Christopher C. Leary, A Friendly Introduction to Mathematical Logic (Prentice-Hall, 2000). Don't be misled by the title: this is not an introduction to symbolic logic per se, but rather an introduction to metalogic. It includes proofs of soundness and completeness theorems for first-order logic, the compactness theorem, the upward and downward Löwenheim-Skolem theorems, and culminates in proofs of Gödel's incompleteness theorems. However, compared with other texts in the area, this one is fairly friendly.
We will also make use of a variety of other materials, including handouts and online materials on the philosophical implications of Gödel's results, and material on alternatives to, and extensions of, classical first-order logic. Especially valuable resources are the Routledge Encyclopedia of Philosophy (available in the library either in hard copy or in a CD-ROM version) and the Stanford Encyclopedia of Philosophy.
MW, 10:30 - 11:30, 2:00 -3:00; TR, 2:30 - 3:30.
I am usually in my office during office hours, but occasionally a meeting or another commitment prevents this. If you just drop by during office hours, you will probably find me in; if you want to see me at another time, or if you want to be certain I'll be in, we can set up an appointment.
There will be a mid-term examination and a final examination. There will be regular shorter assignments -- sometimes homework problems, sometimes short papers. Every member of the class will be expected to give at least two in-class presentations on topics germane to the course: an extension to, or revision of, first-order logic or a metalogical result. There will also be a final project for the course. Percentages: Mid-term, 20%; Final, 20%; presentations and class participation, 20%; Short Assignments, 20%; Final Project, 20%. (Easy to remember!)
Very Rough Schedule
structures and languages
proof of soundness
proof of the deduction theorem
completeness and compactness
proof of completeness theorem
proof of compactness theorem
proofs of upward and downward Skolem-Lowenheim theorems
incompleteness - groundwork
recursive sets and functions
NUM and SUB functions
incompleteness - proofs
proofs of Gödel's first and second incompleteness theorems
significance of the incompleteness results
relation between incompleteness and uncomputability
Penrose: incompleteness shows AI impossible (handout from Penrose)
criticisms of Penrose (Chalmers essay)
Putnam on realism (handout)
criticisms of Putnam (recent Journal of Philosophy article)
axiomatic systems, natural deduction systems, sequent introduction systems
equivalent sets of axioms, rules, etc.
modal logic (handout from Forbes)
intuitionistic logic (handout from Forbes)