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The arguments which favor spelling out the Universe having a begin- ning in this way, also favor spelling out time having a beginning in this way. Time would have a beginning if there was a period of empty time before there was time - which is incoherent. So time could not have a beginning. Time must be without beginning. So if the notion of the Universe having or not having a beginning can be spelled out coherently for universes of different kinds, it will be in terms of a time which cannot have a beginning. Our concept of time is the concept of a background against which things come into being, change, and cease to be. We need it to elucidate the notion of the Universe having a beginning. We would be depriving it of its role in our conceptual scheme which would be the poorer thereby, if we allowed it to be the sort of thing which could itself have a beginning.
Given my fourth thesis that there is no content in supposing that a temporal interval could have any other length than would be measured by a perfect clock, it follows that any time before there was a Universe would have no metric. The beginning of the Universe would be, if there was one on our definition, an actual event. So we can talk of the period of time which ends with that event. But there would be no content to talk about half an hour before the beginning of the Universe as opposed to an hour before that beginning. For 'half an hour before the beginning of the Universe' can only be identified by a possible event - the event of a perfect clock pointing to the hour, such that it would advance in accord with laws of nature by a half-revolution so that it was pointing at the half-hour when the Universe began. But that description will only pick out a definite instant if the clock and any other substances there hap- pened to be would have behaved in accord with laws of nature up to and including the period when substances actually began to exist. But that could not have been - for if the laws had operated, substances would not have come into existence when they did. The beginning of existence of substances (understood in our wide sense) could not have occurred in accord with laws of nature. For laws prescribe which substances or events cause or are necessarily simultaneously correlated with other events. And when there were no substances already existing or events occurring there would be nothing to cause new ones. Put another way - it follows from my four theses that instants which cannot be distin- guished by the actual events which they bound, can only differ if they bound different possible events and that will only be if they are at a different temporal distance from different actual events. So where there is no true metric of temporal distance, there is nothing to make an instant this one rather than that one. Hence any period ending with the begin- ning of the Universe is the same as any other; any time before the beginning of the Universe is amorphous - from which it follows that, if the Universe began, there is nothing to be explained about why it began at this instant rather than that.
The Universe's having a beginning, now interpreted in terms of (2) is compatible with both (1) and (1'). We have seen that there could be a period of empty time even before an infinite series of periods. (1') is also compatible with (2'). It could be instead that the infinite series of periods of the Universe's existence filled the whole of time - there was no empty time left over. But what is not possible is that (1) and (2') both be true. If the Universe has existed only for a finite number of periods of time, then it had a first (initially bounded) period. But time cannot, I have argued, have a first (initially bounded) period. So there must have been time before the universe began. What can the physical cosmologist show us about whether the Uni- verse had a beginning (in my preferred sense)? The scientist observes the present state of the Universe and postulates the simplest laws which will explain its present state. The only way in which he can reach justified conclusions about how things were is by extrapolating backwards from the present state of the Universe in accord with these laws. He may find that we can extrapolate backwards to states of the Universe for an infinite period of time, without reaching impossible states - as once upon a time steady state theory purported to show. Extrapolation from the ways things behave in our narrow region of space-time to how things behaved 101010 billion years ago will be a shaky inference, since it will be derived from a general theory of cosmology claimed to hold over a large period of time but confirmed only by evidence observed in a relatively small region of space over a relatively small period of time. A fortiori, inference to how things were for any n, n years ago can only be tentative in the extreme. But even if the tentative conclusion that the Universe has lasted an infinite number of years were correct, that could be compatible - given my earlier argument - both with the Universe having a beginning and with it not having a beginning. And I cannot see that the scientist's results would favor one of these alternatives against the other. Alternatively the scientist might show that the present data confirm laws of nature such that we cannot extrapolate backwards, to states of the Universe for an infinite period of time, but only for a finite time. Backwards extrapolation might lead us eventually to a singularity - as in current Big Bang theory, 15 billion years ago - such that if there were substances before that singularity, they must have obeyed different laws. But I suggest that in the absence of positive evidence, it is better justified to postulate nothing than something; and if so, the best justified conclu- sion would be that the Universe began a finite time ago. So physical cosmology could never show us that the Universe had no beginning but it could show us (on balance of evidence) that it had a beginning (in the only clear sense of having a beginning which there is). I began this paper by arguing for four modestly verificationist theses about certain concepts crucial in this area, such as 'period' and 'instant.' I then went on to argue that in consequence of these theses the only coherent account which could be given of the Universe having / not having a beginning was in terms of its existence being preceded by / not preceded by a period of empty time. It followed that it is not logically possible for time to have a beginning. It also followed that physical cosmology could never show us that the Universe had no beginning, but it could show us that the Universe did have a beginning
