Abstract Are rational beliefs constrained by formal logic? This book argues that if beliefs are seen in a binary way (either one believes a proposition or one doesn't), then the standard constraints of ’deductive cogency’ (i.e. deductive consistency and deductive closure) are incompatible with epistemic rationality. If, however, beliefs are seen as graded, or coming in degrees, a probabilistic constraint (based on standard logic) is imposed by ideal rationality. This constraint, probabilistic coherence, explains both the appeal of the standard deductive constraints and the power of deductive arguments. Moreover, it can be defended without taking degrees of belief (as many decision-theoretic philosophers have) to be somehow defined or constituted by preferences. Although probabilistic coherence is humanly unattainable, this does not undermine its normative status as a constraint in a suitably idealized understanding of epistemic rationality.
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