Why the taboo on talking about what mathematics is and how it works? A guess: https://meaningness.com/metablog/how-to-think/comments#comment-1627 …pic.twitter.com/P6WZCqybD5
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Why the taboo on talking about what mathematics is and how it works? A guess: https://meaningness.com/metablog/how-to-think/comments#comment-1627 …pic.twitter.com/P6WZCqybD5
The real "mystery" is continuity. I have a mild suspicion that the reals were a mistake, and there's some better construct out there.
It seems likely that math at least ought to contain the rationals! Although the Greeks might have trouble even going that far.
The problem with the rationals is they don't stick to themselves. You need some kind of glue for paths to hold together.
Is the logical/set-theoretic/infinitary construction behind R really necessary, or is there some Q + glue construct we missed?
Really interesting… I vaguely remember reading about a proof that you can’t do anything similar to real analysis unless you bite the bullet
> but I can’t remember any details of that. Failure of the Brouwer program is presumably relevant;t I don’t remember much about that either!
You can do everything with nonstandard reals instead, but they're even worse.
People who get twitchy about noncomputable reals really won't like using an arbitrary ultrafilter.
Ultrafilters are cute and cuddly and have very very big teeth.
show me an ultrafilter
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