May 30, 2010

Past and Future in the Kalam Cosmological Argument

Dr. Craig,

When you came to our school last March to debate Richard Carrier, our philosophy professor Richard Field intended to speak with you about the kalam cosmological argument. He never had the opportunity to have that discussion with you, but he recently passed along his thoughts to me and I told him I would send them to you and let you respond. I'll quote his rather lengthy comments below:

"Again, my response to the argument is that past events are not actual, so the question of whether an actual infinite is possible or not simply doesn't apply to the past. On an intuitive level this certainly seems right. My eating of my breakfast this morning is not an actual event. Neither is Caesar's crossing of the Rubicon. These are events of the past, and as such they are not actual. A common expression, of course, might suggest differently. I can say with perfect sense that "I actually ate my breakfast this morning." But we can quickly put this aside by noting that the word 'actually' is only used for emphasis. I can equally say that "I will actually eat breakfast tomorrow morning" where clearly I am not speaking of an actual event, to which Craig/Sinclair would agree.

The relevant section of the article you sent me is 2.12. First I am surprised that they write "The point is obvious enough . . ." (that an infinite regress of events would be an actual infinite). If one appeals to what appears obvious, as I noted above, I think the situation is quite the opposite. I think it is rather obvious that I am not actually eating my breakfast, when the term 'actually' is used in an ontological rather than an emphatic sense. But let's move on. They curiously appeal to McTaggart's B-series to claim that "there can be no question" that an infinite regress of events would be actually, when in the preceding section they argued against the view that relativity theory establishes the B-series as fundamental. I suppose this was simply aimed at completeness.

But then they raise the question "whether events' temporal distribution over the past on a presentist (A-series) ontology precludes our saying that the number of events in a beginningless series of events is actually infinite." So here it seems is the beginning of the core of their response. First of all, they point out that on this view past events still are countable. I fail to see the relevance of this point, since I fail to see the inferential route by which one gets from "x is countable" to "x is actual." Indeed, NOAA every year counts the number of likely hurricanes that will occur during the coming season. One might object that these are estimates only. But note that Craig/Sinclair's response to the nonexistence of past events is quite appropriate here as well: "any obstacle here is merely epistemic, for aside from considerations of vagueness there must be a certain number of such things." Yes, this is true whether you're talking about past or future hurricanes. They then bring up Aquinas' example of a blacksmith who from eternity has used and broken successive hammers. Well, this shifts the question to that of whether said blacksmith has available to him an infinite amount of material to create an infinite number of discrete hammers. Craig and Sinclair would have to say "no." This would imply an actual infinite, so the blacksmith would necessarily have to recycle. They seem to try to dodge this by saying the present existence of the hammers is irrelevant. Even if all the hammers were destroyed "the number of hammers broken by the smith is the same." Indeed, this would be an infinite number. But the issue here is not the number of hammers involved, but whether they are actual or not. This is all simply red herring.

In their next paragraph the respond to an objection that basically if one must take the past to be an actually infinite, doesn't one have to take the future as such as well. Since this isn't positive argument but simply response, there is no need for me to respond, and I don't find much of anything objectionable in the discussion in any case. But there is one curious sentence that I might point out: "the series of events earlier than an arbitrarily selected future event cannot properly be regarded as potentially infinite." Yes indeed! But whoever said that if the past is not an actual infinite it must be a potential infinite? Why not a nonpotential, nonactual infinite?

This is where I think the root of the problem lies. In an Aristotelian framework we have the actuality/potentiality distinction. Readers of Aristotle can get the impression that this is meant to be an exclusive distinction: if something is actual it is not potential, and vice versa. I don't recall Aristotle ever saying such a thing. The authors attribute such a view to Aristotle. I'll have to look up the reference, but I rather doubt he said any such thing. For Aristotle potentiality had to do with possibilities that might be actualized in a thing, whether they are eventually or not. On this view nothing in the past is potential since there is nothing to realize any such potentialities. Caesar has long ago relinquished his potentialities simply by the sheer fact that he died. So there is nothing that requires that if a thing is nonactual it must be potential. I find this notion rather absurd, and the absurdity is clearly shown by suggesting that past events are potentialities. But by the same token this doesn't require us to say that the past is actual. It is neither actual nor potential. It simply isn't in any manner.

Recall that for Aristotle the potentialities a thing has are determined by what it actually is. I am potentially musical because I am human, and humans have this potentiality. My dog Fetch does not have this potentiality because she is a dog. It follows that if humans (and barring any intelligent aliens) didn't exist then the potentiality for musicality wouldn't exist. "Being musical" would be nonactual and nonpotential. One might object on an Aristotelian basis that human beings would still be a possibility, and since we are made of, inter alia, water and carbon compounds, then these would have the potential of being musical. But nonetheless, there would be no things having this specific potentiality, and thus this specific potentiality would not exist. The fact that it could come into existence is no objection. The possibility of a potentiality is not the existence of that potentiality.

