[FOM] Formalization Thesis

S. S. Kutateladze sskut at math.nsc.ru
Thu Dec 27 13:05:29 EST 2007

Timothy Y. Chow writes
perhaps a more cautious formulation would say that there exists a
category-theoretic proof a category-theoretic theorem T if and only if
there exists a set-theoretic proof of a
set-theoretic translation T' of T.

This is clearly wrong. Category theory can speak about all elementary
toposes whereas ZFC cannot.  This is like standard poetry and poetry
in Braille.
 Timothy Y. Chow writes
 Formalize  model theory *within* ZFC...
 This is impossible. ZFC is an instance of a first order theory,
 that's  all. Model theory is much more.

Sobolev Institute of Mathematics
Novosibirsk State University
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