 First, there is a distinction between permissivism and impermissivism (see Meacham 2014 and Kopec and Titelbaum 2016 for this terminology). For permissive Bayesians (often otherwise labelled “subjectivists”), accordance with the probability axioms is the only clear-cut constraint on the credences of a rational agent. In impermissive forms of Bayesianism (often otherwise called “objective”), further constraints are put forward that significantly restrict the range of rational credences, possibly up to one single “right” probability function in any given setting. Second, there are different attitudes towards so-called principle of total evidence (TE) for the credences on which a reasoner relies. TE Bayesians maintain that the relevant credences should be represented by a probability function \(P\) which conveys the totality of what is known to the agent. For non-TE approaches, depending on the circumstances, \(P\) may (or should) be set up so that portions of the evidence available are in fact bracketed. (Unsurprisingly, further subtleties arise as soon as one delves a bit further into the precise meaning and scope of TE; see Fitelson 2008 and Williamson 2002, Chs. 9–10, for important discussions.)