Many philosophers have argued that the past must be finite in duration because otherwise reaching the present moment would have involved something impossible, namely, the sequential occurrence of an actual infinity of events. In reply, some philosophers have objected that there can be nothing amiss in such an occurrence, since actually infinite sequences are ‘traversed’ all the time in nature, for example, whenever an object moves from one location in space to another. This essay focuses on one of the two available replies to this objection, namely, the claim that actual infinities are not traversed in nature because space, time and other continuous wholes divide into parts only in so far as we divide them in thought, and thus divide into only a finite number of parts. I grant that this reply succeeds in blunting the antifinitist objection, but argue that it also subverts the very argument against an eternal past it was intended to save.
This is how it typically goes. If there are an actual infinite number of subdivisions between any two given spatial or temporal points, then transitioning from 'here' to 'there' or from 'then' to 'now' involves doing exactly what the Kalam purports to render absurd. For example, if the space in between me and the door has an actual infinite number of subdivisions, and I can walk to the door, then there's nothing absurd about traversing an actual infinite. Similarly, if the temporal interval between 'the present moment' and a moment, say, five moments from now, then, at every moment, temporal becoming involves the traversal of an actual infinite number of temporal intervals all the time.
Usually, the critic stops here not acknowledging a position Craig has adopted since the 70's: time is continuous, not discreet. This implies that time isn't composed out of individualized intervals that are latent within time's extent. Puryear's tactic is to admit time is continuous but that such an admission spells trouble for indispensable parts of Kalam.
Puryear quotes Craig:
[T]ime, like space, is infinitely divisible in the sense that division can proceed indefinitely, but time is never actually infinitely divided, neither does one arrive at an instantaneous point. If one thinks of a geometrical line as logically prior to any points which one may care to specify on it rather than as a construction built up out of points (itself a paradoxical notion), then one’s ability to specify certain points, like the halfway point along a certain distance, does not imply that such points actually exist independently of our specification of them . . . By contrast, if we think of the line as logically prior to any points designated on it, then it is not an ordered aggregate of points nor actually infinitely divided. Time as duration is then logically prior to the (potentially infinite) divisions we make of it.Craig, then, espouses the idea that time is continuous.
Puryear then argues the following:
... if continuous magnitudes do not divide into parts except in so far as we conceive or specify those divisions, it follows that space is in itself just one thing, that is, an indefinitely extended simple region. As it is conceived by us, space would indeed be divided into a number of smaller regions. But these divisions would exist only in our thought, not objectively or a parte rei. The same would be true of time, and in order to preserve finitism, would have to be true as well of any continuous magnitudes that are traversed in nature.In footnote 5, Puryear argues that this view seems incompatible with Craig's presentism:
As an anonymous referee points out, Craig’s doctrine that time logically precedes the divisions we specify within it raises some thorny questions in connection with his presentism. For instance, why should we think that only present things exist, when the division within time between past and present is merely one we make? Do we determine what no longer exists by the way we divide time in thought? These are important questions, though I will not explore them here.These questions seem benign. As for the first, the answer is yes. It is a division we make between present and past things. I'd prefer to denominate such things in terms of events (Puryear brings up events in a moment). For example, assuming the universe had a beginning, the universe's first moment no longer exists for presentism. But one can still talk about the 'present' extent of the universe, which is about 13.6 billion years in terms of temporal extent. The mind picked out that particular extent as presently occurring. Does this oblige the presentist to admit that each and every part that extent correspond to something that exists (and is, therefore, 'present' in the metaphysical sense)? No. This cosmic extent is presently ongoing. But that doesn't mean that a past part of the extent, say, 1492, corresponds to a presently occurring, and therefore, existing reality. There is, therefore, a distinction between an existing 'present' extent (though even this is misleading since Craig denies - regarding the metaphysical, non-metrical present - that 'the present' has an extent) and a 'presently' existing extent. Presentism need only endorse the latter. The former is what leads to the absurdity that our conceptual divisions determine reality. The latter has no such corollary.
Some terminology from Puryear:
1. Priority of the Whole with respect to Time (PWT)
2. Priority of the Parts with respect to Time (PPT)
3. Priority of the Whole with respect to Events (PWE)
4. Priority of the Parts with respect to Events (PPE)
Puryear argues:
The point I want to make in this section is simply that PWT entails PWE, so that Craig’s endorsement of the former commits him to the latter. I will then conclude by arguing that at several points the finitist argument against an eternal past tacitly presupposes PPE, i.e., not-PWE, so that Craig’s endorsement of PWT in fact undercuts the very argument his finitism was supposed to support.Perhaps you can see what's going on. Craig endorses the argument that it's metaphysically impossible for an actually infinite collection of events to be formed via successive addition. Per Puryear, if Craig thinks time is continuous, it doesn't seem possible for time to be built-up out of the events noted in Craig's thought experiments involving successive addition. If there is a successive addition of 'parts' of time, that seems to negate the idea that time is continuous. Let's finish Puryear's argument and follow it up with what I think are some of his misconceptions.
