[FOM] Arithmetical soundness of ZFC (platonic)

[praatika@mappi.helsinki.fi]

"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,

Panu





Panu Raatikainen

Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy

Department of Philosophy
University of Helsinki
Finland


E-mail: panu.raatikainen at helsinki.fi

http://www.mv.helsinki.fi/home/praatika/