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Page 579 of Smith, Quentin, 1985, “On the Beginning of Time”, Noűs, vol. XIX, no. 4, pp. 579-584.
On the Beginning of Time
QUENTIN SMITH
Ashley House, 7H, Lockwood Drive, Charleston, SC 29401
In defending the idea that a beginning of time can be coherently conceived the first thing to establish is that the following objection is invalid: 'Everything that begins does so in time; therefore time itself cannot have a beginning. ' This argument relies on the premise that' to begin' means ( 1) there is an earlier time at which the thing or state is not, and (2) there is a later time at which the thing or state is; this premise justifies the conclusion that it is impossible for time to begin since that would involve a time earlier than time. The response to this objection is that 'to begin' has different senses when applied to time and things and states in time. As applied to time, it means:
1. There is an interval of time such that every other interval of the same length is later than that interval.
2. Prior to any interval of a given length, there is at most a finite number of intervals of the same length.
Note that this analysis of a beginning of time concerns intervals ’of the same length' ; if this qualifying phrase is not added, then the analysis would be invalid for a dense time. If time is dense and began, then for each interval of time there is another interval of a shorter length that is a part of that interval and which completely elapses before the interval of which it is a part completely elapses. Before the first hour completely elapses, the first minute does so, and before the first minute, the first second, and so on ad infinitum. This entails that there is no 'first moment' of time in the sense of an interval that precedes every other interval, but there is a 'first moment' in the sense that there is a first interval of each length of time: there is a first hour, a first minute, etc.
But if time is discrete there is a 'first moment' in both senses: there is one interval ( of the shortest length) that is earlier than
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every other interval, and there is also an earliest interval of each length .
The implications of the above analysis of the beginning of time can be further explicated if some arguments purporting to prove the infinitude of time are critically examined. It has been argued by Quinton, Swinburne, Moore, Alexander and Kant, among others, that the earlier-later relational structure of time necessitates the beginninglessness of time. In The Nature of Things Quinton asserts that time-
has no beginning in the sense that there is no date an earlier date than which cannot be significantly described. ..Infinity, we might say, is a necessary feature only of systems of description, not merely those which contain numbers but any which contain such transitive asymmetrical relations as 'smaller than' and 'further than' and 'earlier than.[1]
In one sense Quinton is right, for in regard to any date, e.g. 15 billion years B .C ., an earlier date ( such as 16 billion years B .C .) can be 'significantly described' .But it does not follow that every such description has a reference. It could be that only a finite number of dates that can 'be significantly described' actually existed. If time began 15 billion years ago, then we can have a concept of 16 billion years ago, and a verbal articulation' 16 billion years ago', but this concept and articulation will not signify or refer to anything.
Quinton' s claim that infinity is a necessary feature of systems of descriptions containing the relation 'earlier than' is also open to question. It is possible to construct such a system that is finite; for example, 'earlier than' could be defined as obtaining between terms each of which corresponds to a different number in the series 0-100. In this case, the term corresponding to 0 is the earliest term. Moreover, even if infinity were a necessary feature of these systems, it still would be possible to construct a system representative of a time that begins: 'earlier than' could be defined as obtaining among terms each of which corresponds to a number in the series of positive integers of order type (w) (0, 1, 2, 3, 4, 5,…), such that the term corresponding to 0 is the earliest. This system describes a time that begins but does not end.[2]
Richard Swinburne offers a different argument purporting to show that time is necessarily infinite:
Time, like space, is of logical necessity, unbounded. After every period of time which has at some instant an end, there must be another period of time, and so after every instant another instant.
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Page 581 of Smith, Quentin, 1985, “On the Beginning of Time”, Noűs, vol. XIX, no. 4, pp. 579-584.
For either there will be swans somewhere subsequent to a period T, or there will not. In either case (here must be a period subsequent to T, during which there will or will not be swans. By an analogous argument any period which has a beginning must have been preceded by another period, and hence time is necessarily unbounded.'[3]
The 'analogous argument' for the beginninglessness of time would read:
Before every period of time which has at some instant a beginning, there must be another period of time, and so before any instant another instant. For either there were swans somewhere prior to a period T or there were not. In either case there must have been a period prior to T, during which there were or were not swans.
