Title 
SecondOrder Logic 
Lecturer 
Péter Mekis 
Codes 
BMALOTD322.05, BMILOTD322E.05, BBNFIL301.07 
Time 
Tuesday 16:0017:30 
Venue 
i224 
Prerequisites 
The course assumes familiarity with the basic concepts and methods of standard firstorder logic. 
Description 
Firstorder predicate logic, the standard framework for logical investigations, allows for universal and existential generalizations over individuals. Secondorder 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 firstorder logic, it becomes possible in secondorder logic. But this extended power comes at a price: secondorder 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.

Literature 
 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 SecondOrder Logic.
Oxford UP, 1991.
