[FOM] Alternative foundations?

jkennedy at mappi.helsinki.fi jkennedy at mappi.helsinki.fi
Fri Feb 21 03:09:58 EST 2014

Set theory and category theory are bi-intepretable. As to the below:

> Category theory itself furnishes several examples of objects that  
> have no existence in set theory, such as the category of all sets.

The category of all sets is interpreted in set theory as V_kappa,  
kappa inaccessible.

> However, the main point of HTT as opposed to set theory, as I  
> understand it, is not that set theory does not postulate enough  
> sets, but that HTT allows one to formalize many parts of mathematics  
> in a much less arbitrary manner than in set theory. Frenkel's remark  
> that "mathematical structures constitute but a small island of  
> modern mathematics" should perhaps be taken not to say that these  
> parts would necessarily be unformalizable in set theory, but rather  
> that such a formalization may not be the most useful or enlightening  
> one.
> Staffan Angere
> University of Lund
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