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cousin_it comments on Consistent extrapolated beliefs about math? - Less Wrong
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Sorry, I don't understand what you're talking about. Can you give an example of a theory with uncountably many axioms?
(A): There exists a function f:R->R
and the axioms, for all r in R:
(A_r): f(r)=0
(The graph of f is just the x-axis.)
This might be expressible with a finite axiomatisation (e.g. by building functions and arithmetic in ZFC), and indeed I've given a finite schema, but I'm not sure it's 'fair' to ask for an example of a theory that cannot be compressed beyond uncountably many axioms; that would be a hypertask, right? I think that's what Joshua's getting at in the sibling to this comment.
Example infers more than one representation could exist, which for an object this large would be absurd.