We are a Working Group devoted to the discussion of historical and philosophical issues in symbolic logic, mathematics, and science. We meet on occasional Wednesday evenings for a talk and a lively discussion. The group is funded by the Doreen B. Townsend Center for the Humanities and the Department of Philosophy.
All members of the academic community are welcome to attend. We have regular participants in many different fields, including philosophy, mathematics, history of science, and psychology.
Our next event
February 22, 2017, 6-7:30 PM in 234 Moses Hall
Sean Walsh (Department of Logic and Philosophy of Science, 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 (), 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:  S. Walsh. Predicativity, the Russell-Myhill paradox, and Church’s intensional logic. The Journal of Philosophical Logic, 45(3):277–326, 2016.