Re: Paper and slides on indefiniteness of CH

“It just occurred to me that we already have a consistent maximality
principle which provably contradicts large cardinal existence.

This is not enough evidence to infer the nonexistence of supercompacts
from maximality but this is definitely pointing in that direction!”

Well, how about the closely related

“It just occurred to me that we already have a maximality principle
which provably contradicts ZFC.

This is not enough evidence to infer that ZFC fails from maximality
but this is definitely pointing in that direction!”

Such is the folly of trying to apply an insufficiently analyzed
informal idea in a technical context. There is no substitute for at
least trying to come to grips with the plethora of inconsistent
formulations of so called “intrinsic maximality of the set theoretic
universe” in a philosophically honest way.

Harvey

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