|| Second-Order Logic
|| Péter Mekis
|| BMA-LOTD-322.05, BMI-LOTD-322E.05, BBN-FIL-301.07
|| Tuesday 16:00-17:30
|| The course assumes familiarity with the basic concepts and methods of standard first-order logic.
|| First-order predicate logic, the standard framework for logical investigations, allows for universal and existential generalizations over individuals. Second-order logic extends the expressive power of logical languages by allowing for generalizations over relations and functions, too. This results in huge differences; most notably, while it is impossible to specify a particular infinite structure (like the natural numbers, or the universe of sets) in first-order logic, it becomes possible in second-order logic. But this extended power comes at a price: second-order logic is in many respects too powerful to serve as a foundational framework for mathematics and other formal sciences.
The discussion of the lectures will be partly technical and partly philosophical, and most of it will be based on Stuart Shapiro's and George Boolos' works.
- Lecture notes (updated and uploaded during the course)
- George Boolos,
Logic, Logic and Logic.
Harvard UP, 1998.
- Stuart Shapiro,
Foundations without Foundationalism:
A Case for Second-Order Logic.
Oxford UP, 1991.