There is an often implicit assumption that ordinary, day-to-day mathematics should describe something "real", "existing", that there is "one" true model which can then be used, say, in analysis, For example, it is, in some sense, almost absurd talking about infinite-but-Dedekind-finite sets, which is why some people "believe" in Choice Axiom.
And in this pursuit of "true" model we have questions like that. What if, for example, Riemann hypothesis is true with C but false with not C? Which world we actually live in?
