It may be that a more deep-seated change has taken place within mathematics: the rise of formalism, with Frege, Russell, etc. separated mathematics from intuiti

It may be that a more deep-seated change has taken place within mathematics: the rise of formalism, with Frege, Russell, etc. separated mathematics from intuitions about 'reality'; a formal theorem can't be refuted by saying it's 'unrealistic', since it's a watertight consequence of the chosen axioms and deduction rules. We can attack those axioms and deduction rules as being 'unrealistic', but since Goedel shot down the attempts to define "one true" formalism, it seems that mathematicians have come to accept axioms and logics based on their own merits (e.g. whether they lead to interesting, non-trivial consequences) rather than whether they're accurate models of 'reality'. In this relaxed view, Cantor's arguments make sense from his premises, and it's interesting to entertain the idea of his premises because they lead to such interesting results. Whether or not "completed infinities" are "real" is delegated to the philosophers, while mathematicians 'play the proof game', and change the rules if they make it more fun.