[FOM] ZC vs. ZFC: a pedagogical perspective

Timothy Y. Chow tchow at alum.mit.edu
Sat Jan 30 16:22:16 EST 2010

Jeremy Bem wrote:

>More personally, a peculiarity of my education is that I was
>introduced to ZFC without having independently encountered any math
>that requires replacement.  As such, ZFC was under-motivated.

This takes the discussion in a different direction.  If you think that the 
proper motivation for an axiomatic system for set theory is that it should 
be the most parsimonious system that suffices to formalize the mathematics 
that you've already encountered, then ZC is also under-motivated.

Rather than argue for ZC in particular, perhaps you should argue that the 
student should be introduced to a spectrum of systems, such as those in 
Simpson's "Subsystems of Second-Order Arithmetic," as well as Z, ZC, ZFC, 
ZFC + large cardinals and perhaps others.  This would help dispel the 
common misconception that there is just one system that is uniquely 
privileged to be "the" foundation of all mathematics.


More information about the FOM mailing list