In this paper I identify a family of explanatory demands facing permissivists, those who deny the uniqueness thesis, according to which every body of evidence rationally permits exactly one doxastic attitude for a person to have in light of that evidence. Call a pair of a body of evidence and a proposition a permissive case just in case there is more than one attitude that is permitted for someone who has that body of evidence to take to that proposition. Uniquers claim that there are no permissive cases, and permissivists deny this. The uniqueness thesis is a strong claim, and is vulnerable to counterexamples because it is a universal generalization, and indeed, many permissivists argue for their view by identifying putative counterexamples to the uniqueness thesis. However, in virtue of advancing these putative counterexamples, permissivists incur explanatory demands. If some, but not all, cases are permissive cases, then permissivists owe us an explanation of why some cases are permissive and others are not. Likewise, for each permissive case, permissivists must explain why some attitudes towards the proposition are permitted and others are not. Permissivists draw arbitrary lines between permissive and impermissive cases, and between permitted and impermitted attitudes, giving rise to distinctions which need explaining.
I shall argue that permissivists cannot discharge these explanatory burdens in a satisfying way. After carefully presenting these explanatory demands in section 2, I consider how permissivists might answer them in section 3. I argue that the only permissivists who are able to successfully answer the explanatory demands are extreme permissivists like subjective Bayesians. Most philosophers, however, will find this epistemological outlook implausible because it contains no substantive constraints on rational belief. I also show that previous attempts by permissivists to explain why there are permissive cases merely relocate, rather than answer, the explanatory demands I have identified. The final section argues that permissivists cannot soften up the explanatory demands, either. I show that permissivist cannot appeal to the vagueness of the notion of a permissive case, or of an attitude's being permitted, in order to make the line between the permitted and the impermitted attitudes appear less arbitrary. Nor, I argue, can the permissivist hold that our ignorance of which cases are permissive, and how permissive they are, lessens the explanatory burdens they face.
Unfortunately, permissivists have been most interested in attempting to identify a counterexample to the uniqueness thesis, and have not been concerned with the explanatory demands which they incur in so doing. If my arguments are successful, then, permissivism is a much less plausible view than it is currently given credit for, and, at the very least, permissivists have a lot of work to do in further articulating and generalizing their view so as to provide an adequate explanation of the scope of epistemic permission.