The Center for the Advancement of Logic, its Philosophy, History and Applications
"The Constructible Universe, the Naive Conception, and Intensional Logic"
with Sean Walsh, Department of Logic & Philosophy of Science, UC Irvine
January 15, 2014
Social Science Tower, Room 777
This talk will cover the relationship between three foundational systems: Gödel's Constructible Universe of Sets, the naive conception of set found in consistent fragments of Frege's Grundgesetze, and the intensional logic of Church's Logic of Sense and Denotation. One basic result shows how to use the constructible sets to build models of fragments of Frege's Grundgesetze from which one can recover these very constructible sets using Frege's definition of membership. This result also allows us to solve the related consistency problem and joint consistency problems for abstraction principles with limited amounts of comprehension. Another basic aim will show how to "factor" this result via a consistent fragment of Church's Logic of Sense and Denotation: so one may use the constructible sets to build models of Church's Logic of Sense and Denotation, from which one may then define models of the consistent fragments of Frege's Grundgesetze.
For further information, please contact Patty Jones, firstname.lastname@example.org or 949-824-1520.