November 16, 2008

Philosophical Ponderings

Posted in Uncategorized at 8:46 pm by carolynresearch

I read a book on Friday, “Proofs and Refutations” by Imre Lakatos. A lot of the mathematics education papers I’ve read reference it, and there was a copy in the Math and Stats library, so I decided to give it a read. Much of it is a discussion between students and a teacher in a class, defining and proving things, with a commentary about what has been done. How do they approach a conjecture? What is a proof? How do you decide what is a weakness in a definition, as opposed to a weakness in the proof itself? They start with a conjecture that in a polyhedron, Vertices – Edges + Faces = 2. From that comes a proof, counterexamples, proof analysis, formalism, and an anti-formalist and anti-positivist look at mathematical methodology and intuition. He argues that if we consider mathematics to be simply formal mathematics, well, it becomes boring. The situational logic of informal mathematics isn’t blind guessing, and it isn’t mechanistic.

I found it very interesting, and reminds me how much work has been done on the philosophy and methodology of mathematics. And personally, I like any book where they talk about “Monster-Barring”, and where the almost impenetrable math jargon emerges, is challenged, and tamed.

Reflecting on this, I wonder if computer science should be considered more like mathematics than engineering. I mean, the proof analysis discussed really looks like code review or debugging if I squint just a little. I haven’t read much about the philosophy of engineering – and I think it might be a useful thing to think about.

I remember a couple years back, I took a psychology course and got into a conversation with another student who was into philosophy. He said that physics has an established philosophical basis, and psychology doesn’t, and psychology needs that in order to proceed. I have since learned just how much of the philosophy of physics is not fixed and fully understood. It’s made me think of philosophy of science as a more living thing – not the prescriptive formulae that some philosophy undergrads seemed to tell me about, but an implicit understanding of what “doing science” means.

I’m not even sure what a philosophy of computer science would look like. I’m not at all sure if there’s much out there about it. I should get back to work on my thesis, but once that’s under control, I might go look around for such a thing. I’m hoping to learn some more math in my PhD courses, but I’m also starting to see the value in these fuzzy, squishy ideas that I used to dismiss and not rigorous enough.

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