### Cantor Rulez!!! (A Philospher Writes…)

Why Cantor matters (and Wittgenstein's just an interesting historical oddity): "Writing decades after Cantor's death, Wittgenstein lamented that mathematics is 'ridden through and through with the pernicious idioms of [Cantor's] set theory,' which he dismissed as 'utter nonsense' that is 'laughable' and 'wrong'." (from Wikipedia's entry on Cantor).From the Olympian heights of philosophy, mathematics must seem so grubby, and, well,

*useful*, but to this reader, it's hard to get past Cantor's transfinite numbers for examples of abstract beauty and the stringent clarity of the purely counter-intuitive. I think the first time I read about — and understood — the various comparative transfinite cardinalities of the integers, the rationals, the reals, etc., (and, crucially, the associated proofs) was when I realised I could do

*mathematics*in ways I can't do arithmetic (don't ask me to add things up). To a young Woy Woy boy struggling with high school in the foreign reaches of Canberra, this was a revelation.

Labels: math, philosophy

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