[FOM] Arithmetical soundness of ZFC (platonic)
praatika at mappi.helsinki.fi
Sun May 31 02:05:51 EDT 2009
"Timothy Y. Chow" <tchow at alum.mit.edu>:
> We got to ZFC from ZF and to ZF from Z,
> and the extensions were motivated neither by the desire to find the most
> powerful axioms nor the desire to be totally safe from error. A large
> part of the motivation was to capture actual mathematical practice as
> simply and elegantly as possible.
I am afraid this is not true - unless by "actual mathematical
practice" one means Zermelo's own, at the time highly controversial
proof of the well-ordering theorem from 1904.
I don't think there existed any mathematical practice (unless one
counts the Cantorian intuitive set theory as such) which required
anything like the full power of even Z.
(Please note that these remarks are in no way intended to undermine
the plausibility of ZFC.)
All the Best,
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy
University of Helsinki
E-mail: panu.raatikainen at helsinki.fi
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