relations among possible but non-actual bits of matter. The move here is similar to the phenomenalist's invocation of ‘permanent possibilities of sensation’ to deal with matter existing unperceived (see phenomenalism). The substantivalist is likely to object at this point, maintaining that such possibilities must be ‘grounded’ in an actuality, the nature of space itself, just as ordinary dispositions (such as solubility) are grounded in an underlying actuality (such as the molecular constitution of the matter) (see disposition).

The metaphysical debate between substantivalist and relationist takes on a special character when arguments, originating with Newton, are introduced that try to argue for substantival space as a necessary component in an explanatory structure needed to account for the observable phenomena explained by physics. Newton emphasized the need for a notion of absolute acceleration, acceleration accompanied by the so-called inertial forces. He argued that such acceleration could not be characterized as acceleration relative to some material object, but must be considered acceleration relative to space itself. In any relative acceleration of two objects, one only may experience linertial forces, even though both are accelerated relative to one another. Even in empty space, Newton argued, a test object would still be able to detect absolute acceleration by experiencing inertial forces, although, the universe being otherwise empty, such acceleration could not be relative to another material thing. Optical phenomena provide another such Newtonian argument, since the distinction between inertial motion and non-inertial motion shows up in various optical experiments one can perform as well (such as non-null results for round-trip velocity of light experiments in a non-inertial laboratory).

An important proposal of Mach's was that absolute acceleration might be taken as acceleration relative to ‘the fixed stars’, that is the average ‘smeared out’ matter of the material universe. The phenomena explained by the Newtonian by reference to acceleration with respect to space itself would then be explained by the acceleration of the test object with respect to the bulk matter of the universe.

Einstein's Special Theory of Relativity offers no solace to the relationist, whether of the Machian or some other sort. It is a ‘Newtonian’ -type theory with a definite distinction between objects in absolutely uniform and objects in absolutely accelerated motion. Einstein did have hopes, however, that his theory of gravitation as curved space-time would be a theory in accordance with Machian precepts. It appears, however, that General Relativity is not such a theory. Even in model universes devoid of other matter test objects can distinguish uniform from accelerated motion. Models of the universe can be constructed in which the average matter of the world is ‘in absolute rotation’. Other ‘anti-relationist’ and ‘anti-Machian’ consequences of the theory can be derived as well.

It is very far from clear how to view the substantivalist/relationist debate in the light of contemporary physics. On the one hand modern theories make the very distinction between space (or, rather, space-time) itself and matter dissolve away. Space-time dynamically interacts with matter, has (in certain senses) mass-energy, and so on. Indeed, there exist ‘super-substantivalist’ accounts in which matter is explained a ‘piece' of curved space-time, although they are, at present, merely speculations and not established science. On the other hand various foundational problems in the General Theory of Relativity suggest resolutions of a more relationist, and, indeed, conventionalist sort. For example, interpreted as a naive substantivalist theory the theory appears to be, very surprisingly, radically in deterministic (Einstein's ‘hole’ argument). Much remains to be done to disentangle all of the threads tied up in the substantivalist/relationist debate and to explore the appropriate ‘metaphysical’ background most suitable for contemporary physics.

Of the many revolutions in our conception of space and time arising out of the modern revolution in physics, none is more dramatic than the replacement of space and time as traditionally understood by the unified notion of a space-time. By far the most elegant and coherent framework in which to formalize the laws of nature as empirically discovered (see law of nature)is that, suggested by Hermann Minkowski (1864–1909) and based on the work of Poincaré and Einstein, which takes as the basic elements event locations and their ‘interval’ or space-time separations. Spatial and temporal separations between events are then derivative from this fundamental space-time relationship. In the standard relativistic frameworks spatial and temporal separations are, in fact, relative to chosen frames of reference in the form of motions of an ‘observer’, whereas the space-time intervals are now the sole invariant, non-relativized, relations among events.

General Relativity goes beyond this space-time picture, necessary for the standard formulation of the Special Theory of Relativity, to introduce even more novel elements. In particular the space-time of the Special Theory of Relativity was, like pre-relativistic space and time, an arena in which events occur and, in some ways, a determiner of how they must occur. In the even newer theory the space-time becomes Itself a dynamic element effected by, as well as effecting, the material contents in it.

It is important to note that subsequent to the discovery of the space-time notions needed for the formulation of special and general relativity, it was realized that space-time concepts could also provide deep insights into the structure of pre-relativistic physics. Neo-Newtonian space-time, for example, provides a conceptual framework that allows for the definition of absolute acceleration, needed in the Newtonian theory, but in which absolute velocity, an embarrassment for Newtonian theory because of its lack of observational effects, is undefined. Similarly, a ‘curved’ version of neo-Newtonian space-time provides a framework for the Newtonian theory of gravity that allows one to avoid some well-known paradoxes that infect the theory of gravity as a force in flat space as gravity was understood in the traditional Newtonian formulation.

