square of opposition


Subject to revision. Check http://johnmacfarlane.net/142 for the latest.


Tu Jan 19
What is philosophical logic? Review of propositional logic. Handout with exercises (to be handed in in section next week, but not graded).
Th Jan 21
Review of predicate logic. Handout with exercises (to be handed in in section next week, but not graded).

Unit 1—Quantification

Tu Jan 26
Identity. Numerical quantifiers. Handout with exercises.
Th Jan 28
Generalized quantifiers. Definite descriptions. Handout with exercises.
Tu Feb 2
Generalized quantifiers. Quinean corner quotes. Handout with exercises.
Th Feb 4
Substitutional quantification. Reading: Linsky, “Two Concepts of Quantification,” II, IV, V. Handout with exercises.
Tu Feb 9
Substitutional quantification, continued. Plural quantification introduced.
Th Feb 11
Plural quantification. Reading: Boolos, “To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables).” Exercises.

Unit 2—Modality

Tu Feb 16
Propositional modal logic: semantics and natural deductions. Handout with exercises. Unit 1 problems due.
Th Feb 18
Quine’s objections to quantified modal logic. Reading: Quine, “Reference and Modality.” Optional Reading: Quine, “Three Grades of Modal Involvement.”
Th Feb 23
Smullyan’s response to Quine. The slingshot argument. Optional Reading: Smullyan, “Modality and Description.” Handout with exercises.
Th Feb 25
Kripke’s response to Quine. Reading: Kripke, Naming and Necessity, pp. 34-63 (on apriority vs. necessity), pp. 97-105 (on the necessity of identity).

Unit 3—Logical Consequence

Tu Mar 1
Informal characterizations of logical consequence.
Th Mar 3
Tarski’s definition of logical consequence. Reading: Tarski, “On the Concept of Logical Consequence.” Unit 2 problems due.
Tu Mar 8
Inference rules and the meanings of the logical constants. Reading: Prawitz, “Logical Consequence from a Constructive Point of View,” through p. 678. Prior, “The Runabout Inference Ticket.” Belnap, “Tonk, Plonk, and Plink.”
Th Mar 10
Prawitz’s proof-theoretic account of consequence. Intuitionistic logic. Reading: Prawitz, “Logical Consequence from a Constructive Point of View” (entire).
Tu Mar 15
Motivations for relevance logic. The Lewis argument. Reading: Meyer, “Entailment.”
Th Mar 17
Relevance logic. Reading: Burgess, “No Requirement of Relevance.” Recommended: Anderson and Belnap, Entailment, vol. 1, §§15, 16.1.
Tu Mar 29
Logic and reasoning. Reading: Harman, Change in View, Chapters 1-2.
Th Mar 31
Relevance logic and inconsistent data. Reading: Lewis, “Logic for Equivocators.” Recommended: Anderson, Belnap, and Dunn, Entailment, vol. 2, §§81-81.2.3.

Unit 4—Conditionals

Tu Apr 5
Subjunctive vs. indicative conditionals. Defense of the material conditional. Reading: Thomson, “In Defense of ’’”. Unit 3 problems due.
Th Apr 7
Do conditionals have truth conditions? Reading: Edgington, “Do Conditionals Have Truth-Conditions?”
Tu Apr 12
A modal account of the indicative conditional. Reading: Stalnaker, “Indicative Conditionals.”
Th Apr 14
A counterexample to Modus Ponens? Reading: McGee, “A Counterexample to Modus Ponens.”

Unit 5—Vagueness and the Sorites Paradox

Tu Apr 19
The sorites paradox. Multivalued logics. Reading: Sainsbury, Paradoxes, §§2.1-2.4. Williamson, Vagueness, §§4.1-4.6.
Th Apr 21
Fuzzy logic. Reading: Williamson, Vagueness, §§4.7-4.14.
Tu Apr 26
Supervaluationism. Reading: Williamson, Vagueness, Chapter 5.
Th Apr 28
Evans on vagueness in the world. Reading: Evans, “Can There Be Vague Objects?”


May 6
Paper due.
May 12
Final exam. 3-6 PM, 130 WHEELER