On the beginning of time
Quentin Smith, in a paper published in Noûs, 1985, and titled “On the Beginning of Time,” argues that if one wants to defend that there is a beginning of time, then one has to establish first that the objection “Everything that begins does so in time; therefore, time itself cannot have a beginning,” is invalid. He goes on to say that 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, so that it is impossible for time to begin, since that would involve a time earlier than time.
However, “to begin,” according to Smith, has different meanings 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, and (2) prior to any interval of a given length, there is at most a finite number of intervals of the same length.
The analysis is invalid for a dense time, if the phrase “of the same length” is not added. If time is discrete, there is a “first moment”: there is one interval of the shortest length that is earlier than every other interval, and there is also an earliest interval of each length.
Smith then goes on to describe what Quinton, Swinburne, Moore, Alexander and Kant argued: earlier-later relational structure of time entails the beginninglessness of time. For example, Anthony Quinton (The Nature of Things, p. 88, 1973) 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.”
In regard to any date, an earlier date can be “significantly described,” but it does not follow that every such description has a reference. If time began x billion years ago, then we can have a concept of x+1 billion years ago, but this concept will not signify anything.
According to Smith, Quinton's claim that infinity is a necessary feature of systems of descriptions containing the relation “earlier than” is questionable: it is possible to construct such a system that is finite. “Earlier than” could be defined as obtaining between terms each of which corresponds to a different number in the series 0-100. The term corresponding to 0 is the earliest term. 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 ω (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.
Then Smith states that Richard Swinburne offers a different argument to show that time is necessarily infinite (Space and Time, p. 172, 1981):
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. For either there will be swans somewhere subsequent to a period T, or there will not. In either case, there 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.
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 somewhere 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.
Smith then discusses G. E. Moore's two principles (Some Main Problems of Philosophy, pp. 191-2, 1953):
... 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 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.
Smith reanalyses the situation. The reason to believe the proposition that some time elapses since the beginning of the lecture is because one experiences the lapse of time, i.e., the reason is empirical. There is a logical gap between one's beliefs that lengths of time did elapse and the supposition that lengths of time must have elapsed. To bridge this gap, one must acquire reasons of a different sort than those substantiating one's beliefs that lengths of time did elapse. The latter reasons are empirical, but the former are a priori, based on entailments between concepts. However, no contradiction in the idea that there is an earliest interval of time of every length can be found. Thus, such a priori reasons cannot be found.
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. Moore is taking “certainty” and “must” to refer to necessary truths, and by this he 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.
Smith states that Samuel Alexander also suffers from this type of failure to distinguish the empirical and a priori beliefs about time (Space, Time and Deity, p. 42, 1979; he is talking of space, but means his argument to apply equally to time):
The infinitude of Space and 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.
Alexander's argument reminds Smith Kant's dictum (CPuR A32/B47-8):
The infinitude of time signifies nothing more than that every determinate 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.
Smith asserts that Alexander's claim that each experienced interval of time is experienced as a part of a longer interval is false, because the longest interval of which we have experience by definition is not experienced as part of a longer interval. And we do have experience of a longer interval, for we are not infinitely temporally extended beings who experience an infinite number of longer and longer lengths of time.
Nevertheless, he goes on, the longest interval of which we have experience can be conceived to be a part of a longer interval. In fact, it is an 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 the time is infinite. The conceivability of longer and longer intervals to infinity does not entail their actuality, but merely their possibility. Whether the concepts of these intervals are instantiated is a matter to be decided empirically, by prediction or retrodiction, not by conceptual analysis. Smith believes that, in this respect, Alexander and Kant made an error analogous 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.”
So concludes Smith his argument against the aformentioned thinkers on the beginning of time. But if indeed he truly represents their arguments, these arguments seem to be as featherweight as one can witness in high school debates. They do not make much sense to begin with.
However, “to begin,” according to Smith, has different meanings 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, and (2) prior to any interval of a given length, there is at most a finite number of intervals of the same length.
The analysis is invalid for a dense time, if the phrase “of the same length” is not added. If time is discrete, there is a “first moment”: there is one interval of the shortest length that is earlier than every other interval, and there is also an earliest interval of each length.
Smith then goes on to describe what Quinton, Swinburne, Moore, Alexander and Kant argued: earlier-later relational structure of time entails the beginninglessness of time. For example, Anthony Quinton (The Nature of Things, p. 88, 1973) 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.”
In regard to any date, an earlier date can be “significantly described,” but it does not follow that every such description has a reference. If time began x billion years ago, then we can have a concept of x+1 billion years ago, but this concept will not signify anything.
According to Smith, Quinton's claim that infinity is a necessary feature of systems of descriptions containing the relation “earlier than” is questionable: it is possible to construct such a system that is finite. “Earlier than” could be defined as obtaining between terms each of which corresponds to a different number in the series 0-100. The term corresponding to 0 is the earliest term. 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 ω (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.
Then Smith states that Richard Swinburne offers a different argument to show that time is necessarily infinite (Space and Time, p. 172, 1981):
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. For either there will be swans somewhere subsequent to a period T, or there will not. In either case, there 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.
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 somewhere 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.
Smith then discusses G. E. Moore's two principles (Some Main Problems of Philosophy, pp. 191-2, 1953):
... 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 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.
Smith reanalyses the situation. The reason to believe the proposition that some time elapses since the beginning of the lecture is because one experiences the lapse of time, i.e., the reason is empirical. There is a logical gap between one's beliefs that lengths of time did elapse and the supposition that lengths of time must have elapsed. To bridge this gap, one must acquire reasons of a different sort than those substantiating one's beliefs that lengths of time did elapse. The latter reasons are empirical, but the former are a priori, based on entailments between concepts. However, no contradiction in the idea that there is an earliest interval of time of every length can be found. Thus, such a priori reasons cannot be found.
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. Moore is taking “certainty” and “must” to refer to necessary truths, and by this he 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.
Smith states that Samuel Alexander also suffers from this type of failure to distinguish the empirical and a priori beliefs about time (Space, Time and Deity, p. 42, 1979; he is talking of space, but means his argument to apply equally to time):
The infinitude of Space and 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.
Alexander's argument reminds Smith Kant's dictum (CPuR A32/B47-8):
The infinitude of time signifies nothing more than that every determinate 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.
Smith asserts that Alexander's claim that each experienced interval of time is experienced as a part of a longer interval is false, because the longest interval of which we have experience by definition is not experienced as part of a longer interval. And we do have experience of a longer interval, for we are not infinitely temporally extended beings who experience an infinite number of longer and longer lengths of time.
Nevertheless, he goes on, the longest interval of which we have experience can be conceived to be a part of a longer interval. In fact, it is an 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 the time is infinite. The conceivability of longer and longer intervals to infinity does not entail their actuality, but merely their possibility. Whether the concepts of these intervals are instantiated is a matter to be decided empirically, by prediction or retrodiction, not by conceptual analysis. Smith believes that, in this respect, Alexander and Kant made an error analogous 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.”
So concludes Smith his argument against the aformentioned thinkers on the beginning of time. But if indeed he truly represents their arguments, these arguments seem to be as featherweight as one can witness in high school debates. They do not make much sense to begin with.
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