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@futurebird @dymaxion @whknott

It is not just that the axioms are arbitrary, but that they cannot be specified precisely without contradiction. If you can't define what a "set" is, how can you expect everybody to agree on whether something is a set of not?

Euclid himself assumed a couple of things that should have been explicitly stated as axioms, such as "If a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side."