. Some problems concern space or time individually, while others concern both. These latter have become more prominent recently.
How are space and matter related? Parmenides (see ELEATICS) thought that to say empty space exists would be to say that what is not exists. Aristotle and Descartes too, among others, rejected it. Modern physics blurs the issue by allowing matter and energy to be intertransformed in certain circumstances, and emphasizing fields of force. General relativity theory treats gravity as a property of space rather than of matter, and quantum mechanics complicates the distinction between space and matter.
Until about two centuries ago Euclidean geometry was thought to be unique, and so the geometry of space. It relied on the axiom of parallels, that through a given point not on a given straight line exactly one straight line could be drawn parallel to the given one. But then it was realized that not only was this independent of the other axioms, but consistent systems could be developed if it were replaced by an axiom saying either that more than one such line, or that none, could be drawn. These replacements yield geometries often called hyperbolic or Lobachevskian (N.I.Lobachevsky, 1793–1856) and elliptic or Riemannian (G.F.B.Riemann, 1826–66) respectively. In these systems space is regarded as curved, negatively in Lobachevskian and positively in Riemannian geometry, because it has in three dimensions properties analogous to those of the surfaces of a saddleback and sphere, respectively, in two dimensions. It now becomes an open question what kind of geometry applies to real space, and geometries can be developed for imaginary spaces, which need not be limited to three dimensions. Real space evidently has three, but is this logically necessary (cf. MODALITIES, ANALYTIC)? And what makes a dimension specifically spatial as against merely a parameter or independent variable for some measuring system? Spaces studied by mathematics are metrical if they allow of measurement and topological if they do not. Some transformations of spatial things affect shape and size, and so disturb measurements, but leave relations of betweenness undisturbed: if b was between a and c before the transformation, it remains so afterwards. Topology studies these transformations. The topological transformations of a rubber ball, for example, are those possible with stretching and squeezing but without tearing.
Logical space is a term used by Wittgenstein in his difficult discussion of logical possibility. A place in logical space is given by the sense of an atomic sentence (see LOGICAL ATOMISM), which then describes that place. A rough example: the question whether my cat is black constitutes a place in logical space. When I say that it is black, I describe that place as being of a certain sort. The logical relations between propositions and between the terms in them can then be treated as having some analogy with spatial relations. Later this ‘mapping’ of relations between concepts was often called logical geography. This use of ‘space’ is metaphorical but it suggests the question what makes the analogy an apt one (cf. the above question about dimensions).
The notion of empty space suggests that of time without change. This, however, has been more generally rejected (but see Shoemaker), presumably because there seems to be no analogue here of the effects of perspective. Would the progressive fading of memory serve as an analogue? But this is unreliable and seems to depend in fact, though not in principle, on changes.
Time, more than space, seemed not to be real or measurable because most, if not all of it so far as it consists of periods rather than moments, seems not to exist at any given moment, and what fails to exist now has seemed less real than what merely fails to exist here (Augustine).
A famous attack on the reality of time was made by McTaggart, who distinguished two series of temporal positions. The A series contains notions like past, present, future, which apply to different events at different times. The B series contains notions like earlier than, simultaneous with, after, which permanently link whatever events they do link. He then argues that the B series by itself, without the A series, cannot account for change, and so for time, while the A series involves either a contradiction or a vicious regress. Some try to make the B series basic by defining ‘present’ as ‘simultaneous with this utterance’ (cf. discussion by Broad in Smart, pp. 334–8).
It is hard to describe the ‘passing of time’, for whether time itself flows or we move in time, how fast do these things happen? They seem to need second-order time to occur in (Dunne), but this makes doubtful sense, and only leads to a regress. A further problem arises over our consciousness of change, if we can only experience the present and this is strictly momentary (cf. Augustine’s problem about measuring time when only one instant of it is there to measure). To deal with this, the specious present was used by various psychologists who claimed empirical evidence for it, and philosophers. ‘Specious’ suggests it only appeared to be present. It was usually claimed that the specious present was some short period ending at the present and forming the object of an act of awareness occurring at the present instant. The awareness itself was momentary, but it was awareness of a period of time. The stream of experience was then founded, in complex and controversial ways, on such acts. It has been argued, however, that the whole idea of analysing experience into successive units is mistaken; perhaps the momentary present is only a myth. There still remains the general question of how we acquire our ideas of time and space—e.g. are memory and perception involved? Bergson distinguishes time as viewed by science, which is ‘spatialized’ into a series of moments, like cinema frames albeit mathematically dense, from ‘duration’ as experienced by consciousness, which cannot be so split up.
Time, unlike space, has only one dimension (but see MacBeath), and an apparently irreversible direction. This topic is controversial, but on one view this irreversibility is connected with the second law of thermodynamics, which says that entropy, or lack of organization, tends towards a maximum in isolated systems. For time to be reversed would thus be for this law to be broken. This law can be analysed as an effect of the statistical probabilities governing matter in motion: of all the possible configurations of a set of particles that can follow after a given state the vast majority correspond to a higher degree of disorder than exists in that state. Therefore it seems that the irreversibility of time is guaranteed by, and is simply a reflection of, a mathematical law of probability. But a difficulty arises because this law is symmetrical with respect to time: the above statement of it will hold equally if we replace ‘follow after’ by ‘precede’. Another view analyses the direction of time in terms of that of causation.
Einstein’s special theory of relativity treats space and time together as space-time. The main point of this is that in certain cases whether one event precedes another depends on the observer’s motion relative to the two events, and motion involves both space and time.
