Littlejohn on Kalam

Hey Matthew,

I'm happy to see we are in agreement here. I'm not sure I want to go down in history as the guy who coined the phrase 'Infinity is, like, weird' though.

Your phrase is now stuck in the Google cache for all eternity. You may have more theist supporters than you think. It seems that any theists who conceive of God as eternal in the sense of everlasting are going to want to reject Craig's arguments against actual infinites. As a bit of additional help I see that Morriston actually has a number of papers relating to the Kalam argument.

Just to be clear I'm not against the Kalam argument per se, but Craig's defense of the second premise that the universe began to exist. I do believe it is true that the universe did begin to exist, but Craig's argument fails to show this.

While I don't find the Kalam argument convincing at all, I think it also comes in for an unfortunate amount of unfair criticism. For instance, the inconsistency it claims to locate is not an inconsistency with regard to sets but an inconsistency with regard to actually existing sets of determinate members. In other words, the claim is not about mathematics at all, but about existence. And it is not at all obvious that actually existing sets of determinately existing things can be set in correspondence with each other so as to violate S1 or S2. (I don't see that the reverse is obvious, either, but merely saying, "Oh, but we're talking about infinite sets" isn't going to make the matter any clearer.)

John Byl's paper (a critique) On Craig's Defence of the Kalam Cosmological Argument might also be of interest.

Brandon,

I agree that Craig is trying to make a point about existence. The point I was making in my post, which as far as I can tell is pretty much the same point John Byl is making in his paper, is this. Craig asks us to imagine a library consisting of an infinite number of volumes. He points out that there are strange implications. While these implications are puzzling, people have the same sort of intuitive puzzlement when they are told that the evens can be put in 1-1 correspondence with the odds as well as the naturals. As this is clearly possible (though unintuitive) doesn't this just undercut the argument from intuitive oddness to impossibility that Craig is after? In other words, even when we drop the assumption that the objects we are dealing with are actually existing concrete objects, the implications are, well, odd. Why then think existence is the culprit? Perhaps our best empirical evidence does suggest that there is but a finite collection of moments, but the thought that a purely conceptual argument could demonstrate this is, I think, highly dubious.

Clayton, that doesn't seem very convincing to me; one could very well argue that the reason people find the 1-1 correspondence of evens and natural numbers is precisely their intuitions about what can actually exist. In short, the reason there is the same oddness is that in both cases we find it difficult to think of anything actually existing like that. This wouldn't be a problem for the purely mathematical case given reasons for accepting an actual mathematical infinite; but it would still leave the problem with the question of an actual physical infinite, since the reasons for accepting the actual mathematical infinite are not reasons for accepting an actual physical infinite (since the former is abstract rather than real).

Brandon,

I think I see what you are getting at, but I'm not at all clear why people's intuitions about what could exist would stand in their way of grasping mathematical claims. Anyway, that such intuitions would stand in the way of their grasping true mathematical claims would suggest that their intuitions in this area are wonky and not to be trusted. Further evidence that intuitions in this field are not to be trusted is this. I suspect that many people who succumb to the sort of argument Craig offers are also disposed to endorse the sort of reasoning for the infinitude of space supported by the Lucretius' spear thought experiment. I put it to a test last night in a room of about 100 people and predictably they thought the assertion that space was finite was absurd. That people are so tempted to endorse that line of reasoning suggests that people have contrary inclinations and as such those inclinations are not to be relied on when doing metaphysics.

While your point that reasons for accepting an actual mathematical infinite are not reasons for accepting an actual physical infinite is fine, isn't it important to remember the dialectical situation? We are looking for reasons to deny that there could be an actual physical infinite. Craig says he has some. That is what Craig's argument is intended to establish. Undercutting it in no way depends on demonstrating the possibility of an actual physical infinite but rather undermining alleged demonstrations of its impossibility.

I don't see how this threatens the Kalam argument, though, at least if we trust our best physics, which tells us the universe began to exist and came to exist from nothing. That's pretty much the standard view, and it gives us everything Craig wanted to establish with his denial of the results of our best mathematics, which was developed by Leibniz, by the way, who himself accepted a form of cosmological argument, just not one that assumes a finite past. Samuel Clarke and Thomas Aquinas had also offered pretty much the same argument before Leibniz, so it's not new to him, but my point is that he clearly thought an infinite past theoretically possible and still thought the cosmological argument goes through.

