UC Berkeley

At a fairly high level of abstraction, this work is about some ways in which questions about the correct treatment of the semantic paradoxes and questions about the principles of rationality governing doxastic states can be mutually illuminating.

In the first part of the dissertation, I argue that certain treatments of the semantic paradoxes lead to surprising conclusions about the nature of the doxastic states of rational agents. The semantic paradoxes, such as the liar paradox, provide us with good reason to take seriously various non-classical logics. In addition to the semantic paradoxes, there are also paradoxes that show that some extremely plausible principles of rationality governing doxastic states are inconsistent given classical logic. I show how various non-classical responses to the semantic paradoxes provide us with resources sufficient to resolve these paradoxes. In particular, if we allow that certain statements about an agent's doxastic state, e.g., statements about whether an agent believes a proposition P, may give rise to certain failures of classical logic, then we can hold on to all of our plausible principles of doxastic rationality. I use this fact to argue for the conditional claim that if one is inclined to reject classical logic in response to the liar paradox, then one should allow that statements about an agent's doxastic state may also give rise to failures of classical logic. Since the antecedent of the conditional is reasonable, and the consequent surprising, the conditional is of interest.

In the second part of the dissertation, I argue that attention to questions about the nature of doxastic rationality can provide us with important insights into the correct treatment of the semantic paradoxes. For any non-classical response to the semantic paradoxes, an important question that arises is: what exactly is the cognitive significance of the non-classical semantic statuses employed by the theory? I argue that our earlier reflections on the normative paradoxes show that the standard ways of answering this question are wrong. Given standard accounts of the cognitive significance of non-classical semantic statuses, we can resurrect our normative paradoxes. What this means is that the standard accounts of non-classical cognitive significance are in conflict with certain fundamental principles of doxastic rationality. I argue that in order to reconcile the account of non-classical cognitive significance with these principles we need to say that the correct rational response to paradoxical propositions, such as that expressed by the liar sentence, is for there to be a mirroring non-classicality in one's doxastic state. A rational agent, then, will be such that the claim that it believes the proposition expressed by the liar sentence will have the same non-classical status as the proposition expressed by the liar sentence. What emerges is a new picture of the significance of non-classical treatments of the semantic paradoxes.