Much attention has been directed to alleged interconnections between the spatial and temporal features of the world and other features. There are, for example, several attempts to try and show that some spatial or temporal feature of the world ‘reduce’ to some other feature (see reduction, reductionism). Prominent among these attempts are so-called ‘causal’ theories that allege that some or all spatial or temporal (or space-time) relations can be ‘reduced to’ or ‘defined by’ the causal relations among events. Suggestions of this sort can be found as early as Leibniz. The doctrines only received extensive investigation, however, in the light of the exploration of relativistic space-time theories.

Such claims of reducibility of the spatio-temporal to the causal face many prima facie philosophical problems. There is the problem of understanding the space and time of the immediately perceived in the context of such a causal theory. There are also objections based on claims to the effect that if any reductive relation takes place it must be of the causal to the spatio-temporal and not the other way around. Humean doctrines of causation, for example, presuppose spatial and temporal relations among events in their analyses of the causal relation. (See hume.)

Other problems arise out of the intricate relation between spatio-temporal features and causal features of the world in various space-times of physics. Leibniz had suggested that simultaneity could be understood as non-causal-connectibility, all non-simultaneous events being causally connectible to one another. In Special Relativity this will not do as limitations on the velocity of propagation of causal signals leaves many events not simultaneous with one another all not causally connectible to a given event. Such facts lie behind some of the claims of ‘mere conventionality’ for simultaneity of events at a distance from one another as that notion is used in Special Relativity.

In turns out, however, that as a matter of fact all the metric relations of a special relativistic space-time are provably coextensive with relations among the events defined using causal notions alone. These ‘causal definitions’ of metric relations, however, break down in the context of General Relativity where space-times that are metrically quite distinct can have isomorphic causal structures (see isomorphism). Many subtle philosophical questions need to be explored when any result of contemporary mathematical physics is used to try to either defend or attack some claim of ‘reducibility’ of a spatio-temporal to a causal feature.

In the general relativistic context it is sometimes alleged that at least the topological structure of space-time can be ‘defined’ by the causal structure among events. Once again the claim becomes quite problematic when the details of the physical theories are examined. In space-time that are causally ‘pathological’ many relations of coextensivity between topological and causal relations among the space-time events break down. Here ‘causally pathological’ means that the space-time contains ‘closed causal lines’ or lines that are causal and ‘almost closed’. Such sequences of events that proceed from event to later event but that ‘loop back’ to the origin event have, naturally, many consequences for other philosophical doctrines about the nature of time, causation and determinism as well. Even in these pathological space-times, however, topological structures are ‘fixed’ by richer ‘causal’ notions than that of causal connectibility. The richer notion needed, though, is something like that of a path in space-time being a continuous causal path, suggesting that at least some primitive space-time topological notion (that of continuity at least along paths traversable by a causal signal) is needed to fix the full topology, and casting doubt on the claim of such a ‘definition’ of the topological structure being in any way a reduction of that structure to a purely causal structure. Many issues remain, however, in becoming clear what the claim of a causal reduction comes down to and whether any such claim can be established in the light of both philosophical arguments and results from physics.

A crucial problem for the philosopher of space and time is to understand the manifest ‘asymmetry’ between the past and the future. We remember and have records of the past, but not of the future. We take causal influence to proceed from earlier to later events. We think of the past as ‘fixed’ and unchangeable, but of the future as ‘open’ and indeterminate in nature. What grounds these asymmetries? (See fatalism.)

One important claim is that all of them can be accounted for by the remarkable asymmetry of physical processes in time that are summed up in the so-called increase of entropy of systems. Summarized in thermodynamics by the various Second Laws of Thermodynamics and viewed from the point of view of statistical mechanics as a ubiquitous ‘randomizing’ of the energy of the micro components of macroscopic systems, the entropic increase of systems over time is, if not the only, the dominant physical process that shows a radical asymmetric behaviour of systems toward the past and toward the future. The physical explanation for this asymmetry itself is one that remains a matter of great controversy. All known attempts to ‘explain’ why systems show such an asymmetry in their behaviour in time, including those invoking cosmological asymmetries and temporarily isolated systems ‘branched’ off from the cosmos in general, are fraught with fundamental difficulties.

But, given this asymmetry of processes, can it fully account for the ‘directions of time’ as revealed in the features noted above? Here, again, the question is open. Proponents of the view point to the success of an account of another alleged asymmetry that is shown to be ‘reducible’ to a specific physical process. We might think in an Aristotelian vein of space as having intrinsic ‘upward’ and intrinsic ‘downward’ directions, the asymmetry revealed in many processes and even knowable to us without inference (see aristotle). All would now admit, however, that ‘down’ can simply be taken to be the local direction of the gravitational force. Similarly, the entropic theorist may argue, ‘future’ can be taken simply as that direction of time in which local processes are showing an increase in their entropy parallel, in time, to one another.

Opponents of the view will argue, on the other hand, that the mere fact that systems do increase their entropy, at least as a matter of overwhelming statistical generality, in the future time directions is not sufficient to establish the claim that the ‘ground’ of the past/future asymmetry lies in entropic considerations. What would be required of the entropic theorist would be a convincing demonstration that all our intuitive asymmetries between past and future, including our ‘immediate knowledge' of which temporal direction is which, can be accounted for by reference to the facts of entropic asymmetry alone. Despite very ingenious efforts to establish this claim, however, the question remains very much a matter of dispute.