VI. FINITISM – PART ONE

In his Third Meditation, Rene Descartes offered a unique version of Aquinas’ Cosmological Argument for the existence of God. It goes like this. Everything we experience we experience as not going on forever. Even if something could go on forever, we can only experience that part of it that doesn’t. And yet we clearly have the concept of going on forever. So if not from experience, from whence could that concept have come? From something, or someone, who could experience going on forever. What or who could experience going on forever? Something or someone who does. Let’s call that something or someone God. Quad erat demonstrandum.

Descartes considers, but rejects, the suggestion that we could have constructed the concept of infinity by just concatenating the concepts of finitude and negation. But, he asks, what is finitude if not just not infinite? So finitude is the derivative. The primitive is infinity. And since infinity can’t be experienced, the concept has to have come from outside, and therefore beyond, ourselves.

Okay, so as a proof for the existence of God Descartes’ version of the Cosmological Argument falls a tad short of convincing. But it does show, I think, that the concept of infinity is another one of those enabler concepts. That is, it’s not that to say that something’s this big, or lasts that long, entails that it doesn’t go on forever. It’s that its not going on forever is what allows it to be only this big, or last only that long. So though we can debate the provenance of the concept when we’re more at our leisure, at least with respect to infinity being a primitive rather than a derivative, Descartes appears to have been right.

That infinity is among our enabling concepts doesn’t mean we have to believe anything is infinite. It’s true that we can’t imagine space not going on forever. But that doesn’t mean space does go on forever. It’s true that we can’t imagine a beginning of time. Or an end of it for that matter. But that doesn’t mean time has neither beginning nor end. Going on forever is built into our conceptions of space and time. But conceptions are features of the mind, not of the world. Unless, of course, we’re convinced the world must be as we cannot but conceive it. But that would be a risky conviction. I can’t conceive of my not being, therefore I must be immortal? I’m guessing not.

This distinction between the way the world cannot but appear to us and the way the world is in itself – what he called the phenomenal versus the noumenal – was first drawn for us by Emmanuel Kant. Which is not to say the world couldn’t be pretty much as we conceive it. It’s to say only that if it did we couldn’t know it. What we can know, however – and this has got to be reassuring! – is that the world must be such that we can live in it with the conceptual apparatus we have on board. In the parlance, that the world is largely anthropic. Which, come to think of it, it would have to be – wouldn’t it? – since if it weren’t we wouldn’t be here. Call this, if you will, the Anthropic Principle.

How far do we want to push this? Do we want to say that any belief that hasn’t killed us must have been, on that account alone, likely true? We could, if all we want to do is stay alive. But arguably not, if what we want is to flourish. And yet there are – are there not? – beliefs about the world that are probably false but demonstrably helpful. Or at the very least harmless. Or would be harmless provided they keep their distance from anything we’re tempted to try to do in the world to survive and flourish. I believe I can fly. But I also believe flying is a sin. In concert these two beliefs are harmless. So why would you bother disabusing me of these wonky beliefs?

This is precisely why I don’t care about the Holocaust, global warming, or the filioque. Whether it happened or not, what are you going to do about the Holocaust? Call for the dissolution of the state of Israel because it was founded on a Zionist myth? If it’s happening or not, what are you going to do about global warming? Nothing, because it’s a collective action problem. And since we’re not going to act collectively it does no good to act individually. And if the Holy Spirit proceedeth from the Father and the Son rather than from the Father alone, will you be cleansing the village of those damn eastern Orthodox Christians?

So, one might rightly ask, what difference would it make if space goes on forever or it actually comes to an end somewhere out there? Or whether time does or doesn’t have a beginning and end? Or, in short, whether there’s anything in the world that’s infinite? This is not a rhetorical question. As we’re about to see, the difference lies in whether we can or cannot construct a logically consistent ontology.

If it’s then asked, What difference would it make if we can or cannot come up with a logically consistent ontology?, the answer is what logicians call ‘detonation’. By detonation is meant that, if we allow even one p and not-p in our web of beliefs, then there’s no q that doesn’t follow. P and not-p, therefore the moon is made of green cheese. Or worse yet, p and non-p and so it was a mistake to abolish slavery. Or it wasn’t. Since from p and not-p both q and not-q follow, both conclusions are equally valid.

Alternatively, we can avoid detonation, as I suggested above, by not allowing our p’s and non-p’s to come into contact with each other. And we can do this by indexing our beliefs to their respective domains of discourse. So, for example, the sun rises and sets for the purposes of poetry, but the Earth turns on its axis for the purposes of astronomy. The ship of Theseus remains the same ship but only for the purposes of registry. And so on. So we could say that to keep our mathematics consistent we’ll allow that the occupation of space is infinitely divisible, but for the purposes of constructing a consistent ontology we’ll insist that the occupiability of space is discrete.

And that, as it turns out, is precisely what we are going to end up having to say. Now let’s turn to why we need to say it.

Categories: pure philosophy

Tags: Anthropic principle, Cosmological Argument, Descartes, detonation, Emmanuel Kant, filioque, finitism, global warming, Holocaust, infinity