Philosophical paradoxes

An example of a heuristic is that we use colour boundaries to judge the edges of physical objects in our environment. That's something that we do automatically. We're not aware of doing it, but it's built into our visual systems, and it's not completely reliable. What reveals that, for example, is the use of camouflage in warfare, where you can induce illusions about the layout of objects by camouflaging things, by painting shapes on them where the colours don't correspond to the shapes of the underlying objects.

I think something similar is going on with philosophical paradoxes: we are using heuristics that are built into the way that we think, and we're not aware of using them. And they can lead us into trouble, often into contradictions.

The paradox that it leads to in philosophy is what is sometimes called the Sorites paradox, or the paradox of the heap. If you imagine a heap and then imagine taking one grain away from the heap, you can ask the question: is what's left still a heap? The obvious answer is yes. And that gives you the principle that subtracting one grain from a heap of sand, or whatever it happens to be, still leaves a heap.

But of course, that principle, if you apply it often enough, leads to disastrous results. If you subtract grains of sand from a heap, sooner or later — because there are only finitely many of them in the heap — you will get down to three grains and still be saying it's a heap.

We get into this paradox because we're just applying the same heuristic over and over again. It gives the right results, as it were, 99% of the time. But it's not 100% correct.

Often you can get a very close fit by complicating the theory a lot, by, as scientists say, using lots of parameters. But that kind of very close fitting tends to go badly, because you're fitting to data that are not all correct. And so what turns out to be a better approach in science is to go for much simpler theories, even though they don't fit the data as well as the more complicated ones. In the long run, that means that you're not building the errors from the data into your theory.

That's something that philosophers are not used to doing. Philosophers often are willing to make the theory very complicated in order to accommodate all the data. That is not good scientific practice. And I think that philosophers can do better in handling this kind of problem — that some of the data we are using may be wrong. If we go for simpler theories and don't allow ourselves to complicate and complicate in order to fit the data, that is better scientific practice. And it's quite relevant to philosophy as well.

Editor’s note: This article has been faithfully transcribed from the original interview filmed with the author, and carefully edited and proofread. Edit date: 2026