[throwaway729]

> Err, by "very strong" did you mean "makes (a conjunction of) many claims" rather than "resilient"?

Kind of. I certainly did not mean "resilient"!

when speaking of axioms, typically "strong" means "a lot of stuff follows from the axiom". It's in reference to the deductive power of the axiom, usually when taken as part of a larger system of deduction.

So for example, "False" is a really, really strong axiom in most systems of deduction.

Strong axioms aren't necessarily a bad thing. But if you need a lot of strong axioms, you might be saying something about a very specific hypothetical situation...