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Abstracts should only be useful if they capture something, even imperfectly, about reality.

Since we know there is no such thing as infinity or imaginary numbers (or even something they approximate to or imperfectly capture) then we are left with an awkward question of what it is they really do refer to.

Of course we may, in the future, come up with mathematical theories that do not require us to use these concepts in order to predict reality (though I find that very unlikely, given things like Godel's incompleteness theorem) but even so, we are left with trying to explain what Modus Ponens (if A implies B and A is true then B is true) refers to and without that we can't really reason at all.

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purplecat

May 2025

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