Some theologians and philosophers of religion maintain that, prior to the beginning of the universe, God existed alone in a pre-creation moment. Some friends of a pre-creation moment, such as Richard Swinburne and Alan Padgett, think the pre-creation moment is (1) an interval of time but (2) without a metric. When they say that the interval is without a metric, they mean that there is no fact at all as to how long the interval was. Such intervals are said to be metrically amorphous. Moreover, Swinburne and Padgett would say that God is beginningless because a metrically amorphous interval, qua metrically amorphous, is not finite. Roger Penrose has a similar idea, but for intervals within the history of the physical universe. For Penrose, spacetime acquires its metrication from the presence of mass. Without mass, a region of spacetime is unmetricated, possessing only light cone structure and not the full metric structure.

William Lane Craig has argued that there couldn’t be a metrically amorphous interval of time. According to Craig, an interval of that sort would be infinitely long, and so beginningless. Craig has spent much of his career arguing against the possibility of infinitely long intervals; Craig concludes that the unmetricated interval must be impossible in virtue of being infinitely long. In this blog post, I will briefly summarize Craig’s argument that metrically amorphous intervals are infinitely long. While I am skeptical concerning the possibility of an interval of time external to the physical universe, I think Craig is wrong that metrically amorphous intervals are infinitely long. I will finish the post by summarizing why I think metrically amorphous intervals are neither finite nor infinite.

To summarize Craig’s objection to metrically amorphous time, I am leveraging his 2001 book God, Time, and Eternity. Craig begins his discussion of metrically amorphous time by admitting that his finitist arguments show, at most, that metrical time must have had a beginning and not that time must have had a beginning. Faced with his finitist arguments, someone could hope to avoid an infinite past by invoking a metrically amorphous interval:

But the arguments [against an infinite past] would not be incompatible with the existence of an undifferentiated ‘before’ followed by the beginning of time as we know it. In a metrically amorphous time, there is no difference between a minute, an hour, or an aeon; more exactly, such measured intervals of time do not exist at all. Thus it is a mere chimera to imagine God existing, say, one hour before He created the world. (Craig 2001, p. 268)

Craig argues that, “the Padgett-Swinburne doctrine of divine eternity is demonstrably defective as it stands and so needs revision” (ibid, p. 269). As Craig (correctly) points out, there is a sense in which some intervals can be longer than others in metrically amorphous time. That is, when one interval A is completely nested inside another B, A must be strictly shorter than B (ibid, p. 269). In Craig’s words, “For in the case of intervals which are proper parts of other intervals, the proper parts are factually shorter than the encompassing intervals” (ibid, p. 269). Craig thinks this

entails that prior to t = 0 God has endured through a succession of an actually infinite number of progressively longer intervals, which conclusion is contradicted by the kalam arguments I have defended elsewhere, and we can still ask the questions, ‘Why did not God create the world sooner?’ and ‘Why is it now?’ Thus, all of our difficulties with the infinitude of the past return to haunt metrically amorphous divine eternity. In fact, pace Swinburne, we can even say that such a time would be infinite (pp. 269-270).

But how can we say that a metrically amorphous interval would be infinite? Here’s what Craig writes:

The past is finite iff there is a first interval of time and time is not circular. (An interval is first if there exists no interval earlier than it, or no interval greater than it but having the same end point.) Even a past which lacks an initial instant is finite if it has a first interval. Swinburne’s metrically amorphous past is thus clearly not finite. But is it infinite? The past is infinite iff there is no first interval and time is not circular. Thus Swinburne’s past eternity is infinite. Our inability to compare factually the lengths of non-nested temporal intervals in metrically amorphous time therefore does not preclude our determining that the past as a whole is finite or infinite (p. 270).

Here, Craig has provided several definitions:

1. An interval is first if there exists no interval earlier than it, or no interval greater than it but having the same end point.
2. The past is finite iff there is a first interval of time and time is not circular.
3. The past is infinite iff there is no first interval and time is not circular.

