[FOM] Micro Set Theory

[Joe Shipman]

I suppose so, but I wasn't really trying to defend the idea of oracles so much as saying that here's an easily definable finite object which is practically as hard to understand as math in general is. 

My other point is that I would like to know if interesting math questions can be translated more directly into questions about V_n than by coding proofs as elements of V_7, because V_6 and V_5 are much more accessible objects than V_7 is.

-- JS

Sent from my iPhone

On May 18, 2013, at 10:40 PM, Mitchell Spector <spector at alum.mit.edu> wrote:

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.
> ...


Joe,

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 results?

Moreover, wouldn't it continue to be a creative art to figure out what questions to ask?

Mitchell