The verb postulate means to claim or assume the truth of something without proof.
As an example Newsday recently released an article saying that "If Romney loses in a very close race [for the presidency], historians no doubt will postulate that he lost because of his failure to release his tax returns."
Synonyms include: speculate, take for granted, propose, put forward, premise, assert, guess, hypothesize, and theorize.
The noun postulate means something that is generally accepted or self-evident.
As an example, Caspionet reports on Kazakhstan celebrating its Constitution Day saying "The Article 1 of our Constitution provides that Kazakhstan is a welfare state so we fulfill this postulate through major efforts and through our country’s social and economic modernization."
Synonyms include: idea, faith, principle, thought, belief, conviction, philosophy and view.