Pace Craig, given his set of definitions, a metrically amorphous interval is clearly finitely long. Why? Divide a metrically amorphous interval into finitely many sub-intervals however you’d like. No matter which way you divide a metrically amorphous interval, there will clearly be a first sub-interval. Wherever you put your first division, there is an interval before that division. Since — by construction — there were no earlier divisions, there are no intervals earlier than the one prior to the interval in question. Moreover, there couldn’t be a greater interval with the same end point. But maybe we’ve gone too fast. Perhaps Craig has in mind dividing the metrically amorphous interval into infinitely many sub-intervals. There is clearly still a first sub-interval. Simply take the entire metrically amorphous interval. There is no interval greater than that having the same end point. Hence, there is a first sub-interval.

Nonetheless, the three definitions are bad, as we can see by examining what they would imply about metricated intervals. Consider that, elsewhere, Craig and co-author James Sinclair wrote,

[…] we can say plausibly that time begins to exist if for any arbitrarily designated, non-zero, finite interval of time, there are only a finite number of isochronous intervals earlier than it; or, alternatively, time begins to exist if for some non-zero, finite temporal interval there is no isochronous interval earlier than it (Craig and Sinclair 2012, p. 99).

For example, if the past is finitely long, then the past includes no more than some finite number of hours. Presumably, this is intended as a sufficient, not necessary, condition for time to have had a beginning. This condition implies that any finitely long metricated interval of time, when sub-divided into isochronous sub-intervals, includes a first isochronous sub-interval, e.g., a first hour. But we cannot distinguish finite from infinite metricated intervals in terms of whether they include a first interval, where we’ve set aside whether the intervals are isochronous. For example, consider the past hour. Regardless of whether the past is finite or infinite, there is an interval prior to the past hour, with no interval before it; such an interval is first, but not necessarily isochronous with the past hour. If the past is infinitely long, the first interval is simply infinitely long. There is no interval earlier than the infinitely long interval preceding the past hour and there is no greater interval that ends at the beginning of the past hour.

This is where I agree with Swinburne: instead of regarding a metrically amorphous interval as finite or infinite, we should regard a metrically amorphous interval as neither. This is so for at least three reasons. First, a metrically amorphous interval cannot be divided into ishochronous sub-intervals, since each sub-interval is metrically amorphous. For that reason, we cannot use the most natural or intuitive sense of being finite or infinite. Second, there is no intrinsic non-metrical distinction between finitely long continuous open intervals — such as the open interval between 0 and 1 on the real line — and infinitely long continuous open intervals — such as the open interval between 0 and infinity on the real line. Starting with the two intervals, and stripping away the metrication for both intervals, we are left with two intervals without any discernible differences. For that reason, I don’t understand how there could be intuitively correct definitions of either ‘finite’ or ‘infinite’ that did not make use of metrical facts. And if there couldn’t be such definitions, there cannot be definitions of ‘infinite’ or ‘infinite’ that apply to metrically amorphous intervals. Third, intuitively, an infinitely long interval is one that is longer than any finitely long interval. But there is no way to compare the length of a finitely long interval to the length of a metrically amorphous interval. We cannot say that a metrically amorphous interval is longer than any other interval. Hence, the view that metrically amorphous intervals are infinitely long violates important intuitions about what it takes for an interval to be infinitely long.

Disclaimer: The posts on the Cosmotherium should never be taken as definitive and I am typically not completely convinced of what I post here. This is my place for working out my views without the pressure or rigor of publication.

References

Craig, W.L. 2001. God, Time, and Eternity. Springer.

Craig, W.L. & Sinclair, J. ‘On Non-Singular Space-times and the Beginning of the Universe’. In Yujin Nagasawa (Ed.), Scientific Approaches to the Philosophy of Religion. Palgrave Macmillan, pp. 95–142.