Event Detail

Wed Feb 22, 2017
234 Moses Hall, 6–7:30 PM
Working Group in the History and Philosophy of Logic, Mathematics, and Science
Sean Walsh (LPS, UC Irvine)
Interpreting Categorical Grammar in Church’s Intensional Logic

Church’s intensional logic was an attempt to axiomatize the relation which a Fregean sense bears to a referent in the circumstance that there is a linguistic expression which expresses the sense and denotes the referent. In some recent work ([1]), fragments of Church’s intensional logic have been developed which resolve the paradoxes of propositions by weakening comprehension. In this talk, we survey these fragments and assay the extent to which the traditional Montagovian interpretation of categorical grammar into the intensional theory of types can be mirrored by a interpretation of categorical grammar into the fragments of Church’s intensional logic.

References: [1] S. Walsh. Predicativity, the Russell-Myhill paradox, and Church’s intensional logic. The Journal of Philosophical Logic, 45(3):277–326, 2016.