Professor Stout
Office hours: 8:30-10 MWF, 11-11:30
T
Office C209C Center for Natural Sciences, 556-3038
Nerode and Shore: Logic for Applications, second edition, Springer Verlag, 1997
Crossley, Ash, et. al. What is mathematical logic?, Oxford, 1972
Logic is the formal analysis of valid patterns of argument and deductive inference. This has been one of the concerns of philosophy since Aristotle. Since mathematics requires careful deductive reasoning and provides a systematic way to study patterns and structures, logic and mathematics have had a symbiotic relationship, particularly in the last century. Since Boole (in the mid 1800's) mathematicians have formalized logic so that it can be studied as part of the subject matter of mathematics as well as providing a careful check on the kind of reasoning allowed in mathematics. Computers can be thought of as logic cast in silicon. Computer science uses logical notions in design of programming languages and the analysis of computing paradigms. Computers are also used in automated reasoning, searching for proofs in suitable formal systems. Logic sits firmly on the boundary between the three disciplines of mathematics, philosophy, and computer science. (Meetings of the Association for Symbolic Logic often have papers by philosophers, mathematicians, and computer scientists in the same sessions. They provide an interesting contrast in academic cultures.)
This course will study formal logic as used in the foundations of mathematics and the analysis of philosophical argument: classical propositional calculus and predicate calculus with a special focus on syntax, semantics, soundness, completeness, compactness, decideablity and incompleteness. We'll look at model theory and proof theory as ways to apply mathematical thinking to questions in logic. We will ask what kinds of questions in logic can be solved in a deterministic fashion and will provide an algorithmic approach to decide logical questions which can be decided. Nerode and Shore use tableau methods to provide a unified approach to a lot of different kinds of logical systems. We will also look at natural deduction systems and see how the tableau methods can be translated into that language. Hilbert style systems of formal deduction are more difficult tounify with this approach.
Along with our understanding of classical logic, we will look at how mathematical structures can shed light on non-classical logics: many-valued logics, intuitionistic logic (which may be thought of as dealing with states of knowledge rather than truth), fuzzy logic (which deals with vagueness), modal logic (addressing questions of necessity, possibility, and tense), and categorical logic (a framework which can include all of these in a natural way). These are topics close to my research interests and they provide several possible topics for student research projects. Some of these logics are closely tied to current developments in the logical foundations of theoretical computer science.
This course presupposes some prior exposure to formal logic: Philosophy students should have had Phil 102; math students should have Math 200 or 220; Computer Science students are assumed to have CS 256 (which has a corequisite of Math 220).
There will be two class period length exams (100 points each), two small projects/papers (50 points each), and a larger final project (100 points). In addition I will assign homework problems designed to help you understand the material we are covering in class. The projects will have options suited to philosophical, mathematical, or computational approaches. The final project should be chosen to relate to the rubric you are taking the course under.
I use a straight scale for determining grades. To allow flexibility at boundaries, I reserve the right to change the boundaries, but I will draw them no higher than
A : 90% or over
A- : [87,90)
B+ : [83,87)
B : [78,83)
B- : [75,78)
C+ : [70,75)
C : [65,70)
C- : [60,65)
D : [50,60)
F : below 50%
The line for passing will not move, the others may move downward.
Classes and office hours are what you pay tuition for, so take advantage of them. If you don't come to class you will not learn the material with the same emphasis that I put on it. That will hurt your exam scores and detract from what you learn. I do not deduct points for classes missed. Make-up exams are usually only given when I have accepted a good excuse in advance of the exam.
Work handed in for a grade is expected to be your own work. On Take Home exams and individual projects there should be no collaboration: this will be made explicit on the assignment sheet. On daily homework there is something to be gained by talking and working with your fellow students; the writeup, however, should be your own. If you use outside sources, cite them. If you get help from an individual, give credit. It is not wise for you to neglect learning how to do the work on your own, since exams will all require all work to be done individually. Any cheating on exams or collaboration on assignments where it has been explicitly prohibited will be treated as a violation of the policy on academic dishonesty in the student handbook and will be reported to the Associate Provost.
Last updated 1/9/2002
lstout@sun.iwu.edu