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