Philosophy

What good is it to study philosophy? I have always wondered what it is that philosophers have actually accomplished. For example science marches on without need for philosophy of science. The philosophy of mathematics is almost completely useless to a working algebraic topologist. If philosophers are really concerned about the world, why not study mathematics, natural, social science, etc?

Comments

I'm sure that you are right: most algebraic topologists don't give a moment's thought to what goes on in the philosophy of mathematics. But that's only fair: most philosophers of mathematics don't give a moment's thought to the nitty gritty of algebraic topology (well, maybe there are two or three hardy souls who know a fair bit about the roots of category theory in topology, but that's a pretty specialist topic!). Topologists and philosophers mostly have very different fish to fry.

So why not study topology, and just ignore the philosophy of maths? Fine, if what you are interested in is the behaviour of sheaf cohomologies and the like. Similarly, why not study neuroscience, and ignore the philosophy of mind? Fine, if what you are interested in is how our brains work at different levels of functional organization.

But suppose you start getting interested in how all those different scientific enquiries fit together? For example, the scientific study of our cognitive psychology seems to suggests that our cognitive abilities all involve the brain's causal operations as a physical organism. On the other hand the abstract structures and mappings beloved by algebraic topology don't seem to live in the physical world (you can't kick or grab a sheaf cohomology, for example). So ... erm ... how do our brains, so to speak, get hooked up with them? How can we really know anything about the mathematical abstracta?

Now this isn't a question for the neuroscientist and it isn't a question for the topologist either, but it would be good to make more sense of how beings that are as the neuroscientist says we are can possibly come to know about the sorts of things that the topologist seemingly successfully talks about (but on second thoughts, what are those sorts of things?). And note we are not stopping being "really concerned about the world" in trying to come to an overall story about the furniture of the universe that tells us inter alia about how people with just physical stuff in their heads can come to know about the abstract mathematical realm. But we are now indeed in the characteristic territory of philosophy (and specifically, of the philosophy of maths). As Sellars famously put it, “The aim of philosophy is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term” -- that's certainly not an unworldly topic but it is equally not a topic for particular special-interest social, physical, or mathematical sciences either.

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