[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.
Tim
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