February 1, 2014, by Stephen Mumford

An Unknowable Truth

We have to be humble sometimes and admit we are not capable of knowing everything that is true. This should be uncontroversial for surely there are many truths about the past all evidence of which is now erased. It is either true or false that a dinosaur sneezed on this exact spot 100 million years ago, for instance, but we have no way of knowing which.

It’s worried me for a long time, however, that there are even truths about the way the world is now that are in principle unknowable. During my PhD studies, I chanced upon the following problem. The world might be made up of smallest possible entities, such as hadrons and quarks. Such entities might be absolutely simple, containing no smaller components. Or the entities of the world might all be complex, containing ever-smaller and smaller constituents, all the way down, infinitely. Some call this latter possibility a gunky world where there is no bottom level of smallest possible things, but always something even smaller.

Philosophy doesn’t seem able to tell us whether the world contains smallest components or is gunky with unending smaller entities. Philosophy deals with a priori reasoning and there seems no principle of reason that dictates either that there are smallest things or that there are no smallest things.

Now when unaided reason fails to tell us the truth, we usually say that we should turn to empirical science, which is a posteriori: knowable only through experience of the world. But there is little comfort here on the question at hand. Bertrand Russell pointed out that while we can know that something is complex, we can never know that it is absolutely simple. When we think we have found the smallest entities, such as electrons, we cannot be sure that they are genuinely simple or that they contain hidden complexity. So when we think we have a smallest possible thing, we still need to bombard it with particles and try to split it apart to see if it has hidden components, as done at CERN in Geneva. But even when we fail to split something, we still cannot be sure it’s not just a very tough nut to crack, keepings its inner parts secret from us. It appears, then, that we also cannot know empirically whether the world is built form smallest possible things or everything has smaller components within.

This puts us in an uncomfortable position. The two options I’ve outlined seem coherent. The world has to be one way or the other. But we cannot know which account is true either a priori or a posteriori. Neither philosophy nor science can give us a definitive answer and nor is it clear that they could do so if they worked together.

I’ve no doubt that some will say none of it matters. If we have no way of knowing which of two options is true, there are those who say it’s a meaningless choice. Some of us don’t think that, however. That there are unknowable truths, beyond our capability of grasping, fills us with a sense of awe and wonder. And a bit of epistemic humility, after all, is no bad thing.

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