
To Settle Infinity Dispute, a New Law of Logic (2013) - dil8
https://www.simonsfoundation.org/quanta/20131126-to-settle-infinity-question-a-new-law-of-logic/
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dmfdmf
I was glad to see the oft forgotten, and correct view in my judgment,
Aristotelian position that infinity is never actual, always a potential. The
number line is open-ended not "going to infinity" as the flawed modern
approach puts it.

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Tobu
The set of integers is the first infinity in ZF. Maybe you could reason a bit
about integers without building a model of them, but you wouldn't have a set
theory and you wouldn't have access to algebra.

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dmfdmf
I think you are begging the question by accepting ZF (and that basis for
algebra)and then rejecting any possible alternatives by saying you'd lose
algebra. This is not true, even the article mentioned that much of math can be
founded on infinity as potential, just a different approach. The issue really
is a question of philosophy and what are axioms, what is knowledge and what is
math.

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fsk
There's no way to know which axiom is "correct", because you can't actually
build a physical infinite set.

