Wednesday, November 3, 2010

Reading the Principia Mathematica

....I'm remembering that, every time I go a while without reading much Russell, I forget just how smart Russell was. (The classic example is that most people don't notice that Russell anticipated and responded to the Gettier problem as far back as Problems of Philosophy.) In any case, predictably, given my interests, the most interesting part of the early chapters, for me, is his take on the Liar. People often tend to discuss his (and Whitehead's) type theory only as a solution to the set-theoretic paradoxes, but even if one rejects it for those purposes, their type-theoretic solution to the semantic paradoxes remains independently interesting.

I think this solution is actually fairly interesting. I don't think he's right about the roots of the problem, but the solution has a lot going for it. (In some way, in fact, I find it a whole lot more attractive and plausible than some still-popular approaches to the Liar, like Kripke's.) It's extremely "unified," solving a lot of other problems at the same time, it doesn't require the rejection of any intuitively compelling logical principles, or any instances of the T-Schema (or the Capture and Release rules), it doesn't require any weird principles about certain sentences not being "contructable," it fits everything together in a tight, coherent framework, and it has interesting consequences for such apparently distant subjects as epistemic skepticism.

Again, all that said, I don't entirely buy it.

....but do expect a series of posts on Russell's Take On The Liar Paradox in the next week or two.


M.K. Hobson said...

Have you ever read "The Last Witchfinder" by James Morrow? The Principia Mathematica is actually a character in that book. It's quite brilliant.

Ben said...

Cool. I'll definitely have to read that.

The only Morrow book I've ever read is "Blameless at Abbadon," which I loved. (Big early influence on my views about the whole God thing.)