First, let's consider why Puryear believes that PWT implies PWE.
As changes, events are intimately bound up with time. They take some time to occur, and typically have both a beginning and ending in time. To have a particular example before us, let us suppose that event E is a certain raising of my right arm which begins at t1 and ends at t2. The point I want to emphasize here is that in order for E to be a distinct event—distinct from what was happening with my arm prior to t1 and after t2—it is necessary that t1–t2 be a distinct period of time. But given PWT, there is no such distinct period apart from our conceptual activity: as it is in itself, time is just one long duration, without any temporal parts, not a sequence of intervals that add up to a longer one. It is not due to nature (physis) but to convention (nomos) that t1–t2 is a distinct part of time. Hence, to the extent that there is a distinct event E, it is not because nature divides the history of the universe up into distinct events; rather, we make those divisions by conceiving of history as so divided. Just as in itself time is merely one long duration, on this view it follows that history is in itself just one long event. PWT entails PWE.There are a couple of points worth noting.
1. Events take time to occur.
2. Events have a beginning and ending in time.
3. PWT implies that periods of time depend on conceptual activity.
4. Time (in itself) is one long duration.
5. Time (in itself) is not a sequence of intervals.
6. History (in itself) is one long event.
It's unfortunate that Puryear hasn't read Craig's essay The extent of the present (Journal International Studies in the Philosophy of Science Volume 14, 2000 - Issue 2). The essay would have benefited from it. In it, Craig defends the view that 'the present' (or 'the now') is "a non-metrical notion which must be completed by the mention of some event or interval in order to have a measure, in which case what is present varies with one's context" (Craig, abstract). Craig summarizes his view on a Reasonable Faith Podcast (More Questions on God and Time April 19, 2011) thus:
So the view that I have suggested is the following: that “now” is not a metric concept, and therefore it doesn’t have any intrinsic duration. When we talk about what is happening now we always have to specify the unit of time, or the metric, or the event of which we are speaking. So, for example, it makes sense to talk about the present century, or the present hour, or the present second. [5] It makes sense to talk about the present session of Congress, or the present Supreme Court sitting. And these will have different durations depending on what the word “present” is modifying.
And so I would suggest that there is no such thing as “the now” in terms of picking out a sort of intrinsic unit of duration. Rather, it's ambiguous, and what is now will depend upon the event or the unit that you're characterizing as being now. And when you pick a duration, like the present war, that will be composed of phases that can be delineated as the past phrase, the present phase, and the next phase to come, and those could be subdivided ad infinitum. But those are simply conceptual divisions that we make in the event. I want to say that apart from these conceptual divisions we make that time isn't really composed of points or instants at all. Rather instants are mathematical fictions that we make up when we want to denominate a specific point or instance in time.
I would say the same about the geometrical line. I don't think the geometrical line is literally a composition of points. Rather we can denominate points on the line when we want to specify distances, for example. But I would say the line as a whole is logically prior to any of the divisions that we want to make in it. And similarly the event or the unit that we specify in time is logically prior to any subdivisions that we want to make of it. And so that's the best sense that I can make of this difficult question: there is no such thing as “the extent of the now or the present,” rather this is an ambiguous term that can be applied variously to different events and measures.In the spirit of the above 6 points, let's enumerate 13 more (I'll put an asterisk before the numbers to indicate the qualification that they're Craig's points):
*7. "The Now" is not a metrical concept.
*8. "The Now" doesn't have intrinsic duration.
*9. Talk about "The Now" involves specifying a unit of time, a metric, or an event.
*10. "The Now" is ambiguous (when picking out a unit of duration).
*11. What is now depends on the event specified.
*12. Events are composed of past, present, and future phases.
*13. Such phases can be sub-divided.
*14. Such sub-divisions are conceptual.
*15. Time isn't composed of points/instants.
*16. Specified events/units IN time are logically prior to conceptual sub-divisions.
*17. There is no such thing as "the extent of The Now".
*18. There is no such thing as "the extent of The Present".
*19. The Extent of the Now/Present is ambiguous until applies to events/measures.