However, Swinburne ' s assertion that' either there were swans some- where prior to a period T or there were not' is true only if prior to a period T there was another period in which there were or were not swans. This assertion does not prove that prior to any period T there was a time, but assumes it. Suppose this assumption be denied; in this case for some period T there was no prior period, and consequently the disjunction, 'either there were or were not swans prior to T' , is false. In this instance, it is true that swans existed if at all only at T or some later time, but this entails, not that no swans existed prior to T, but that there was no prior period in which swans either existed or did not exist.
It should be added that if the argument form Swinburne employs were valid, then the existence of anything could be proven. The form is clearly manifest in this statement of the argument:
Either there is a period earlier than a period T that contains swans, or there is a period earlier than T that does not contain swans; in either case there must be a period earlier than T.
The argument form is:
Either there is an x that is F, or there is an x that is not F; in either case, there must be an x.
This form permits such material interpretations as:
Either there is a unicorn which is walking on the moon, or there is a unicorn which is not walking on the moon; in either case there must be a unicorn.[4]
According to G. E. Moore, the earlier-later structure of time renders it 'self-evident' that time is infinite. Moore propounds two principles--
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Page 582 of Smith, Quentin, 1985, “On the Beginning of Time”, Noűs, vol. XIX, no. 4, pp. 579-584.
...the principles that before any or every length of time, there must have elapsed one other equal to it, and that after any or every length of time, there must have elapsed one other equal to it. What are we to say of these two principles? They do seem to me to be self-evident; but I confess I do not know exactly how to set about arguing that they are self-evident. The chief thing to be done is, I think, to consider them as carefully and distinctly as possible, and then to see whether it does not seem as if they must be true; and to compare them with other propositions, which do seem to be certainly true, and to consider whether you have any better reason for supposing these other propositions to be true than for supposing this one to be so. Consider, for instance, the proposition that, since I began to lecture this evening, some time certainly has elapsed. Have you any better reason for believing this, than for believing that, if so, a length of time equal to this one must have elapsed before it? And that this must be true of every length of time equal to that which has elapsed since I began to lecture? I cannot see that you have any better reason for believing the one proposition than for believing the other.[5]
I think a reanalysis of the situation Moore presents shows that it does not seem as if these principles 'must' be true. If I had been attending Moore's lecture, then my reason for believing the prop- osition that some time elapsed since the beginning of the lecture is that I experienced some time to elapse. That is, the reason is empirical. And certainly i do believe that a length of time equal to this one elapsed before this one. But my reason for this is also empirical: I experienced such a length of time to elapse before the lecture. However, I do not believe that this must be true of every length of time equal to that which elapsed since the beginning of the lecture. This is because there is a logical gap between my beliefs that lengths of time did elapse and the supposition that lengths of time must have elapsed. To bridge this gap, I must acquire reasons of a different sort than those substantiating my beliefs that lengths of time did elapse. The latter reasons are empirical, but the former are a priori, based on entailments between concepts. But since I find no contradiction in the idea that there is an earliest interval of time of every length, such a priori reasons cannot be found.
I think the seeming plausibility of Moore's example is based upon his claim that I am 'certain' that a length of time elapsed since the beginning of the lecture and that I believe that a length of time equal to this one 'must' have elapsed prior to it. Now in ordinary language we sometimes do use these words to convey our feeling of confidence in the empirical proposition that something did happen, so it seems not unnatural for Moore to describe our
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empirical beliefs in this way. However Moore is or is also taking 'certainty' and 'must' to refer to necessary truths, and by this means he effects a 'smooth and easy transition' as it were from the beliefs about the experienced time during and before the lecture to the belief about the necessary infinitude of time. The problem, however, is that as expressive of my belief that time elapsed during and before the lecture, 'certainty' and 'must' do not refer to necessary conceptual truths about time, but convey my confidence in my observation that time has passed.
