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Bad example. Cantor's theory is controversial to this day. "Classical logic was abstracted from the mathematics of finite sets and their subsets …. Forgetful o
by resource0x 6y ago
Bad example. Cantor's theory is controversial to this day.
"Classical logic was abstracted from the mathematics of finite sets and their subsets …. Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. This is the Fall and original sin of Cantor's set theory."
-- Hermann Weyl
- openasocket 6y agoI wouldn't really consider Weyl as an example of a modern day critic, considering he died in 1955. I think you'd be hard pressed to find a modern mathematician that rejects the diagonalization argument, outside of finitists, which are pretty far from the mainstream. I mean the proof that there is no bijection from a set to its power set is pretty straightforward and constructive. I'm pretty sure the proof is valid even in intuitionist logic.
- cambalache 6y agoBy whom? Almost all mainstream mathematicians rightfully lionize Cantor's main contributions, as David Hilbert so eloquently put it: "No one shall expel us from the paradise Cantor has created for us" Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können