I'm not sure one is more or less fundamental than the other. It does seem fair to say that as far as differential equations are concerned a completely different foundational setting wouldn't make any difference. So it isn't analogous to reductionism in that the behavior isn't brought about by the local interaction of pieces under the hood.
I'm not sure one is more or less fundamental than the other.
Really? You don't think the demonstrable reducibility of other branches of mathematics to set theory means anything?
It does seem fair to say that as far as differential equations are concerned a completely different foundational setting wouldn't make any difference.
This is actually a vacuous statement, because if it did make a difference, you wouldn't call it "a completely different foundational setting" of the same subject. Similarly, it wouldn't "make any difference" i...
Did computer programming make you a clearer, more precise thinker? How about mathematics? If so, what kind? Set theory? Probability theory?
Microeconomics? Poker? English? Civil Engineering? Underwater Basket Weaving? (For adding... depth.)
Anything I missed?
Context: I have a palette of courses to dab onto my university schedule, and I don't know which ones to chose. This much is for certain: I want to come out of university as a problem solving beast. If there are fields of inquiry whose methods easily transfer to other fields, it is those fields that I want to learn in, at least initially.
Rip apart, Less Wrong!