Axiomatic set theory isn't just for "pedantry" and mechanical reasoning, though that's an important application. It's also like a telescope array that allows us

Axiomatic set theory isn't just for "pedantry" and mechanical reasoning, though that's an important application. It's also like a telescope array that allows us to see ever further into Cantor's paradise and the universe (multiverse?) of mathematics. The upper levels of transfinite set theory are especially breathtaking and somewhat scary [1]. Hugh Woodin spoke a little bit about this in a presentation on the Ultimate L conjecture: "There's the other possibility: set theory is completely irrelevant to physics... That's almost more interesting because if this conjecture is true, we've argued there's truth here for set theory, and it's a truth that's not about the physical universe. To me that's almost more remarkable, that there could be some conception of truth that transcends truth that we see around us." The presentation is called The Continuum Hypothesis and the search for Mathematical Infinity [2]. [1] http://cantorsattic.info/Cantor's_Attic http://cantorsattic.info/Cantor's_Attic [2] https://www.youtube.com/watch?v=nVF4N1Ix5WI https://www.youtube.com/watch?v=nVF4N1Ix5WI.