A Treatise on Time and Space

J. R. Lucas

• Publisher: Routledge
• Year: 2018
• ISBN:
  9780429685163
• Edition: 1
• Topic: Philosophie
• Subtopic: Geschichte & Theorie der Philosophie

Originally published in 1976. This comprehensive study discusses in detail the philosophical, mathematical, physical, logical and theological aspects of our understanding of time and space. The text examines first the many different definitions of time that have been offered, beginning with some of the puzzles arising from our awareness of the passage of time and shows how time can be understood as the concomitant of consciousness. In considering time as the dimension of change, the author obtains a transcendental derivation of the concept of space, and shows why there has to be only one dimension of time and three of space, and why Kant was not altogether misguided in believing the space of our ordinary experience to be Euclidean.The concept of space-time is then discussed, including Lorentz transformations, and in an examination of the applications of tense logic the author discusses the traditional difficulties encountered in arguments for fatalism. In the final sections he discusses eternity and the beginning and end of the universe. The book includes sections on the continuity of space and time, on the directedness of time, on the differences between classical mechanics and the Special and General theories of relativity, on the measurement of time, on the apparent slowing down of moving clocks, and on time and probability.

I Time by itself

§ 1

The nature of time

Time is more fundamental than space. Indeed, time is the most pervasive of all the categories. Some theologians say that God is outside time, but it cannot be true of any personal God that he is timeless, for a personal God is conscious, and time is a concomitant of consciousness. Time is not only the concomitant of consciousness, but the process of actualization and the dimension of change. The many different definitions of time given by philosophers reflect its many different connections with other fundamental categories. Time is connected with persons, both as sentient beings and as agents; it is connected with modality, and the passage from the open future to the unalterable past; it is connected with change, and therefore with the things that change and the space in which they change.

These different connections are responsible both for the importance of the concept of time and for the difficulty we experience in defining it. We cannot philosophize long about any subject without coming up against the problem of time. But as we wrestle with it, we find ourselves repeating St Augustine’s lament: “Quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio.” (“What is time? if nobody asks me, I know, but if I want to explain it to some one, then I do not know.”) [1] It is a universal experience. We know what time is, we are all familiar with it, but all feel uneasy when it comes to expressing it in words. We listen with respect when we are told that time is a moving image of eternity,

[2], or the measure of change with respect to earlier and later,

[3], or that time is extension, extension perhaps of mind [4], or that it is a concomitant of concomitants,

[5], or that it is the order of events, or that it is the form of becoming, or the possibility of change, or, more modernly, that time is what the clocks say, or that it is the independent variable in the laws of mechanics [6], or that it is the fourth dimension, and therefore unreal and only imaginary, because it involves

.

But although we listen with respect, we do not give our wholehearted assent. None of these sayings, true, perhaps profound, though they are, seems to express all that we mean by the word ‘time’. Time means more than all these. Not only do we use the word in many different locutions [7], but it seems something too universal, too pervasive, ever to be encapsulated in a few words. We cannot say what time is, because we know already, and our saying could never match up to all that we already know. Yet we cannot be content merely to know wordlessly, and to ward off the questioner, like Meno, by saying that he could not ask us what time was unless he already knew. For we get puzzled by time. Not only are we unable to answer other men’s questions, but we cannot think straight about it by ourselves. We are always being driven into quandaries and paradoxes by the various analogies that present themselves. “Time like an ever-rolling stream bears all its sons away”, but where to? The present is with us – we know that. But the future, which is not yet present with us, and the past, which no longer is present with us, where are they? Where are the days of yesteryear? Indeed, does even the present exist? How large is it? Surely, on reflection, we are compelled to admit that it is no size at all – but then it cannot constitute any part of time and must be altogether nothing. Or again, we talk of time going fast or going slow – “Time goes faster”, we are told, “as one gets older”; but this, however natural, is also awkward, since it is only by reference to time that we measure fastness or slowness.

Measuring time seems equally mysterious. We can measure space by moving a ruler – a standard length – around, and, if in doubt, bringing it back again, and checking that all the readings are repeatable. But we cannot take a standard second around, and lay it off sixty times against a minute yesterday, and then against a minute today, and back to check yesterday’s minute again. Measurements, so called, of time are essentially unrepeatable, and for that reason alone suspect to the scientific mind. Yet we rely on them with great confidence, so much so that we talk of what our measuring instruments read as being “the time”. Perhaps we should not. A B.B.C. announcer, more refined, said “The right time is twenty to eight”, but Miss P. Wacholder of Hull objected, “Surely time is never wrong – our clocks and watches may be, but never time.” [8] It is difficult to talk, difficult to think, about time straight. It is too immediate and pervasive to get into focus, too intangible and insubstantial to grasp or comprehend.