Getting back to the status of the past, Craig and Sinclair's arguments notwithstanding, I see no conceptual barrier to an infinite past. Consider this question: is there anything about any moment of time that precludes there being a previous moment of time? Aristotle argued that in fact any moment of time requires a previous moment. I'm not sure I can accept that, but I am quite sure that moments of time do not preclude predecessors. Well if this is true it must be true of all past moments of time, which allows for an infinite past. Or we can offer the same argument more concretely. Is there anything about a given event that precludes previous events? Again I would say no, thus allowing for an infinite past series of events. Now there is an old theological view according to which every state of the world at any moment is independent of every other state of the world at other moments, thus requiring God as a sustainer of the world. This would suggest that absent God no current moment could have a predecessor. Even Descartes felt compelled to offer such an argument. But apart from offering compliments to God I see no reason to believe this, and in fact our common sense says quite the opposite, and I think quite the opposite is true. Present states of affairs very much depend on past states of affairs. My existence very much depends on my parents getting together and doing all the right things, and so it is generally true of things of the world."

Sorry again about the length of the comment, but hopefully it has given you plenty of content to respond to.



Nice to hear from you again, Landon! I trust your doctoral studies are going well.

Your professor's objection to the argument against the infinitude of the past has been pressed by a number of contemporary critics, including most prominently Graham Oppy and Wes Morriston, to whom I have forthcoming replies in International Philosophical Quarterly and Faith and Philosophy respectively.

Now in the first place we need to get clear on what the issue before us really is, especially since I think your prof is not altogether clear about this. The question simply is: if the series of distinct, past events is beginningless, then how many events have occurred prior to the present event? It seems to me that the answer is obviously "an actually infinite number" of events.

That this answer is correct seems perspicuous on a so-called B-theory or tenseless theory of time, that is, a view of time according to which all events in time are equally real and temporal becoming is merely a subjective feature of consciousness. The number of past events in a beginningless universe on such a view would be obviously actually infinite, since it would be akin to a spatial array of items. But now introduce temporal becoming. Why wouldn't the number of past events be exactly the same? After all, they're the same events!

Aristotle and his medieval progeny like Thomas Aquinas sought to avoid this conclusion by claiming that the number of past events is potentially infinite, since past events no longer exist. But this answer strikes me as plainly wrong-headed: in order for the past to be potentially infinite, the series of past events would have to be at every point finite but growing toward infinity in the earlier than direction, which is absurd, contradicting the nature of temporal becoming. While the series of future events from any past/present point might be said to be potentially infinite if time goes on forever, that description cannot apply to the series of past events.

Neither could we say that the number of events that have occurred prior to the present event is finite, for that would imply that the series of past events had a beginning, Q.E.D.

But "actually infinite," "potentially infinite," and "finite" seem to exhaust the alternatives in answer to the question before us. What other alternative is there? I don't even know what your prof means by a "nonpotential, nonactual infinite." Since the only types of infinite that there are are the actual infinite and the potential infinite, his claim sounds logically incoherent.

Now the sort of absurdities I mention with respect to an actually infinite number of things don't depend, as your prof seems to think, on the things' all existing at the same time. To use the simplest example, in an infinite series of past events, the number of odd-numbered events is the same as the number of all the events, even though the latter collection includes all the odd-numbered events plus an infinite number of even-numbered events as well. Whether or not you agree with me that this is absurd, the alleged absurdity has nothing to do with the items' all existing simultaneously.

Now here's where things get really interesting. The critic (though not your prof) usually retorts, "All right, if the number of past events in a beginningless series of events is actually infinite, then the same is true of the number of events in an endless series! So if the argument against the infinitude of the past is sound, then neither can the future be infinite."

Now I agree that on a B-theory of time the difference between past and future is inconsequential, so that the argument would apply to both series. But note that this consequence of the argument does nothing to refute the argument; it merely occasions theological problems for the person who believes, as Christians do, that the future is endless due to, say, personal immortality.

By contrast, on an A-theory or tensed view of time, according to which temporal becoming is an objective feature of reality, the asymmetry of time wrought by temporal becoming becomes metaphysically significant. On a tensed theory of time, it makes sense to say that the series of events later than any event in the past/present is merely potentially infinite, that is, at every point finite but growing toward infinity as a limit. It is far from clear that the A-theorist is unable to draw a meaningful distinction between the actuality of the past and the potentiality of the future. Future events have not as of yet been actualized, whereas past and present events have been actualized. It might be said that if the future is endless, then there will be an actually infinite number of events. But on a tensed theory of time that is false: there will never be an actually infinite number of events. The number of events will always be finite but growing toward infinity as a limit.

By the way, this purely philosophical reasoning for the potential infinity of the future has begun to penetrate physical cosmology as well. Take a look at the fascinating article "A Note on Infinities in Eternal Inflation" by George Ellis and William Stoeger (available online at http://arxiv.org/abs/1001.4590v1 January 27, 2010), especially the closing paragraphs. Really interesting stuff!

Finally, note that in his final paragraph your prof seems to commit a logical fallacy. He infers that because

1. For any event, it is possible that that event have a predecessor [(x) ◊ (∃y) (y < x)],

it therefore follows that

2. It is possible that for every event there is a predecessor [◊ (x) (∃y) (y < x)].

But this is a mistake; for any event you pick, it's possible that there be one event prior to it; but that in no way implies that it's possible that all events have predecessors.