Over at Culture11, Will Wilson (a mathematics student at Yale) has an interesting article up, Screaming Shapes & Seven-Dimensional Donuts:
It is clear that reductionist and demiurgic approaches to science have stood unchallenged on the intellectual landscape for too long, and their profound philosophical and cultural implications left to unfold freely. Many will complain that explanation and understanding -- which shift the purpose of inquiry away from mere accuracy and toward knowledge of propriety -- is not the role of science. This may be true in the aftermath of the divorce of science from philosophy won by the positivists, but perhaps it is time that this split be healed in a way that allows us to gain in both humility and wholeness. Thom's theory alone may be unsatisfactory, but it points the way towards what is needed: a rigorous unification of prediction and explanation that is aware of its political and cultural implications; a postmodern natural philosophy for the masses.
That's the conclusion. You have to read the whole thing to understand what Will is getting at. I am myself a "Three cheers for reductionism!" fellow, but I'm curious if any mathematicians might weigh in (I'm not familiar with René Thom's work, which is the launching point for Wilson's essay).