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March 20, 2006
Neat! Economy of thought
Why favour a simple theory over a more complicated one? Isn't this ultimately a religious prejudice? That there should be an underlying order in all things that is beautiful in its own right. Or that things must be made so as to be intelligible to us?
With empirical knowledge there is the danger of over-fitting data that is itself subject to error. So a tendency to prefer the stark beauty of simplicity—to suspect that truth cannot needlessly complicated—can be of pragmatic benefit despite not being absolutely justifiable.
[I had a piece ready which related this to Bayesian learning. But there was too much detail given the rather slight point being made. Short version: belief networks… Bayesian learning… prior probability… arbitrary fudge factor… bias towards simpler hypotheses.]
None of which has any bearing on maths.
It is elegant that a theory of sets can be developed without without assuming the existence of any non-set elements. But I can't see this as an awe-inspiring genesis of all things out of the void that is the empty set. I see it as a cute trick. This is similar to untyped lambda calculus, which provides a formalism for computable functions without requiring any non-functions with which to compute. A minimalist approach do doubt makes for simpler proofs. But I suspect the real appeal is that it is just plain neat.
Which isn't to say that this a bad thing. It is possible to get caught up in foundations (all very well if you like that sort of thing) whereas the history of maths might be better viewed through its gems and its monstrosities.
Posted by robin2 at March 20, 2006 11:29 PM
Comments
gems and monstrosities is more Deleuze's approach, I think. It's worth noting that a common misunderstanding of Badiou's position is to think it's a metaphysical thing: that everything 'really is' made out of the void in some sense; whereas he says that 'mathematics is ontology' is a statement about discourse, not about reality: so if set theory provides our most direct access to being, it's not because being 'is' set-theoretical, it's because it allows us to talk about what is presented to us in so far as it is presented. Not entirely clear what difference this makes though...
Posted by: robin[theotherone] at March 24, 2006 08:50 AM
I'd have thought Deleuze was more of one for monstrosities than gems.
Regarding the metaphysics of the void: I was aware when making the comment that it was unfair, but I'll stand by it. (If that makes any sense.) A misunderstanding is still in the neighbourhood, even though it's a wrong turn. (OK, that's worse.)
Posted by: robin2 at March 24, 2006 10:30 PM
have you ever thought of compiling a book of your aphorisms?
Posted by: robin[theotherone] at March 25, 2006 12:29 PM