A different and historically earlier, though not completely separate, issue is whether space and time are absolute or relational (‘relative’ is also used, but often kept for the Einstein view). Are space and time independent of the objects in them, as the absolute view says, or are they merely sets of relations between objects, so that it does not make sense to talk of absolute directions or absolute motion? The questions mentioned above about empty space, and time without change, are relevant again here. The question about motion has largely centred round rotation and centrifugal force, i.e. the relations between force and acceleration.
Also, are space and time parallel, in the sense that all, or nearly all, that can be said of the one can be said of the other, e.g. can a thing move around in time as it can in space? This raises questions about the relations between objects and events.
A question that has had some discussion recently is whether space and time are necessarily unique. Could there be a set of objects spatially and temporally related to each other but not to us? (For a different use of the same idea cf. D.K.Lewis’s treatment of POSSIBLE WORLDS.) And could there be duplicate universes in space or time? If we went off in a rocket, travelling in what by all available tests was a straight line, and eventually reached what appeared to be a second earth, could we decide whether it really was another one or whether we had somehow come back to this earth? Similarly, could there be a ‘mirror universe’, i.e. could the universe contain a point or axis of symmetry? (Cf. INCONGRUENT.) The ‘duplicate universe’ question was asked earlier about time than about space (cf. METAPHYSICS for the doctrine of eternal recurrence, and in general cf. LEIBNIZ’S LAW). Finally could time be closed or circular? And could it have a beginning or an end?
On the infinite divisibility of space and time see ZENO’S PARADOXES.
H.G.Alexander (ed.), The Leibniz-Clarke Correspondence, Manchester UP, 1956. (Clarke defended Newton’s absolute view in a series of letters to Leibniz, who defended the relational view. Alexander’s introduction discusses later writers too.)
Aristotle, Physics, IV. (Place, void and time.)
H.L.Bergson, Time and Free Will, Allen and Unwin, 1910 (French original, 1899), chapter 2. (Duration. His later works ascribe it to the world itself as well as to consciousness.)
J.W.Dunne, An Experiment with Time, 1927, 3rd (revised) edn, Faber, 1934, revised edn, Macmillan, 1981.
R.Flood and M.Lockwood (eds), The Nature of Time, Blackwell, 1986. (Series of lectures, taking account of modern physics.)
Paul Horwich, Asymmetries in Time, MIT Press, 1987. (Offers a unified treatment of various areas where asymmetries of time arise.)
*R.Le Poidevin and M.MacBeath (eds), Oxford UP, 1993. (Mainly reprinted essays, including McTaggart, Quinton and Shoemaker. Has annotated bibliography.)
M.MacBeath, ‘Time’s square’ in Le Poidevin and MacBeath. (Could time have more than one dimension?)
D.H.Mellor, Real Time, Cambridge UP, 1981. (Defends McTaggart’s attack on A series, and rejects tensed facts, but keeps B series.)
*W.Newton Smith, The Structure of Time, RKP, 1980. (General introduction.)
G.Plumer, ‘The myth of the specious present’, Mind, 1985. (Discussion, with references. Cf. also R.M.Gale, ‘Has the present any duration?’, Nous, 1971.)
A.Quinton, ‘Spaces and times’. Philosophy, 1962, reprinted in Le Poidevin and MacBeath. (Are space and time unique? Cf. also K.Ward. ‘The unity of space and time’, M.Hollis. ‘Box and Cox’, Philosophy, 1967.)
C.Ray, Time, Space and Philosophy, Routledge, 1991. (Introduction to various problems arising from modern science.)
F.Reif, Statistical Physics, McGraw Hill, 1965 (vol. 5 of Berkeley Physics course), chapter 1. (Elementary account of the view that irreversibility of time is related to statistical physics.)
W.C.Salmon, Space, Time and Motion: a Philosophical Introduction, Minnesota UP, 2nd edn, 1980. (Moderately elementary introduction to issues from modern physics.)
L.Sklar, Space, Time and Spacetime, California UP, 1974. (Extended introduction to effects of modern science on philosophy of space and time. Requires some fairly elementary mathematics.)
*J.J.C.Smart (ed.), Problems of Space and Time, Macmillan, 1964. R.Gale (ed.), The Philosophy of Time, Macmillan, 1968. (These two volumes contain, with some overlap, many relevant discussions, with editorial introductions. Several of the authors mentioned above are included, including McTaggart in Gale.)
R.K.Sorabji, Matter, Space, and Motion, Duckworth, 1988, chapter 10. (Could time be circular?)
R.Swinburne (ed.), Space, Time and Causality, Reidel, 1983. (Discussions, often technical, of absolute versus relative, time and causation, quantum mechanics, the Einstein-Podolski-Rosen paradox.)
R.Taylor, ‘Spatial and temporal analogies and the concept of identity’, Journal of Philosophy, 1955, reprinted in Smart. (Defends parallelism of space and time. Cf. also J.M.Shorter, ‘Space and time’, Mind, 1981. On objects and events see F.I.Dretske, ‘Can events move?’, Mind, 1967. A.Quinton, ‘Objects and events’, Mind, 1979, P.M.S.Hacker. ‘Events and objects in space and time’. Mind, 1982.)
L.Wittgenstein, Tractatus, 1921, trans. D.F.Pears and B.F.McGuinness, RKP, 1961. (Logical space. Very difficult.)
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