Philosophy and Science – let the healing begin

The title is a bit of a joke; I was thinking of this book title, which strikes me as kind of amusingly ham-fisted.

But clearly philosophy and (natural) science have a strained relationship. Most scientists I know are fairly disparaging about philosophy. Pure mathematicians tend in my experience to like philosophy and, not coincidentally, to actually know what it is; what they do is similar in many ways. I can’t really blame scientists for their attitude, however, since the kind of philosophy to which they tend to be exposed is the kind least likely to interest or impress them.

Take, for example, this video, in which Angie Hobbs and Mary Midgley do a very poor job of trying to convince Laurence Krauss that philosophy is useful for physics. I’m not really sure that what either of them popularizes as ‘philosophy’ has much to do with the kind of philosophy I like, but my purpose here isn’t to denigrate their work. It’s just difficult to see how any philosopher could have a hope of convincing a physicist on this point without having a far stronger background in physics, or at least in mathematics, than either of these disputants appear to have. Why not use Nancy Cartwright (I mean this Nancy Cartwright, not Bart’s voice on The Simpsons)?

The strategy Hobbs and Midgley employ also seems wrong to me. Somebody like Krauss isn’t going to listen to long convoluted arguments about the deep interconnectedness of all thought or the supposed distinction between Being and beings (?!). Most likely he just wants at least one example of how philosophy might decisively contribute to physics. Such examples are rare but not impossible to find. Let me just quote (with slight modifications) an earlier post in which I described such an example as explained by Michael Dummett:

Modern physical theories represent various physical changes as functions, taking real numbers representing temporal instants as their arguments. But if one holds a classical view of mathematics, it is mathematically possible for such functions to be discontinuous; one could have, for example, a variable oscillating an infinite number of times within a finite interval. Physicists have no compelling way of proving that this does not or cannot occur. By contrast, Dummett notes, ‘in the “intuitionist” version of mathematics proposed by Brouwer, a function defined on all real numbers will be demonstrably continuous’. Thus an intuitionist rather than a classical version of mathematics might provide physicists with an explanation for the impossibility of changes represented by discontinuous functions, something that is otherwise not well explained in their theories. Yet, Dummett points out, physicists almost universally ‘ignore or are unaware of constructive [including intuitionist] mathematics’.

So maybe they’d benefit from doing some more philosophy of mathematics. If the arguments for constructivism are compelling, this could serve physics indirectly by providing an explanation for the absence of discontinuous functions in nature. This is only one very small and somewhat esoteric example. But the claim that philosophy has NOTHING to offer to science is a negative general claim, and a single example suffices to refute a general negative claim. Even for a constructivist.

So let the healing begin.

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