Some of these difficulties are susceptible to straightforward philosophical analysis. By considering carefully how we know that some temporal assertion is correct or incorrect, and how we actually set about assigning magnitudes to temporal intervals, we can resolve many of our difficulties. But not all. Our difficulties about time are not due merely to our being insufficiently self-conscious about our use of language and measuring instruments. Time is puzzling not only because it is unlike anything else in our conceptual universe, but just because it is part of our conceptual structure and is connected to a number of other parts. These different connections give us different perspectives on the concept of time, indeed almost different concepts. Time is related to change, and through change to the things that change and the space in which they change. But quite apart from change, time is related to consciousness, and hence with persons. More important to our concept of personality than bare sentience is the fact that we are rational agents who make plans for the future and choose between alternatives presented to us and know ourselves as being the beings who have done what we have done. Time, therefore, is linked with personality in two ways: not only is it given to each one of us in experience, as an essential concomitant of consciousness, but it is a necessary condition of activity, and an integral part of each man’s notion of what it is to be himself. Without time no agent could act, for to act is to bring about something that we want to come to pass, and time is the passage from possibility to actuality, from aspiration to achievement. If I am never able to give an answer to the question “What are you doing?” I am not a responsible agent, but insane. But if I can say what it is I am doing, then I must be able also to say what I have just been doing in the immediate past, and what I am just going to do in the immediate future; for actions are not isolated instantaneous happenings but are intelligible only within a pattern of activity. In order to be an agent, I must know what I am doing, I must remember what I have done in the immediate past and realize what I intend todo in the immediate future. Without time there could be no activity. And even if we could isolate individual actions it would still make no sense to talk of agents acting timelessly or of deeds done outside them.

Different approaches bring different aspects of time into prominence but no single approach can reveal the whole nature of time, and each needs to be supplemented on occasion by the others. In the same way there are many concepts of space, which in turn reflect their multiplicity back into time. It is for this reason that profound thinkers have given their different definitions of time, each one of which has seemed to reveal some important aspect of the truth. It may be possible in the end to give a unified account which reconciles their divergent insights in one coherent theory; but it would be a mistake to begin like this. Both the difficulty and the importance of the concept of time arise from there being different perspectives on it, which partly although not altogether overlap, and which we superimpose on one another to obtain a concept, or family of concepts, of great complexity and richness. To appreciate it fully, we need to approach it in different ways, and to experience the tension engendered by its diverse conceptual limbs. In particular, illumination often comes by considering the various puzzles that have perplexed men when they have thought about time. We shall consider first the puzzles that arise from our bare awareness of the passage of time. We shall start with the puzzle of time going quickly or slowly, which we shall resolve by distinguishing between public and private time; and then go on to deal with St Augustine’s problem of the ever-shrinking present. These both turn on topological considerations. We shall complete a survey of the topological properties of time, which can largely be established by arguments from consciousness alone. We shall then consider time as the condition of activity and as the actualization of the potential future into the fixed past, and discuss the directedness and the serial nature of time. Only then shall we turn to the time of the scientists, the dimension of change and physical process, which can be measured but is too featureless and insubstantial to grasp or comprehend. This will lead us to one concept of space, which in turn leads us on to the more general concept still of space-time. Theories of space, together with those of Newtonian mechanics and relativity, have a profound bearing on our understanding of time, and raise questions that sometimes require a radical reappraisal of our untutored institutions and sometimes need, rather, a rational reaffirmation of what we have always known to be true.

[1] St Augustine, Confessions, bk XI, ch. XIV, xvii.

[2] Plato, Timaeus, 38; see further below § 13, pp. 75–6

[3] Aristotle, Physics, IV, 11, 220a 25.

[4] St Augustine, Confessions, bk XI, ch. XXVI, xxxiii; quoted below § 2, p. 14.

[5] Epicurus, as interpreted by Demetrius of Sparta apud Sextus Empiricus, Adversus Mathematicos, X (i.e.

, B), 219.

[6] Quoted, e.g. by H. Margenau, The Nature of Physical Reality (New York, 1950), p. 136.

[7] For many other uses of the word ‘time’, see F. Waismann, “Analytic-Synthetic, II”, Analysis, IX (December 1950), pp. 26–8.

[8] Radio Times (11 February 1965).

§ 2

Time and consciousness

Time is related to consciousness. I cannot conceive of a mind being conscious of something about whom the question ‘when?’ does not arise, whereas there are many states of consciousness for which the question ‘where?’ does not naturally arise. I can feel anger or elation, or can recollect the past, or can try to prove a mathematical theorem without having any spatial experience or any idea of where I am located in space; whereas I cannot enjoy any state of consciousness at all without having some idea of its being before or after some other states of consciousness, and being something of which it must always be intelligible to ask when I had it. I may be unable to answer – our sense of time is often unreliable – but it is necessarily an intelligible question; whereas the question ‘Where were you angry?’ or ‘Where did you try to prove Taylor’s theorem?’ is not a very natural question, and need not be even intelligible. Disembodied minds are conceivable and would be non-spatial, whereas timeless minds seem quite inconceivable. We might express this by saying that minds are only contingently located in space, but necessarily “located” in time. Space and time are thus importantly different. Whereas we do not have to be able to ask or answer the question where a mind is having an experience, it is unintelligible to claim that we cannot say, and cannot even ask, when it is, or was, or will be, having an experience. And, per contra, whereas I can conceive of a space that is totally disconnected with the space in which I happen to be, I cannot conceive of a time disconnected with my time; that is, there cannot be a time or any temporal event such that the question ‘What is its relation to me?’ cannot arise. Witness the phrase ‘Once upon a time …’, which by blocking the question ‘when?’ conveys the implication that what is narrated never really happened (see further below, § 7, p. 37).

The connexion between consciousness and time is important not only in showing the difference between time and space, but in refuting certain positivist analyses of time in terms of change, and in establishing the continuity of time independently of any physical considerations about the nature of change or of space. One of the reasons why time is puzzling is that we are immediately and irresistibly aware of it, and therefore often find the rational reconstructions offered by philosophers intuitively wrong. Although cons...