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Qiaochu_Yuan comments on Why you must maximize expected utility - Less Wrong
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In the nomenclature that I think is relatively standard among mathematicians, if a theorem states "if P1, P2, ... then Q" then P1, P2, ... are the hypotheses of the theorem and Q is the conclusion. One of the hypotheses of the VNM theorem, which isn't strictly speaking one of the von Neumann-Morgenstern axioms, is that you assign consistent preferences at all (that is, that the decision of whether you prefer A to B depends only on what A and B are). I'm not using "consistent" here in the same sense as the Wikipedia article does when talking about transitivity; I mean consistent over time. (Edit: Eliezer uses "incoherent"; maybe that's a better word.)
Premises.
Again, among mathematicians, I think "hypotheses" is more common. Exhibit A; Exhibit B. I would guess that "premises" is more common among philosophers...?
I usually say “assumptions”, but I'm neither a mathematician nor a philosopher. I do say “hypotheses” if for some reason I'm wearing mathematician attire.