The fact that people get hung up on the truth or falsehood of set theoretic axioms like Choice or CH is a weird messy holdout of mathematical platonism and we should be taking Godel's completeness theorem more seriously. (No, not his incompleteness theorem. The other one)https://twitter.com/nex3/status/1199086783222255616 …
-
Show this thread
-
I mean not that you actually need the completeness theorem for this - we can construct models of all these things perfectly well without it - but it's funnier if I put it that way.
1 reply 0 retweets 5 likesShow this thread -
Also topology should be taught as part of a first course on set theory and logic and real analysis should be taught assuming it as a foundation.
3 replies 0 retweets 5 likesShow this thread -
David R. MacIver Retweeted David R. MacIver
(OK, sorry, that's false, we can construct models of these things perfectly well *given a model of ZF* , but we only get to assume those exist because of the completeness theorem)https://twitter.com/DRMacIver/status/1199101911225552896 …
David R. MacIver added,
2 replies 0 retweets 0 likesShow this thread -
Apparently all my most obscure opinions are about mathematics education, so while I'm at it: history and philosophy of mathematics should both be a mandatory part of a maths degree.
4 replies 1 retweet 12 likesShow this thread
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.