The Department of Logic & Philosophy of Sciences Colloquium Series and Center for the Advancement of Logic, its Philosophy, History & Applications (C-ALPHA) present

"Commitment, Closure, Consequence"
with Colin Caret, Underwood International College, Yonsei University

Monday, April 14, 2014
2:00-4:00 p.m.
Social & Behavioral Sciences Gateway, Room 1321

The recent literature on logic and paradox divides between advocates of non-transitive and non-contractive theories. In this talk, Caret will argue that the only viable option in this debate is to reject contraction. The argument turns on the normative role of logic in the cognitive economy. Logical consequence codifies the relation between belief and commitment, i.e. the operation that determines what an agent is committed to in virtue of what she believes. Caret will argue that such commitments are complete in an important sense. The driving intuition is that the normative force of doxastic commitment ramifies counterfactually, in that an agent cannot rationally disbelieve any of the commitments she would have if she were to believe all of her commitments. As a result, doxastic commitment is what Tarski called a closure operation. The relation of logical consequence, in turn, is a closure relation on belief states. On any generalization of logical consequence qua closure relation on beliefs, it must be a transitive relation. However, if beliefs aggregate in more fine-grained collections than ordinary sets, then there are counterexamples to contraction that are consonant with the conceptual role of logical consequence. Caret will argue that there is a conception of propositional content on which beliefs aggregate into multisets rather than sets. This shows that transitivity is a constitutive feature of logical consequence, while contraction is not.

For further information, please contact Patty Jones, patty.jones@uci.edu or 949-824-1520.