This essay is, primarily, a discussion of four results about the principle of maximizing entropy (MAXENT) and its connections with Bayesian theory. Result 1 provides a restricted equivalence between the two: where the Bayesian model for MAXENT inference uses an "a priori" probability that is uniform, and where all MAXENT constraints are limited to 0-1 expectations for simple indicator-variables. The other three results report on an inability to extend the equivalence beyond these specialized constraints. Result 2 established a sensitivity of (...) MAXENT inference to the choice of the algebra of possibilities even though all empirical constraints imposed on the MAXENT solution are satisfied in each measure space considered. The resulting MAXENT distribution is not invariant over the choice of measure space. Thus, old and familiar problems with the Laplacian principle of Insufficient Reason also plague MAXENT theory. Result 3 builds upon the findings of Friedman and Shimony (1971; 1973) and demonstrates the absence of an exchangeable, Bayesian model for predictive MAXENT distributions when the MAXENT constraints are interpreted according to Jaynes's (1978) prescription for his (1963) Brandeis Dice problem. Lastly, Result 4 generalizes the Friedman and Shimony objection to cross-entropy (Kullback-information) shifts subject to a constraint of a new odds-ratio for two disjoint events. (shrink)

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails (...) because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief . One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective Bayesian norms are tied up in the very notion of degrees of belief. (shrink)

Probabilism in epistemology does not have to be of the Bayesian variety. The probabilist represents a person''s opinion as a probability function; the Bayesian adds that rational change of opinion must take the form of conditionalizing on new evidence. I will argue that this is the correct procedure under certain special conditions. Those special conditions are important, and instantiated for example in scientific experimentation, but hardly universal. My argument will be related to the much maligned Reflection Principle (van Fraassen, 1984, (...) 1995), and partly inspired by the work of Brian Skyrms (1987). (shrink)