In this course we study a logistic system rich enough for the formalization of a large portion of mathematics: the first-order predicate calculus with identity and function symbols. We will prove, among other things, that the system is consistent, sound, and complete. To understand these metatheorems we need to be conversant with a whole raft of logical concepts beginning with the fundamental concepts of derivability and logical consequence. To prove the metatheorems we need to understand the concept of a metaproof and how such proofs are constructed. This requires in turn knowledge of mathematical induction. Many of our definitions and metaproofs use the concepts of set theory. So we will need to discuss Russell's paradox (which must be evaded if one is to have any set theory at all), review the basic concepts of set theory, study some of the basic strategies of set theory (such as proof by diagonalization), and prove a few of the classical theorems about plain, or unordered, infinite sets. All of this leads eventually to a study of formal theories. At the end of the course we will discuss the concepts relating to formal theories, analyze several formal theories including formal number theory, and come within sight of Gödel's first incompleteness theorem.

PHIL 470 will be followed in spring quarter of 2010 by PHIL 471, a biennial course on uncomputability and incompleteness, which takes up where PHIL 470 leaves off.

Texts: Benson Mates, Elementary Logic 2^nd edition(1972).         

Paul Teller, A Modern Formal Logic Primer, 2 volumes, at http://tellerprimer.ucdavis.edu/

Additional supplies: 3-ring binder for handouts.

Exercises. There will be an exercise for each class period. To receive full credit for an exercise you must attend class on the day the exercise is due. If you miss class, you can still receive partial credit as long as the exercise reaches me before the exercises are graded. (Exercises are usually graded immediately following class.) The book is closed on an exercise as soon as the grades are recorded.

Final. There will be a two-hour final on Wednesday, December 16th, 8:30-10:20 in our regular classroom. Your performance on the final will determine one-third of your final grade.

Grades. The class will be graded on a curve. Given that most of you earned a 4.0 in an elementary course in symbolic logic, the average IQ in the class must be quite high. As a consequence, one would expect the curve to also be on the high side. The flip side of the coin is that it will be a challenge to earn a 4.0.

Academic Integrity. Though academic honesty has never been a problem in this course, I would call your attention to the Student Honor Code at:

http://depts.washington.edu/grading/issue1/honesty.htm

The section under Collaboration is particularly relevant if you join a study group. Note also that if you hand in work for someone who is absent, it is dishonest not to append a note indicating this fact.