October 10, 2005

No pie for you!

Because I'm lazy and forgot to take a picture of it before I cut into it. It's damn tasty, though.

And now for something completely different.

In Book V of the Physics (or somewhere around there), Aristotle gives a teleological argument against the reduction of biological beings to mere complicated material structures. Briefly, he argues that organisms are organized into structures with a particular end (telos), the well-being of the organism itself. Even the most charitable version of reductivism cannot give an account of this telos, and hence cannot be true.

Now, prima facie, this conflicts with the sort of evolutionary account that's fundamental to contemporary biology, but I think the Aristotelian teleology of the organism can be cashed out in terms of the reproductive success basic to natural selection.

One of the major metaphysical accounts of mathematics for the past 100+ years has been logicism, the idea that (major parts of) mathematics can be reduced to formal (symbolic) logic. Mic Detlefsen (my advisor) has interpreted Poincare (the father of topology, and one of the greatest mathematicians in the history of the subject) as arguing that logicism cannot give an account of the way a mathematician views her theorem as playing an important role in the development of the field of mathematics as a whole.

There seems to be an interesting parallel here. What repercussions follow from interpreting Poincare's point as a teleology of mathematics?

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