The principle of compositionality says roughly that the meaning of each (declarative) sentence depends on the meaning of its parts and the way those parts are combined into that sentence. Let compositional meanings be whatever that can play the meaning-role in (an appropriate version of) the principle of compositionality. But can we say more about what compositional meanings are? Here is the orthodox answer: the compositional meaning of each sentence S is the objective truth condition of S—objective in the sense that the truth value of S is independent of who assesses S. That is the orthodox, but my goal is to find the best heresy. I will examine top 3 most developed heresies, which take compositional meanings to be: context change potentials, attitudes expressed, and assessor-relative truth conditions, respectively. They correspond to: dynamic semantics, expressivist semantics, and relativist truth conditional semantics, respectively. I will use Ockham-Grice’s razor to argue that there is a better heresy—though less developed to date—according to which compositional meanings are what I call acceptability conditions. If time permits, I will explain how we might develop the acceptabilist heresy into a formal semantics, and use it to give a new, better explanation of the linguistic phenomenon in which ‘or’  behaves like ‘and’ when it meets ‘might’.