Jeremy,

Doesn't it threaten a version of the Kalam argument? In particular, doesn't it threaten the purely conceptual version that Craig was trying to run? Of course nothing said here threatens an aposteriori version and it may well be that given our best empirical evidence, the universe has a finite temporal dimension, but that is a different argument. (I would quibble, however, with the suggestion that it is part of the best theory that the universe 'came to exist' from nothing. It seems that there are philosophical interpretations of the empirical data according to which there is a natural but necessary entity. Moreover, the language of coming to be suggests temporal passage, but with no time to pass prior to the Big Bang, reading scientific accounts of the Big Bang in this way would be akin to saying that we could head North from the North Pole. Anyway, as it is near impossible to speak intelligibly without using temporal language, maybe nothing really hung on that remark of yours?).

You are right too in pointing out that there are versions of the cosmological argument that are completely independent of whether there has in fact been an infinite collection of times. Aquinas from what I can recall in fact rejects the possibility of providing a purely conceptual argument for the finitude of the past.

Clayton, it seems to me that people's intuitions about what could actually exist fairly commonly interfere with their intuitions of mathematics; indeed, it seems to me that they have arguably done so in the case of mathematicians themselves (as witnessed by the history of imaginary numbers, or of the infinite itself, and so forth). If people have difficulty making sense of what it would be for something actually to be X, they have difficulty making sense of the mathematics of X. Nor need this imply anything whatsoever about those same intuitions in the area of actual existence itself: all one has to argue is that in the mathematical case the intuition is illegitimate because it is not an intuition of mathematical existence but of actual existence; but that this does not follow in the case of actual existence, since the intuition is an intuition of what can actually exist and therefore not mis-applied. In other words, your argument treats the intuition as equally wonky in both cases; but one can just as easily interpret its wonkiness in one case as being due to an illegitimate transfer from a non-wonky case to which the intuition really does apply.

The problem I have with your argument (it's admittedly a problem I have with Craig's argument as well) is that it appears to make use of an uncritical appeal to intuition (Craig in one way, you at a meta-level) without in fact investigating the nature of the intuition itself. Without an account of the nature of the intuition itself, neither argument actually moves anywhere; the conditions and circumstances under which the intuition are legitimate (if any) are simply guessed at. Whether the intuition is wonky or not can't be decided under such circumstances. And likewise, the interpretation of your group's answers will depend on what one's view of the nature of the intuition is, and what its provenance is. Because it's that which will tell us whether we're getting any cross-contamination from other (mis-applied) intuitions or not.

On the issue of demonstration, Craig's arguments that an actual infinite is impossible always proceed by identifying some property of the infinite and insisting that it's obviously absurd for that to be the case with actual, determinate existence. I see no way to undercut this unless by giving a reason to think that it's not absurd; that people get confused about transfinite mathematics, for instance, is no reason to deny that there are real intuitions of absurdity in such mathematics. At most it means that we need to filter out contaminating intuitions in order. But again, whether an intuition is contaminated by other, mis-applied intuitions depends on the nature of the intuition in that given case.

Jeremy: I agree that a cosmological argument can go through even in the case of an infinite past -- indeed, I think all the best ones do.

Interesting thoughts all around. The standard response to Craig seems to be "Yes, the infinite is weird, but that's the nature of the infinite." After all, the classical concept of God involves seems to involve some counter-intuitive notions as well.

It seems to me that a successful rebuttal to this type of argument would explicate the internal contradictions in the notion of an infinite series. In other words, it would show, first, how an infinite series must still be a series and necessarily possess some standard properties, like have a definite number of members which themselves have definite properties. Second, it would show that no such series could also be infinite.

Take the claim that, "Typically we think of 'has more members' as meaning has a greater number, but this makes no sense when talking about infinites." If "more" does not refer to a greater quantity, then what does it mean? It seems that a fundamental property of any series is that it involves quantity, and "more" is synonymous with "greater than". A series which had more members than another and did not have more members than another would be a contradiction.

Cheers,

Dave