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This may seem a bit extreme, but, in my opinion, while in mathematics (and especially in physics) there is a fair amount of scaffolding, what they do in mathema
by Koshkin 5y ago
This may seem a bit extreme, but, in my opinion, while in mathematics (and especially in physics) there is a fair amount of scaffolding, what they do in mathematics is, actually, they discover things that do exist in reality in one form or another. (It is important to understand that few, if any, things in mathematics are pure fantasy; the objects and relations studied there are pretty much forced upon us - which, incidentally, is yet another evidence in support of their having real significance, i.e. as something lying outside our consciousness and acting there independently from it.)
- andi999 5y agoYes, but the reals (or the power set of the reals) are really a bit dodgy. The Nana h tarski paradox shows a big disconnect with reality. There is other axiom models without AOC, which allow for every subset to be measurable, but they seem to have their own problems.
- Koshkin 5y agoThe reals exist in nature in the same sense as, say, 𝜋 does (which occurs as the natural limit in a particular Monte Carlo experiment). The paradox that you mentioned is, rather, disconnected from our intuition, from which reality itself is, too, disconnected (if you think of quantum mechanics, for example).