FOM: In defense of Conway
shipman at savera.com
Wed May 5 12:32:09 EDT 1999
>Mathematicians like Conway, Johnstone,
>McLarty, Whiteley, Tragesser, et al could be expected to unjustly
>dismiss the metatheorem as irrelevant, pedantic, not sufficiently
>attuned to the ``mysterious dimension'', etc etc, yatta yatta yatta.
>This expectation is based on their past behavior.
>Don't forget that, according to Johnstone, Conway is the founder of
>the Mathematician's Liberation Movement. The tyrannical force that
>Conway wants to liberate mathematicians from is none other than f.o.m.
You are being unfair to Conway here. Please read "On Numbers and Games"
before accusing him of anti-foundationalism. Conway clearly appreciates
the importance of proper foundations and knows exactly what he is
talking about. He wants to liberate mathematicians from excessive
fussing about formalization in works of ordinary mathematics, and
explicitly states that the foundational work of proving metatheorems
justifying the alternatives to the standard foundations one is creating
still needs to be done, but that it can be done once and for all. See
"Appendix to Part Zero", ONAG pp.64-67, which is foundationally
well-informed and deals with exactly the distinctions you are accusing
him of ignoring.
-- Joe Shipman
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