Philosophy 520: Philosophical Applications of Symbolic Logic
Dr.
McGrew, Spring 2007
Required Texts: There are two required texts for this course: E. J. Lemmon, Beginning Logic, and Susan Haack, Philosophy of Logics. Additional material (which is fair game for tests and quizzes) will be passed out in class or made available on the web. Students are responsible to get internet access through WMU (it's free) and make use of it to obtain relevant materials as assigned. The web address for this class is:
http://homepages.wmich.edu/~mcgrew/GradLogic07.htm
Course Description: In the twentieth century, symbolic logic has become the philosophers analytical tool par excellence. The aim of this course is to give students a firm understanding of elementary symbolic logic through the first order predicate calculus and to explore extensions of elementary logic such as second-order logic with identity, the family of modal logics, deontic logic, epistemic logic, and tense logic, as well as variants like many-valued logics and probability logic and even more exotic systems like protothetic. Along the way we will give considerable attention to philosophical issues involving the interpretation of logical notions, the interplay between logic and the history of philosophy, and some central questions in the epistemology of logic. By the end of the course, students should have a clear sense of the scope of elementary logic, facility in its use, an understanding of the relations between elementary logic and some of its more prominent extensions and variants, and an understanding of the implications of the basic metatheoretical results.
This is a graduate course that presupposes a prior course in symbolic logic at the level of Phil 225 or (preferably) Phil 320. We will move rapidly and the material covered will, at times, be more difficult than that in the average graduate seminar. Exams will include proofs and translations as well as conceptual questions. Students who are unable or unwilling to do this sort of work are strongly urged to take some other course.
Course Requirements: This course meets Tuesday and Thursday of each week at 2:00 p.m. except for scheduled holidays. Missed exams and quizzes cannot generally be made up without a medical excuse. Attendance and class participation are taken into account in the determination of the final grade. In particular, I reserve the right to subtract five points from the final semester grade for each unexcused absence beyond the third. Students are expected to come to class having done the reading indicated on the syllabus and may be subjected to quizzes without notice.
Academic Integrity: You are responsible for making yourself aware of and understanding the
universitys policies and procedures that pertain to Academic Integrity. These
policies include cheating, fabrication, falsification and forgery, multiple
submission, plagiarism, complicity and computer misuse. If there is reason to
believe you have been involved in academic dishonesty, you will be referred to
the Office of Student Conduct. You will be given the opportunity to review the charge(s).
If you believe you are not responsible, you will have the opportunity for a
hearing. You should consult with me if you are uncertain about an issue of
academic honesty prior to the submission of an assignment or test.
Grading: Aside from attendance, the course grade will be based on two exams in the middle of the semester, homework and pop quizzes (if any), and a final. The exams will be weighted equally at 25% of the grade apiece. The grading scale is:
|
A 93-100 |
B 83-87 |
C 73-77 |
D 60-67 |
|
B/A 88-92 |
C/B 78-82 |
D/C 68-72 |
E below 60 |
Note: The following course schedule is tentative. Because the material
is difficult, some of it may take longer than the indicated time. You are expected
to do the readings in accordance with the sequence of topics even if we are off
schedule. Any alterations in examination dates will be announced in class ahead
of time.
(1-3)
Propositional Logic
Week 1: Jan 9, 11
Indroduction to the
course. A map of some logical systems and
their relation to classical bivalent propositional logic. The syntax of propositional logic. Formation rules. Basic inference rules.
Week 2: Jan 16, 18
Semantics of propositional
logic. Derived
sequents, shortcuts, and proof strategy in natural
deduction. Counterexampling through semantic models. Semantic
tableaux.
Week 3: Jan 23, 25
Truth-functionality, functional completeness
and disjunctive normal form.
Formal semantics for propositional logic. Truth under an interpretation. Polish notation for
propositional logic.
(4)
Semantic Issues in Propositional Logic
Week 4: Jan 30, Feb 1
The connection between formal connectives and natural language
counterparts. Non-truth-functionality of subjunctive
conditionals. The indicative conditional and the paradoxes
of material implication. Assertability, implicature, and robustness.
(5)
Metatheory of Propositional Logic
Week 5: Feb 6, 8
Metatheoretic properties: soundness (consistency) and
completeness. The relation between syntax and semantics.
Here is the first Extra Credit Assignment!
(6-8) Modal and Quasi-modal Extensions of
Propositional Logic
Week 6: Feb 13, 15
Modal extensions of propositional logic. Formation rules and
semantics of the ~
and
operators. Possible worlds. Difficulties
in the interpretation of modal sentence logic.
Week 7: Feb 20, 22
Hierarchy of modal inference systems. Modal systems as models of semantic notions (e.g. analyticity). Reiteration and Tarski. Modal semantics for counterfactuals.
Week 8: Feb 27, Mar 1
Quasi-modal operators. Deontic logic, epistemic logic, and tense logic. Aristotelian
conception of the bearers of truth; related conception of necessity.
(9) Many-valued Logics
Week 9: Mar 13, 15
Alternative valuations systems for
propositional logic. Fatalism, indeterminism, and Lukasiewiczs
three-valued logic. Probability logic.
(10-11) Predicate Calculus
Week 10: Mar 20, 22
Predicate logic. Syntax and formation rules of predicate logic. Basic inference rules, derived sequents, and proof strategy.
Week 11: Mar 27, 29
Second order quantification. Basic metatheoretical results.
(12) Semantics
of the Predicate Calculus
Week 12: Apr 3, 5
Truth under an interpretation. Substitutional vs. objectual semantics. Polish notation for predicate logic.
(13) Modal
Extension of the Predicate Calculus
Week 13: Apr 10, 12
Quantified modal logic and essentialism. Quines three grades of modal involvement. The analysis of definite descriptions. Possible worlds once again.
(14) Protothetic Extension of the Predicate Calculus
Week 14: Apr 17, 19
Protothetic and the representation of self-reference and self-refutation.