[FOM] Why ZF as foundation of mathematics?
Timothy Y. Chow
tchow at alum.mit.edu
Wed Nov 20 11:54:54 EST 2013
Zuhair Abdul Ghafoor Al-Johar wrote:
> So why ZF is mentioned for that purpose if much weak class\set theories
> can do the job of formalizing mainstream mathematics in set theory?
This question presupposes that weakness is a strength.
For most anyone not actively working in foundations, an existence proof of
a foundation suffices, just as most people don't care to know anything
about non-measurable sets other than that they exist. It's useful to have
a standard answer that you can cite, but for non-specialist purposes it
doesn't matter too much what exactly the standard is.
If, of course, there is some motivation for coming up with a weaker
foundation, then people can, and have, come up with alternatives to ZF.
But I don't see the point of trying to change what people consider to the
be the standard. "The nice thing about standards is that there are so
many to choose from."
Tim
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