Phil 710 – Seminar: Logical Consequence

Spring 2007. Thursdays 1:00-3:30pm in Bartlett 212
Prof. Kevin Klement

Course description:
An examination of the philosophical controversies surrounding the nature of logic itself. What is logic, or “a logic”? What is the logical consequence relation? What are the bearers of this relation? What, if anything, makes logical truths true? Are the standard (Tarskian) mathematical definitions of logical truth and logical implication philosophically correct? Can there be multiple correct “logics”? Is logic dependent on the mind or on language? What makes a logical constant different from other meaningful symbols? Prerequisites: Graduate student with strong background in formal logic, or consent of instructor.

Contact info:
My office is 353 Bartlett Hall. My office phone is 545-5784. My office hours are Mondays 2pm-3pm, Thursdays 11am-12pm and by appointment. I'm often in my office many other times. Feel free to drop by any time. You may also e-mail me at klement@philos.umass.edu. Our course web page is http://courses.umass.edu/klement/710/
 
Texts:
Short readings will be made available for photocopy in the metal cabinet on the 3rd floor of Bartlett, or will be distributed by e-mail, or are available on JSTOR.

Course requirements:
Your final grade will be based on the following requirements, (1) in-class participation (15%), (2) one class presentation (15%), (3) weekly assignments (25%), and (4) a final term paper (45%).

Weekly Assignments: You are expected to carefully read the selected texts for each session before the seminar meeting and come prepared to discuss them. To help facilitate this, each week you are expected to write a 1-3 page essay in which you (1) summarize the reading, (2) identify any criticisms or points of discussion (including points in need of clarification) involving the reading. These essays are due at the start of class on the day on which we will be discussing the relevant readings. You will be graded on 1-5 scale, with 1 representing a barely acceptable essay, 2 representing a deeply problematic essay, that misrepresents the views of the philosopher or philosophers in question or commits other abuses of philosophical method, 3 representing an essay that is slightly lacking in some area, but generally acceptable, 4 representing a good essay that performs the desired tasks as expected, and 5 representing an essay with substantial and original insight. (You should never expect to receive anything above 4. A student receiving a 4 on every assignment should still expect a good grade for this portion. I will only award a 5 to an essay that surpasses my expectations.) In determining your grade, I will take into account only your 10 highest scores of 12 possible essays. This means you may either drop your two lowest scores, or simply not write two essays (or combine the two options). You need not prepare an assignment for the week you will be presenting.

Presentation: Early in the semester, each student will choose (or be assigned) one week in which he or she is expected to give a presentation on the readings for that week (approx. 20 minutes), to be given at the beginning of the seminar meeting, and should also be prepared to lead the discussion for that class period. The presentation should (1) summarize the main points of the readings, though at his or her discretion the presenter may focus on certain issues he or she finds most interesting, (2) identify any questions or concerns the presenter has with understanding or interpreting the material, which he or she would like to discuss in class, (3) critically discuss one or more philosophical issues raised in the readings, as a starting point for seminar discussion.

Term Paper: Each student is prepared to write a 15-25 page term paper that aims to contribute something original to the discussion of any of the texts, philosophers or philosophical issues discussed in the course. The paper should constitute critical and original discussion of the philosophical issues concerning the nature of logic and/or the logical consequence relation. The amount of outside research done for the paper is left to your discretion, but a careful search of the relevant secondary material is strongly recommended. It is due either at the end of finals week (May 25), or by the first day of Fall Semester (if you take an incomplete).

Phil 710: Seminar – Logical Consequence
READING SCHEDULE

Feb. 1 — Course Introduction

Feb. 8 — Classical depictions: Aristotle, Organon, various short passages; Bernard Bolzano, Theory of Science, selections; Frege, “Logic”, selections from The Foundations of Arithmetic and The Basic Laws of Arithmetic and other short writings

Feb. 15 — Russell, chap. 1 of The Principles of Mathematics and “Mathematics and Logic” (chap. 18 of Introduction to Mathematical Philosophy), Wittgenstein, Tractatus Logico-Philosophicus §§4.2-5.143 (recommended §5.2-5.5151)
    
Feb. 22 — Tarski, “The Concept of Logical Consequence” (from Logic, Semantics, Metamathematics); textbook presentation of model-theoretic definitions (e.g., Mendelson, Introduction to Mathematical Logic, 4th ed. chap. 2, pp. 50-66)

Mar. 1 — Quine, The Philosophy of Logic, chaps. 1, 3, 6-7

Mar. 8 — Peacocke, “What is a Logical Constant?” Journal of Philosophy 73 (1976): 221-40, McCarthy, “The Idea of a Logical Constant,” Journal of Philosophy 78 (1981): 499-523.

Mar. 15 — Tarski, “What are Logical Notions?” History and Philosophy of Logic 7 (1986): 143-154; Sher, “A Conception of Tarskian Logic,” Pacific Philosophical Quarterly 70 (1989): 341-68.

Mar. 22 — No class (Spring Break)

Mar. 29 — Etchemendy, The Concept of Logical Consequence, chaps. 3-8

Apr. 5 — McGee, “Two Problems with Tarski’s Theory of Consequence,” Proceedings of the Aristotelian Society 92 (1992): 273-292. Priest, “Etchemendy and Logical Consequence,” Canadian Journal of Philosophy 25 (1995): 283-292.

Apr. 12 — Ray, “Logical Consequence: A Defense of Tarski,” Journal of Philosophical Logic 25 (1996): 617-77. (Recommended: Hanson, “Ray on Tarski on Logical Consequence,” Journal of Philosophical Logic 28 (1999): 607-618.)

Apr. 19 — Susan Haack, Philosophy of Logics, chaps. 9, 11-12

Apr. 26 — JC Beall and Greg Restall, “Logical Pluralism,” Australasian Journal of Philosophy 78 (2000): 475-98; Goodu, “What Exactly is Logical Pluralism?” Australasian Journal of Philosophy 80 (2002): 218-230.

May 3 — OPEN (TBA)

May 10 — OPEN (TBA)

Possible “Open” Topics:
- the nature of logical form
- more on the relata of the consequence relation: propositions vs. sentences, etc.
- more on the dependence of logic on the mind/language
- more on non-classical logic
- debate over the status of higher-order logic (--does it count as “logic” proper?)
- constructivist theories of consequence
- more historical stuff
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