Determinism in one sense is the theory that all events, including human actions, are governed by laws and hence are necessary. Some think that it can be refuted simply by identifying entrenched beliefs that contradict it, i.e., simply by establishing incompatibilism. Others think that this is not enough, that if determinists uncover the right sort of evidence, they can use that evidence against any contrary beliefs, however well entrenched. In that case, attention must be paid to contingent facts about human behaviour. Probably a combination of the two approaches is the best strategy. Obviously, ascertaining what the facts are, and what their relevance is, cannot be done independently of analysis and logic. Yet a concentration on incompatibilism seems particularly vulnerable to stalemate. Hence the need arises to investigate whether concepts formed during the analytical inquiry are actually true of anything, independently of questions of entrenchment. To confirm this suspicion about the limitations of analysis, I shall consider two perceptive and well-regarded arguments for thinking that determinism clashes with a belief in alternate possibilities.