Graduate Student / Postdoc Seminar
Property Theories with Unrestricted Comprehension
Speaker: Hartry Field
Location: Warren Weaver Hall 1302
Date: Friday, October 26, 2012, 1 p.m.
By an analog of Russell's Paradox, property theories with unrestricted comprehension are inconsistent—in classical logic. But there are ways to weaken the logic to make them consistent. Indeed, there are ways to do this where the logic reduces to classical logic in the fragment that doesn't include the property-instantiation predicate.
For this to be of much interest, we need to make the general logic (for the full language with the instantiation predicate) natural, and close to classical. To what extent can these vaguely stated goals be achieved? At the moment there are some positive results, but also reasons for wanting improvements, and many open questions as to how much improvement is possible.
In the talk I'll discuss both reasons why this program is of mathematical as well as philosophical interest, and some mathematical techniques that might help answer some of the open questions.