Half-baked Philosophy (Part 2)
So for the past couple of days I've been holed up with Mark Steiner's "The Applicability of Mathematics as a Philosophical Problem". Those of you who know me may well wonder what the hell I'm doing in this part of the philosophical terrain, since my history with mathematics is a long story of unrequited love. But, alas, here I am at the tail end of a philosophy of physics course, and I think I'll be writing on this.
One observation: I'd love Steiner to be my grandfather. He throws in jokes into the footnotes that actually made me laugh out loud a couple of times.
Anyway, my half-baked idea for the day approaches. So at one point in the book, Steiner argues that math is anthropocentric because it relies on standards of beauty and convenience, which are contingently dependent on us being the kinds of creatures we are. And that's fine, as far as it goes, because, really, who's going to argue for Platonism these days? (I know of one very awesome and well-respected person here at U of T who does, but that just goes to show you that we may all be crazy, but at least in a socially acceptable ways.) Anyway, so that got the apostate biologist in me thinking, because Steiner mentions evolutionary stories about the origins of our preferences and aesthetic tastes and all that. But I don't think he spun the just-so stories enough. My intuition is that if I keep spinning the stories, I may just end up with something (a) true and (b) interesting for this paper.
A first approximation of a sketch of the ballpark of the topic: mathematical practice is a cognitive exaptation of the aesthetic impulse, on which a lot more needs to be said. For example: aesthetic pleasure can be related to seeking. What are we seeking? How about intelligibility? That's related to sense-making which, on a cool and wacky reading of life (enactivism) is actually pretty foundational to all living things. So maybe math is a second-order sense-making where the first order is the concepts we bring to the world. In that way math is pretty much philosophy except cooler and involving different syntax, a kind of artificial language which evolves its terminology unlike the ossified structures of natural languages, which constantly breed confusion because they have to apply to the world in addition to being exapted by philosophers to serve different ends. So both philosophers and mathematicians are beneficial cognitive mutants. (I mean the truly great mathematicians/philosophers, not the merely professional.) But also, to go back to sense-making for a second, there may be a wacky kind of universality to math, at least maybe biologically, or counterfactually that may run as follows: creatures with certain kinds of first-order cognitive structures could, if circumstances are right, develop certain kinds of second-order abstractions, and even higher-order abstractions from that.
Whew. So where does wading in that thicket leave me? Is there anything to pull out of that? Maybe the idea that Steiner's just-so story about math doesn't go deeply enough. It's not just an aesthetic impulse that governs math. IT could be a seeking impulse. For what it's worth.
Oh, have I mentioned this is my essay-formulating week, so any kind of structured thinking (or semi-structured thinking) is helpful.
(I beg forgiveness on the jargon. But this is how I think most efficiently. One day I may in fact define these terms. It would help me as well.)
More on Steiner soon.
Consider: "Words move, music moves / only in time; but that which is only living / can only die."
One observation: I'd love Steiner to be my grandfather. He throws in jokes into the footnotes that actually made me laugh out loud a couple of times.
Anyway, my half-baked idea for the day approaches. So at one point in the book, Steiner argues that math is anthropocentric because it relies on standards of beauty and convenience, which are contingently dependent on us being the kinds of creatures we are. And that's fine, as far as it goes, because, really, who's going to argue for Platonism these days? (I know of one very awesome and well-respected person here at U of T who does, but that just goes to show you that we may all be crazy, but at least in a socially acceptable ways.) Anyway, so that got the apostate biologist in me thinking, because Steiner mentions evolutionary stories about the origins of our preferences and aesthetic tastes and all that. But I don't think he spun the just-so stories enough. My intuition is that if I keep spinning the stories, I may just end up with something (a) true and (b) interesting for this paper.
A first approximation of a sketch of the ballpark of the topic: mathematical practice is a cognitive exaptation of the aesthetic impulse, on which a lot more needs to be said. For example: aesthetic pleasure can be related to seeking. What are we seeking? How about intelligibility? That's related to sense-making which, on a cool and wacky reading of life (enactivism) is actually pretty foundational to all living things. So maybe math is a second-order sense-making where the first order is the concepts we bring to the world. In that way math is pretty much philosophy except cooler and involving different syntax, a kind of artificial language which evolves its terminology unlike the ossified structures of natural languages, which constantly breed confusion because they have to apply to the world in addition to being exapted by philosophers to serve different ends. So both philosophers and mathematicians are beneficial cognitive mutants. (I mean the truly great mathematicians/philosophers, not the merely professional.) But also, to go back to sense-making for a second, there may be a wacky kind of universality to math, at least maybe biologically, or counterfactually that may run as follows: creatures with certain kinds of first-order cognitive structures could, if circumstances are right, develop certain kinds of second-order abstractions, and even higher-order abstractions from that.
Whew. So where does wading in that thicket leave me? Is there anything to pull out of that? Maybe the idea that Steiner's just-so story about math doesn't go deeply enough. It's not just an aesthetic impulse that governs math. IT could be a seeking impulse. For what it's worth.
Oh, have I mentioned this is my essay-formulating week, so any kind of structured thinking (or semi-structured thinking) is helpful.
(I beg forgiveness on the jargon. But this is how I think most efficiently. One day I may in fact define these terms. It would help me as well.)
More on Steiner soon.
Consider: "Words move, music moves / only in time; but that which is only living / can only die."
posted by A. D. at 11:09 PM
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