The failure to distinguish clearly our empirical and a priori beliefs about time also underlies Samuel Alexander's argument for the necessary beginninglessness and endlessness of time:
The infinitude of Space or Time is another of their experienced features and like their continuity is a percept extended by thought. ..The sensible or perceptual datum is that each finite time is a part of a longer one. The infinite Time is the perceptual datum as qualified by the introduction of this conceptual element. The something or other which we feel to be the longer time of which a finite time is a fragment becomes extended into totality. ..The infinite Time is thus the positive object of which the finitude of any given portion, apprehended as finite, is the limitation.[6]
Alexander's argument is reminiscent of Kant's dictum that-
The infinitude of time signifies nothing more than that every de- terminate magnitude of time is possible only through limitations of one single time that underlies it. The original representation, time, must therefore be given as unlimited.[7]
First it must be pointed out that Alexander's claim that each experienced interval of time is experienced as a part of a longer interval is false, for the longest interval of which we have experience by definition is not experienced as a part of a longer interval. And we do have experience of a longest interval, for we are not infinitely temporally extended beings who experience an infinite number of longer and longer lengths of time.
Nevertheless, the longest interval of which we have experience can be conceived to be a part of a longer interval. In fact, it is an a priori truth that for each finite interval a longer and limiting interval can be conceived. In this sense the representation of the infinity of time underlies a priori the representation of any finite time. But this does not mean that time is infinite. For the conceivability of longer and longer intervals to infinity does not entail their actuality but merely their possibility.[8] Whether the concepts of these intervals are instantiated is a matter to be decided em-
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Page 584 of Smith, Quentin, 1985, “On the Beginning of Time”, Noűs, vol. XIX, no. 4, pp. 579-584.
pirically, by prediction or retrodiction, not by conceptual analysis. Alexander and Kant have in this respect made an analogous error to Quinton's; they tacitly inferred from 'it is necessarily the case that for each finite interval a longer interval is thinkable' to 'it is necessarily the case that for each finite interval a longer interval is actual.'[9]
[1] Anthony Quinton, The Nature of Things (Boston: Routledge & Kegan Paul, 1973), p. 88.
[2] W. H. Newton-Smith believes Quinton's argument is mistaken only because we can refuse "to employ [Quinton's] particular system of descriptions". Cf. The Structure of Time (London: Routledge & Kegan Paul, 1980), p. 103. This is incorrect. Even if we could not employ any other system, Quinton's argument would still be mistaken, for not all the descriptions in Quinton's system need refer. Newton-Smith also seems to believe that in order to construct alternate systems of descriptions in which time is described as beginning, it is necessary to define the earlier-later relations "on finite sets" (Ibid); this is not the case, for these relations could be defined on the set with order type (w).
[3] Richard Swinburne, Space and Time, 2nd ed. (New York: St. Martin's Press, 1981), p. 172.
[4] 'For a different analysis and critique of Swinburne's argument, see Newton-Smith's chapter on the beginning and ending of time in The Structure of Time, op. cit.
[5] G. E. Moore, Some Main Problems of Philosophy (New York: The Macmillan Co., 1953), pp. 191-2
[6] Samuel Alexander, Space, Time and Deity, Vol. I (Gloucester, Mass., Peter Smith, 1979), p. 42. In this passage Alexander is talking of space, but means his argument to apply equally to time. Accordingly, I have substituted 'Time' and the relevant temporal expressions for 'Space' and the spatial expressions.
[7] Immanuel Kant, Critique of Pure Reason, trans. N. Kemp Smith (New York: St. Martin's Press, 1965), p. 75 (A32/B47-8).
[8] I am not using 'conceivability' here in the sense in which round squares and wooden iron are conceivable, but in the sense that whatever is not self-contradictory is conceivable.
[9] Although it is possible that time began, it is not necessary, not even if the world began. Cf. Quentin Smith, "Infinity and the Past", Philosophy of Science, forthcoming in 1985 or 1986, and "Kant and the Beginning of the World", The New Scholasticism, Vol. LIX, No. 3, Summer, 1985. For further relevant discussions of time, see "The Mind- Independence of Temporal Becoming", Philosophical Studies, Vol. 47, No. 1, January, 1985, and The Felt Meanings of the World: A Metaphysics of Feeling (West Lafayette, IN: Purdue University Press, 1986), Chapters Four and Six.