Philosophy 510, Philosophical Logic, USC, Spring 2008
Scheduled for: T Th 11.00-12.30, WPH 104.
Professor James Higginbotham (MHP 205B, 740-4624 and GFS 301K, 821-2308,
higgy@usc.edu, Office hours: T 12.30-2.00, and by appointment). Blackboard address:
to be supplied.
Description
This is a course in logical theory, with USC PHIL-350, Intermediate Symbolic Logic, or
the equivalent as a prerequisite, providing knowledge of several important parts of logic
wanted both for more advanced study in logic itself and for contemporary research
especially in philosophy of language, syntactic and semantic theory, metaphysics,
philosophy of science, and philosophy of mathematics. Students coming from related
disciplines, including linguistics, mathematics, and computer science, will be introduced
to now classical advanced material that has been critical for contemporary developments
in these subjects.
Course Requirements and Marking
Texts and Readings
Required texts are:
Boolos, George S., Burgess, John P., and Jeffrey, Richard C. (2007). Computability and
Logic. 5th edition. Cambridge: Cambridge University Press.
Fitting, Melvin and Mendelsohn, Richard L. (1998). First-Order Modal Logic.
Dordrecht, Holland: Kluwer Academic Publishers.
The instructor will provide notes on those parts of set theory that are not fully explained
in the above texts. Classical basic references such as Paul Halmos, Naive Set Theory, and
Hrbacek and Jech, Introduction to Set Theory, will be on Reserve in the Hoose Library of
Philosophy. We shall also adapt some methods from the elegant introductory textbook of
Wilfrid Hodges (A Shorter Model Theory, Cambridge: Cambridge University Press).
Assignments and Marking
There will be five Problem Sets assigned during the term, each due within a week of
receipt. There will be no final exam, but the last Problem Set will be due on a date fixed
by the Final Examination Schedule. The Problem Sets will each count for 20% of the
grade. They will include problems from the texts and problems composed by the
instructor.
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Class Schedule and Topics
These are organized below by weeks (1-15, indexed by the date of the first Tuesday of
the week). 'BBJ' abbreviates Boolos, Burgess, and Jeffrey, 'FM' Fitting and Mendelsohn.
If time permits, we will extend the discussion of applications of modal logic to current
topics such as conditionals and counterfactuals, and other intensional notions.
Week 1, 1/15. BBJ Chapters 1 & 2. Enumerable sets; Cantor's Theorem and related
results. pp. 3-22.
Week 2, 1/22. BBJ Chapter 6. Recursive functions. pp. 63-72.
Week 3, 1/29. BBJ Chapter 7. Recursive relations. pp. 73-82. First problem set
assigned 1/31.
Week 4, 2/5. BBJ Chapters 9 & 10.1 of Chapter 10. Syntax and Semantics of first-order
logic. pp. 101-119. First problem set due 2/7.
Week 5, 2/12. BBJ 10.2 of Chapter 10 & Chapter 12. Metalogical Notions; Models. pp.
119-123 & 137-149.
Week 6, 2/19. BBJ Chapter 13. The existence of models. Compactness and the
Löwenheim-Skolem theorem. pp. 153-162. Second problem set assigned 2/21.
Week 7, 2/26. BBJ Chapter 15. The arithmetization of syntax. pp. 187-197. Second
problem set due 2/28.
Week 8, 3/4. BBJ Chapter 16. Numeralwise representability of recursive functions;
Robinson's Arithmetic. pp. 199-218.
Week 9, 3/11. BBJ Chapter 17. Indefinability, Undecidability, and Incompleteness
(Gödel's first incompleteness theorem). pp. 221-227. Third problem set assigned 3/13.
Week 10, 3/25. FM Chapter 1, first part. Propositional Modal Logic. pp. 1-21.
Week 11, 4/1. FM Chapter 1, second part. Logical Consequence in Propositional Modal
Logic. pp. 21-45.
Week 12, 4/8. FM Chapter 4 through 4.6. Interpretation of Quantifiers. Fixed domain
models. pp. 81-101. Fourth problem set assigned 4/10.
Week 13, 4/15. FM Chapter 4, 4.7-4.9. Varying domain models. The Barcan formula
and its converse. pp. 101-115. Fourth problem set due 4/17.
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Week 14, 4/15. FM Chapter 8 & Chapter 11 through 11.4. Existence and Quantification;
Existence and Designation. pp. 163-186 & 230-245.
Week 15, 4/22. BBJ Chapter 27. Modal Logic and Provability. Relevant results
(Gödel's second incompleteness theorem; Löb's theorem) sketched as background. pp.
327-340. Fifth and final problem set assigned 4/24. Due on date determined by final
exam schedule.
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