Published online by Cambridge University Press: 16 October 2009
In this paper, I address two connected issues that arise when one considers a rational agent facing a decision problem. One is whether or not the agent may find that the dictates of rationality are such that they cannot all be followed. For example, one may ask whether or not the requirements on the agent's actions imposed by rationality can conflict in an irreconcilable way, making it impossible to satisfy all of them. Put differently, one may ask whether or not any apparent conflict of this type must in fact be capable of rational resolution. I shall say that an agent who is in a position in which the requirements of rationality cannot all be satisfied faces a feasibility dilemma, and I shall characterize certain conceptions of rationality that differ according to whether or not they admit such a possibility. A second issue concerns the number of options that may be deemed rational in a decision problem. Is rationality sufficiently determinate that it always dictates precisely one choice, or may there be more than one rationally permissible option? Is there anything about rationality itself that guarantees that any of the possible options could rationally be chosen? I shall call this issue – whether the concept of rationality itself places any limits on the number of options that may be deemed rational in a given problem – the numbers problem.