Let's see how such points address Puryear's 6 points above. First, Craig would agree with 1 (that events take time to occur). That point is covered by *12. Second, *12 also seems to cover 2 (events have a beginning and ending in time). Third, regarding 3, much depends on what Puryear means by 'periods of time'. In line with *9 and *11, Puryear argues that when specifying the event of "raising of my right arm", "which begins at t1 and ends at t2", "in order for E to be a distinct event.... it is necessary that t1-t2 be a distinct period of time" (Puryear). Puryear supposes that PWT implies that such periods of time are a product of our conceptual activity. Per *12, it seems like Craig could understand 'periods of time' in terms of Craig's 'phases' while not having to identify such 'phases' with Real Time (independent of units of measure, particular durations or metrics or intervals). Fourth, with 4, it depends on what Puryear means by 'time'. If 'Time (in itself) is Craig's Real Time, then 4 is false. For Craig, once a particular duration is specified, the conditions of *12 apply, along with the idea one shouldn't identify *12's phases with Real Time. The phases, along with the events such phases compose, along with any units, measures, intervals, or metric, seem to be the kinds of things that have duration. Fifth, referring to 5, Craig would agree that Time (in itself) - if it refers to Real Time - is not a sequence of intervals. Intervals seem to be instants with intrinsic duration or a metrical concept or a temporal unit. Sixth, per 6 above, is true but benign if *12 is kept in mind.
Let's see if Puryear's expansion on this point subverts Craig's 13 points:
The point can also be made this way: Setting aside spatial complexity, there can only be as many distinct events as there are distinct periods of time. But according to PWT, there is in nature only one period of time, that is, the whole of time. Thus in nature there can be only one event, the whole of history. Any subevents that we conceive within this one large event do not exist as such in nature but only in thought.
Let us illustrate with another example. Suppose hypothetically that the universe has existed from eternity past and that throughout this time there has been a certain planet orbiting a certain star at regular (finite) intervals. Given this assumption, it seems natural to think that this planet’s motion can be described not just as one infinitely long circular motion, but as an infinite sequence of circular motions, each of which began at one time and ended at another. However, this assumes that time naturally divides into this sequence of intervals, whereas according to Craig this is not the case. Hence we may well conceive of the history of the motion of this planet as an infinite sequence of finite motions, but as things are in themselves, there is really only one long motion that we conceptualize as a sequence.First, Craig would agree that the number of events and the number of periods of time would seem to be (at least) the same. If events take time, there is a period of time during which an event occurs. But Puryear seems to misapply PWT to Craig's own views. For Craig, there is not a 'period of time' in nature; in nature (which, for Craig, is Real Time) the Present or the Now cannot consist of a 'period of time' until it applies to events, measures, units, or intervals. Until such an application, Craig argues, the duration of 'Time in Nature' is ambiguous. Thus, 'in nature' (if this is Craig's Real Time) there are no events, for in Real Time the ascription of any duration to such a time is ambiguous until it's metrically circumscribed by an event, even if that event is "the whole of history". Second, regarding the example of the planetary motion in a past-eternal universe, I agree with Puryear that there's a distinction to be made between
- an infinitely long circular motion
- an infinite sequence of circular motions
Puryear approaches this from another direction here - that finitism is committed to PWE:
If we take events to be changes, then they are just as infinitely divisible as time. For any such event, no matter how short, can always be divided into two subevents at any point we like. But if events are infinitely divisible and they are also composed of their (temporal) parts, then they must be not only potentially divisible to infinity but actually infinitely divided. In other words, if the parts are prior to the whole and the whole exists, then the parts must exist. But if the existence of the whole presupposes the existence of the parts, and the parts go to infinity, then there must actually be an infinity of parts. For the finitist, however, this presents a serious problem. For it would entail that any event is in fact an actually infinite sequence of subevents, so that the occurrence of the event involves the sequential occurrence of all the subevents. According to the finitist, however, it is impossible for any such sequence of events to occur. Thus, given that events are infinitely divisible, the finitist is forced to say that with events, as with space and time, the whole is prior to the parts. In other words, the finitist is committed to PWE.There is not much here to disagree with. This is basically a reiteration of the rationale for why finitists opt for PWT and PWE (otherwise, there will be an actually infinite number of sub-divisions). And *16 seems to confirm this anyway. Thus, Craig wouldn't hold to PPE regarding events. As is evident from the Podcast, Craig doesn't adhere to the view according to which temporal intervals are "jumpy", and that "time is composed of little time atoms called chronons" (podcast). Hence, Puryear's discussion of PPE regarding either time or events is superfluous insofar as it applies to Craig. Craig rejects the view. It seems to me that Craig can also (therefore) just reject the relevancy of the view that event-atomicity implies time-atomicity.
At this point, Puryear seeks to apply his insights to what he calls 'The Finitist Argument'. Here's how he presents it (I'll change the numbers of the premises to agree with the numbering in this blog):
20. If the universe did not have a beginning, then the past would consist in an infinite temporal sequence of events.
21. An infinite temporal sequence of past events would be actually and not merely potentially infinite
22. It is impossible for a sequence formed by successive addition to be actually infinite.
23. The temporal sequence of past events was formed by successive addition.
24. Therefore, the universe had a beginning.Puryear claims that PWE 'undermines' 20.
For if events do not divide into parts except in so far as we divide them in thought, then we must admit that just as time is in itself merely one long interval, the history of the universe up to the present is in itself just one long event.
