Logic & Philosophy of Science Colloquium


Edward N. Zalta
Stanford University, CSLI

"Frege, Boolos, and Logical Objects"

Authors: David J. Anderson and Edward N. Zalta

In this talk, we discuss Frege's theory of "logical objects" (extensions, numbers, truth-values) and the recent attempts to rehabilitate Frege's theory of them. We focus on George Boolos's work and show that the `eta' relation he deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the `eta' relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for Logical Objects and banishes encoding (eta) formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: (a) the theory of extensions, (b) the theory of directions and shapes, and (c) the theory of truth values.

Friday, November 21, 2003
SST 777
3 pm

Refreshments will be served