Philosophy 416: MODAL LOGIC
Winter 1998
Stephen Yablo

COURSE DESCRIPTION

Modal logic is the logic of necessity and possibility, and by extension of analogously paired notions like validity and consistency, obligatoriness and permissibility, the known and the not-ruled-out. This a first course in the area, based on Hughes & Cresswell's A New Introduction to Modal Logic. A solid background in first-order logic, including soundness and completeness results, is essential. Topics to be covered include (some or all of) alternative systems of modal logic, Kripkean "possible world" semantics, strict implication, modal predicate calculus, modality and existence, contingent identity, intensional objects, counterpart theory, and the logic of actuality. The emphasis will be more on technical methods and results than philosophical applications.

INSTRUCTOR

Stephen Yablo, 2235 Angell Hall
ph: 763-3744 (my office), 764-6285 (dept. office)
email: yablo@umich.edu

OFFICE HOURS

Thursdays 1:30-3:00, 2235 Angell Hall.

TEXT

• Hughes & Cresswell, A New Introduction to Modal Logic, (Routledge, 1996), available @ Shaman Drum (313 S. State, 662-7407)
• Depending on interest, mimeographed articles handed out in class.

WEB PAGE

Basic information associated with the course, including this syllabus, homework, and handouts can be accessed through the PHIL 416 Web Page. Point your Web Browser -- Netscape Navigator or some comparable program -- at the URL address http://www-personal.umich.edu/~yablo/416.html

REQUIREMENTS

weekly homework	40%
in class midterm (February 20)	20%
final exam (April 23, 1:30- 3:30)	30%
participation, improvement, etc.	10%

HOMEWORK

Homework is assigned each Friday and returned the following Wednesday, except that HW 8 is returned 3/11 due to Spring Break.

Number	Distributed	Due
1	1/9	1/14
2	1/16	1/21
3	1/23	1/28
4	1/30	2/4
5	2/6	2/11
6	2/13	2/18
7	2/20	2/25
8	2/27	3/11
9	3/13	3/18
10	3/20	3/25
11	3/27	4/1
12	4/3	4/8
13	4/10	4/15
14	4/17	4/22

COURSE SCHEDULE

All readings are from Hughes & Cresswell, New Introduction to Modal Logic. This schedule is tentative and may be departed from! Classes marked with an R are ones for which outside readings will (may) be assigned.

Week 1: Basic Propositional Notions

• Jan. 7: Propositional Syntax and Semantics, 3-8
• Jan. 9: Propositional Validity, 8-13

Week 2: Basic Modal Notions

• Jan. 12: Modal Syntax & Semantics, 13-17, R
• Jan. 14: Modal Validity, 17-21
• Jan. 16: Our "Base" Modal Logic K, 23-33

Week 3: System K

• Jan. 19: MLK DAY -- NO CLASS
• Jan. 21: Duality in K, 33-36
• Jan. 23: Soundness of K, 36-41

Week 4: Extensions of K

• Jan. 26: Systems T and D, 41-48
• Jan. 28: System S4, 51-57
• Jan. 30: Systems B and S5, 58-64

Week 5: Testing for Validity

• Feb. 2: Semantic Diagrams, 72-84
• Feb. 4: Application to S4 and S5, 85-92
• Feb. 6: Review

Week 6: Modal Metalogic

• Feb. 9: Completeness and Consistency, 111-117
• Feb. 11: Completeness of K, T, B, S4, and S5, 117- 121
• Feb. 13: Review

Week 7: Glimpses Beyond

• Feb. 16: Neighborhood Semantics and Lewis's Counterfactuals, 221-224, R
• Feb. 18: Probabilistic Semantics, 227-228, R
• Feb. 20: MIDTERM EXAM

Week 8: Modal Predicate Logic

• Feb. 23: Predicate Calculus, 235-243
• Feb. 25: Modal Predicate Calculus, 243-250
• Feb. 27: De re and De Dicto, 250-254

***********SPRING BREAK***********

Week 9: Modal Predicate Metalogic

• Mar. 9: Completeness of Modal Predicate Calculus, 256-262
• Mar. 11: Completeness in Modal Predicate Calculus, 262-265
• Mar. 13: Review

Week 10: Shifting Domains

• Mar. 16: Validity without the Barcan formula, 274-280
• Mar. 18: Completeness without the Barcan Formula, 280-283
• Mar. 20: The converse Barcan Formula, 289-292

Week 11: Existence and Identity

• Mar. 23: Existence Predicates, 292-302
• Mar. 25: Possibilist Quantification, 303-4
• Mar. 27: Identity, 312-317

Week 12: Descriptions and Identity

• Mar. 30: Definite Descriptions, 318-323
• Apr. 1: Descriptions and Scope, 323-326
• Apr. 3: Contingent Identity, 330-335, R

Week 13: Intensional Objects

• Apr. 6: Unaxiomatizability of Plenitude, 335-342
• Apr. 8: Intensional Objects and Descriptions, 342- 346
• Apr. 10: Review

Week 14: Special Topics

• Apr. 13: First-Order Modal Theories, 349-350, R
• Apr. 15: Multiple Indexing and Actuality, 350-353, R
• Apr. 17: Counterpart Theory, 353-358, R

Week 15: Wrapping Up

• Apr. 20: Review
• Apr. 23: FINAL EXAMINATION, 1:30-3:30