VII. FINITISM – PART TWO

The issue here is Zeno’s Paradox and how to resolve it. To get from here to there I first have to cover half the distance, then half the remaining distance, then half the distance still remaining, and so on. And so, because this goes on ad infinitum, I can never get there. In fact I can’t even cover that first half, or the first half of the first half, and so on ad infinitum. In fact I can’t seem to move at all! So, concluded Zeno, either motion is an illusion, or else we have to radically rethink how motion is possible. Since I do get from here to there, it follows that motion is possible. But how?

The answer, I submit – and I’m not entirely alone in this – is that though space is infinitely divisible, the occupiability of space is not. That is, an object doesn’t move through space. It appears here, and at the next moment it appears in the space immediately adjacent to it. So what we count as movement – and we know this from how films are made – is actually just a series of stills, presented to us in succession with sufficient rapidity that we don’t notice. Why not? Because we can’t. Because the duration of each still, though finite, is too short for any cognising agent to capture.

So yes, motion is an illusion, but the illusion is made possible by the nigh-but-not-infinitisemal atomicity of the occupiability of space and the nigh-but-not-infinitesimal atomicity of time. Is this plausible? Of course not. But it does solve Zeno’s Paradox. And so plausible or not, and break our teeth on it though we must, we seem to have no choice but to embrace it. Space is infinitely divisible, but there’s an atomicity to it such that nothing can be partially in partially out. Time is infinitely divisible, but there’s an atomicity to it such that nothing can be only partially obtaining at that moment. In short, it’s stills all the way down.

This speaks to the atomicity of space and time. But what about their external dimensions? Does space go on forever? Yes, but the occupiability of space does not. That is, there’s a point beyond which there can be nothing. Yes, time could go on forever, were it not that there’s a moment beyond which nothing can change. But since time is a measure of change, where everything is at a standstill, so is time. There are, to be sure, realists about time, according to whom time is not a measure of change. It’s a measure of, well, itself. But if so, how could the passage of time be measured? And if it can’t be measured, in what sense is it passing?

Too quick. Nothing in our bite-the-bullet solution to Zeno’s Paradox says anything about why there has to be a point beyond which there can be nothing, or a moment beyond which everything is at a standstill. So the arguments for the necessity of those two claims – their necessity for constructing a consistent fundamental ontology – will have to go on the back burner, at least for now. But we will get back to those two arguments, assuming – I am, after all, 74 – the flag doesn’t fall on these deliberations before I get there.

Categories: pure philosophy

Tags: atomicity, finitude, infinity, occupiability, space, time, Zeno's Paradox