To the extent that it forms a sequence of events, it does so only in so far as we divide it into parts, and since we can only divide it a finite number of times, it forms at most only a finite sequence.
It might be supposed that the past could be divided into subevents en masse simply by specifying a way of dividing it into events of a certain duration; for instance, we could stipulate that the past divides into consecutive events lasting one second each [cf. Craig and Sinclair 2009: 106].
Regardless of what duration we chose, it would follow that if the universe had no beginning, the past would consist in an actually infinite sequence of such events. This, however, will not work.
As I noted in §3, the finitist reply advocated by Craig can succeed only if it requires that divisions be individually specified, since otherwise it would be possible to specify an actual infinity of divisions within a finite region of space or time, in the way suggested by Morriston [2002: 162].
But the very same move that allows the finitist to block Morriston’s objection also prevents the finitist from using a similar strategy to specify an infinity of divisions within the history of the universe.
Hence, given PWE, premise (1) of the original argument is false. Even if the universe had no beginning, it would not follow that reaching the present involves traversing an infinite multitude. At most it would require traversing an infinite magnitude, something to which finitists have typically raised no objection.I don't feel the sting of this objection at all and I fear it's because I may be misunderstanding it. It seems to me that the finitist is engaging in a reductio of sorts. That is, assume (per impossible) that the universe is past-eternal. If it is, then, even if PWE or PWT is the case, it would still be possible to conceptually sub-divide such an interval/metric/extent/unit/period into an actually infinite number of parts only if the subdivisions involve an actually infinite number of arbitrary, but equal, non-zero, finite intervals (etc.) regressing into the past. This is the kind of infinite regress that is conceptually possible (after all, Craig affirms the mathematical legitimacy of the actual infinite) assuming (per impossible) that the universe is past-eternal (where the impossibility is broad logical impossibility). But what is neither conceptually nor broadly logically possible, is engaging in a series of subdivisions wherein the intervals are not all finite, not equal, not non-zero, and/or not arbitrary. This impossibility is due to PWE/PWT.
Puryear also argues that PWE spells trouble for 21:
For if the universe had no beginning, and its history is in itself just one long event which we divide in thought, then the temporal sequence of past events into which that history divides would not be actually but only potentially infinite.
It would be actually finite, but always further divisible and thus potentially infinite. From this point of view, Aristotle and Aquinas were in a sense right to hold that an eternal past would be only potentially infinite.This strikes me as obscure. I am to believe that the history of the universe is and is not an actual infinite. It is an actual infinite in terms of its analogy with infinite spatial extent (I think); it is not an actual infinite in terms of being composed of an actually infinite number of intervals (as Craig specifies they have to be). I believe what I said above undermines this worry. The conceptual subdivisions have to be specified when applied to the history of a past-eternal universe and this seems to me to be wholly compatible with PWT/PWE. For Craig admits that one's conceptual bracketing of the history of a (per impossible) past-eternal universe is itself a whole that is logically prior to its parts. One then applies a specific "way of dividing" events "of a certain duration", where that "certain duration" is specified in the way Craig has specified it. Once the specification is conceptually applied to one's initial conceptual bracketing, you have conceptually delineated what wasn't there before (and so the composition is a conceptually created composition that didn't exist prior to the conceptualization), an arbitrary, but equal, non-zero, finite collection of intervals that compose the initial conceptual bracketing temporally posterior to the application of the specification for subdividing the initial bracketing. That there is a temporally posterior composition doesn't seem to me to contradict PWE/PWT in the least. To me, the composition has to come before the specifications we make - and the specifications have to be a certain way. If the specifications are another way, and the composition comes after the specifications, it seems to me that PWE/PWT isn't threatened at all. Therefore, premise 21 seems to be in good shape.
Puryear also claims that PWE "undercuts" premise 23.
To characterize the past as a sequence of events formed by addition is to presuppose that the parts are prior to the whole (PPE). But if the whole is in fact prior to the parts, then the temporal sequence of past events is not formed by addition but by division.What I've said above undermines this as well. It's not necessarily the case that a sequence of events formed in the relevant way involves PPE, as I just argued above. And therefore it doesn't seem to me to be necessary that the temporal sequence Craig is emphasizing involves division, rather than addition.
In the next blog, I'll respond to Puryear's follow-up essay: Finitism, Divisibility, and the Beginning of the Universe: Replies to Loke and Dumsday.
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