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TheOtherDave comments on The Useful Idea of Truth - Less Wrong
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It's kind of entertaining watching this exchange interpreting my earlier comments, and I'm sort of reluctant to disturb it, but FWIW my usage of "simplicity" was reasonably well aligned with your conception, but I'm not convinced it isn't well-aligned with shminux's, as I'm not really sure what "work" refers to.
That said, if it refers to cognitive effort, I think my conception is anti-aligned with theirs, since I would (for example) expect it to be more cognitive effort to make a typical prediction starting from a smaller set of axioms than from a larger set of (mutually consistent) axioms, but would not consider the larger set simpler.
My guess is that the larger set will have some redundancy, i.e. some of the axioms would be in fact theorems. But I don't know enough about that part of math to make a definitive statement.
I agree that if it's possible, within a single logical framework F, to derive proposition P1 from proposition P2, then P1 is a theorem in F and not an axiom of F... or, at the very least, that it can be a theorem and need not be an axiom.
That said, if it's possible in F to derive some prediction P3 from either P1 or P2, it does not follow that it's possible to derive P1 from P2.