Logic & Philosophy of Science Colloquium


C. Anthony Anderson
University of California, Santa Barbara

"Quantified Modality in the Style of Frege and Church"


The Frege-Church approach to intensional logic has been neglected for a number of reasons - probably the main one being the apparent complexity of the notation and the success of "possible world semantics" in connection with modal logic. This, I think, is a mistake. The complexity of the primitive notation can always be mitigated in practice by appropriate abbreviations. And the underlying ideas produce additional clarity even in such thoroughly studied matters as the de re/de dicto distinction. Further, eventually intensional logicians will have to fully face up to the inadequacy of possible world models for formalizing the propositional attitudes. In this paper I outline a construction of modal logic along Fregean lines, but with some changes in detail and with some changes in emphasis as compared to Church's formalization of the logic of sense and denotation.

Here I emphasize mainly the expressive resources of the logic rather than details of axiomatization. I will discuss in these terms (1) the de re/de dicto distinction, (2) an argument of Church's against the S4 principle and some remarks about this by John Myhill and by Brian Skyrms, and (3) Kripke's examples of "intermediate scope" modal contexts.

Friday, November 7, 2003
SST 777
3 pm

Refreshments will be served