### The Kalam Argument, Zeno's Paradoxes, and Omniscience

In my previous post on this topic I argued (a) that Craig's argument against the possibility of actually infinite collections of real things doesn't work given presentism, and (b) Craig's argument against the possibility of traversing an actually infinite series in finite, step-wise fashion doesn't work given a B-theory of time.

My post generated quite a discussion among three of my commentators (Tom, HammsBear, and Don Jr). In this follow-up post I'd like to address a couple of the issues they raise.

1. The first issue concerns (a). Both HammsBear and Tom suggest that, given my proposal that presentism works best when combined with a version of theism in which God's memories provide truthmakers for truths about the past, Craig's first argument would work against a presentist who held that time had no beginning for that would mean that God has an actually infinite number of memories of past events.

Frankly, I don't see this as a big issue. It seems to fare no better or worse than another challenge to Craig's argument, namely, that an omniscience God would have to know an actually infinite number of propositions (e.g., 1+1=2, 1+2=3, etc.). Hence, either Craig's argument works, in which case it implies that God cannot be omniscient, or we have to conclude that the argument doesn't work. But this seemingly nasty dilemma has, I think, a straightforward reply: God's knowledge is a single unified gestalt - in one cognitive act he grasps all there is to know about all there is to know. Thus, we shouldn't think of God's knowledge as built-up piecemeal from atomic propositions but rather as a continuous field that contains all true propositions virtually, from which particular truths may be distinguished by abstraction. In much the same way, a continuous geometrical plane is not built-up out of discrete points but is a field within which endless numbers of points may be picked out by abstraction. This is not a new proposal, by the way, but the classical way of thinking about God's omniscience.

2. The second issue concerns (b) by way of Zeno's paradoxes of motion. Do these paradoxes imply that there is, say, an actually infinite number of spatial points between any two locations, or an actually infinite number of events between any two times? If so, then any sort of change or motion would require traversing an actually infinite collection in stepwise fashion.

One response (proposed by HammsBear) is finitism - space and time come in finite indivisible quanta. This view (defended by A.N. Whitehead) deals nicely with Zeno's paradoxes - if correct, then between any two places there can only be a finite number of places and between any two times there can only be a finite number of events. On the other hand, finitism is very counter-intuitive. First, even if Planck time shows that there is a physically minimal quantum of time, it is metaphysically possible that that quantum be smaller, indefinitely. So in some other possible world the quantum is smaller, and so forth for any non-infinitesimal quantum. What, then, makes the quantum the size it is? Second, imagine two quantum-sized particles travelling in a parallel line in the same direction, with the first going exactly twice as fast as the second. Suppose they both start at (t0,x0). Clearly, when the first particle is at (t4,x4), the second one will be at (t2,x2), but where is the second particle when the first is at (t3,x3)? It seems that it would have to be between (t1,x1) and (t2,x2). By hypothesis, however, no such location exists. That's weird.

A second response to Zeno's paradoxes, and the one I favor, is the one proposed by Aristotle. Basically, Aristotle introduced a distinction between actual and potential infinites (the same distinction Craig uses in the kalam argument). The number of points between any two places, said Aristotle, is potentially infinite in that it is endlessly divisible, but not actually infinite. In other words, continuity is metaphysically prior to discontinuity - discontinuities can only exist in a more fundamental continuity. Here's a mathematical analogy: What is more basic, the line or the points on the line? Aristotle would say the line. Points have zero dimension, so you can string them together end to end and never build up a line of any length whatsoever. You could, of course, pick a point and drag it, thereby defining a line segment, but to drag it in the first place there has to be some kind of continuous field in which to drag it.

Of course, this doesn't remove all the perplexity behind Zeno's paradoxes, but either approach, Aristotle's or the finitist's, would give us a way to avoid countenancing an actual infinity of spatial places or temporal events.