@Meaningness I got lost on the 'bag' paragraph.
@Meaningness Be interested to see a formalism that, intuitively, starts 'here' and works 'out' rather than goes up from a foundation.
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@St_Rev I think that’s the idea, actually! you start by specifying the behavior of a class of mathematical objects. There’s no bottom. -
@St_Rev Example from the paper is that Dedekind cuts and Cauchy sequences are *not* real numbers as working mathematicians think about them. -
@St_Rev You should be able to just say what reals do without having to specify an “implementation”. -
@St_Rev Non-standard reals get you that, but you need several metric tons of cast-iron machinery. -
@Meaningness Which...is an implementation -
@St_Rev Well, you need the implementation to prove that you can use the axioms without worry. Then you can throw away the implementation. -
@Meaningness I don't understand. I guess that's in the article though. -
@St_Rev I haven’t read the article; I don’t know! Looks like a lot of machinery, I’m afraid, and not much in the way of theorems.
End of conversation
New conversation -
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@Meaningness But arguably that was a major weakness for 19th century mathematics and Hilbert did everyone a service. IDKlolThanks. Twitter will use this to make your timeline better. UndoUndo
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.