Philosophers have spent a great deal of time debating whether intransitive preferences can be rational. I present a risky decision that poses a challenge for the defender of intransitivity. The defender of intransitivity faces a trilemma and must either: (i) reject the rationality of intransitive preferences, (ii) deny State-wise Dominance, or (iii) accept the bizarre verdict that you can be required to pay to relabel the tickets of a fair lottery. If we take the first horn, then we have a (...) synchronic refutation of intransitivity, an improvement on widely criticized diachronic arguments. I sketch possible responses that may rescue intransitivity and argue that each response is possible but generates an explanatory debt. I conclude by showing how the challenge here clarifies the foundations of decision theory without transitivity, conditional on some explanatory debt being payable. (shrink)

I raise skeptical doubts about the prospects of Bayesian formal epistemology for providing an adequate general normative model of epistemic rationality. The notion of credence, I argue, embodies a very dubious psychological myth, viz., that for virtually any proposition p that one can entertain and understand, one has some quantitatively precise, 0-to-1 ratio-scale, doxastic attitude toward p. The concept of credence faces further serious problems as well—different ones depending on whether credence 1 is construed as full belief (the limit case (...) of so-called partial belief) or instead is construed as absolute certainty. I argue that the notion of an “ideal Bayesian reasoner” cannot serve as a normative ideal that actual human agents should seek to emulate as closely as they can, because different such reasoners who all have the same evidence as oneself—no single one them being uniquely psychologically most similar to oneself—will differ from one another in their credences (e.g., because they commence from different prior credences). I argue that epistemic probability, properly understood, is quantitative degree of evidential support relative to one’s evidence, and that principled epistemic probabilities arise only under quite special evidential circumstances—which means that epistemic probability is ill suited to figure centrally within general norms of human epistemic rationality. (shrink)