[FOM] Micro Set Theory
spector at alum.mit.edu
Sat May 18 22:40:21 EDT 2013
Joe Shipman wrote:
> If V_0 is the empty set and V_(i+1) is the power set of V_i, then the elements of V_7 have
> infeasible size and can code objects smaller than 2^65536, so that an oracle for the theory of
> V_7 would allow answers to any mathematical question we care about (for example "Does the Riemann
> Hypothesis have a proof from ZF + your favorite large cardinal axiom of length < 10^1000 ?"),
> thereby rendering mathematicians obsolete.
I haven't thought about V_7 specifically, but I'm unconvinced about a claim that an oracle for any
finite set would render mathematicians obsolete.
Wouldn't mathematicians take the information gleaned from the oracle and build on it to get further
Moreover, wouldn't it continue to be a creative art to figure out what questions to ask?
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