Predicate Modal Logics and Non-standard Set Theories
A weekly seminar devoted to exploring the application of non-standard logics to philosophical problems.
Next Meeting
Feb 27The next meeting will be on Friday, February 27, 2009 in Cordura 100 at 12:00–13:15. Our guest speaker will be Wilfried Sieg. His talk is entitled “Uncovering Aspects of the Mathematical Mind”.
Brief Synopsis: The basic Comprehension Principle of so-called “naive” set theory is the at first sight plausible statement that every property determines a set, namely the set of all objects which satisfy that property. This was shown to lead to a contradiction in ordinary logic by Bertrand Russell, using the supposed set of all sets that are not members of themselves. Subsequent work on the foundations of set theory has concentrated on axiomatic systems in which the Comprehension Principle is considerably restricted; but then to carry out the usual set-theoretic constructions, many other special axioms had to be added to these “standard” approaches. An alternative that has been pursued by a number of researchers with non-standard set theories is to retain the unrestricted Comprehension Principle admitting various forms of self-membership while avoiding inconsistency by means of a restriction of the underlying logic.
In January we will go through the book Fixing Frege, by John Burgess. After the organizational meeting on the 9th, we will review Chapter 1 of Burgess's book on January 16, then Chapter 2 on January 23. John Burgess will come at the end of the month and (January 30) to talk about his book. (Burgess will also give a presentation in the Mathematical Logic Seminar on January 27 that may be of interest [title and abstract].)
In February we will go through the book Types, Tableaus, and Gödel's God, by Melvin Fitting, on using higher-order modal logic to study Kurt Gödel's proof of the existence of God. The book is out-of-orint, but can be found on reserve at the Tanner Library in the Philosophy Department. Some of the book's content is available online via Google Books.
Support from the Humanities Center and the Symbolic Systems Program is gratefully acknowledged.