[FOM] Foundational Frameworks

[Hendrik Boom]

Mario Carneiro
March 31, 2016  2:54 AM:
> 
> "The reason you say "not sure about NF" probably is that there is no
> known interpretation of NF into ZFC or ZFC with large cardinals. And
> correct me if I am wrong, but all of the other systems that you accept
> there are known to be interpretable in ZFC or ZFC with infinitely many
> strongly inaccessibles?"
> 
> Actually the main reason is because I have not been convinced that it
> is consistent, although I think that there is some recent work to
> build a model of NF using permutation models of ZFA or something
> similar. But yes, it amounts to the same thing: I feel uncomfortable
> until I see an embedding into a natural extension of ZFC.

Could it be tht the reason we accept ZFC is the same as the reasons 
cryptographers accept particular one-way functions?  The people have 
been trying to crack them for a very long time and have not succeeded?
In the course of which we have gained some intuition about which 
particular properties of a theory or a cryptosystem are dangerous and 
know to avoid them?

-- hendrik