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

Review of predicate logic. Handout with exercises (to be handed in in section next week, but not graded).

Identity. Numerical quantifiers. Handout with exercises.

Generalized quantifiers. Definite descriptions. Handout with exercises.

Generalized quantifiers. Quinean corner quotes. Handout with exercises.

Substitutional quantification.
Reading: Linsky, “Two Concepts of Quantification,” §§II, IV, V. Handout with exercises.

Substitutional quantification, continued. Plural quantification introduced.

Plural quantification. Reading: Boolos, “To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables).” Exercises.

Propositional modal logic: semantics and natural deductions. Handout with exercises. Unit 1 problems due.

Quine’s objections to quantified modal logic. Reading: Quine, “Reference and Modality.” Optional Reading: Quine, “Three Grades of Modal Involvement.”

Smullyan’s response to Quine. The slingshot argument. Optional Reading: Smullyan, “Modality and Description.” Handout with exercises.

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).

Informal characterizations of logical consequence.

Tarski’s definition of logical consequence. Reading: Tarski, “On the Concept of Logical Consequence.” Unit 2 problems due.

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.”

Prawitz’s proof-theoretic account of consequence. Intuitionistic logic. Reading: Prawitz, “Logical Consequence from a Constructive Point of View” (entire).

Motivations for relevance logic. The Lewis argument. Reading: Meyer, “Entailment.”

Relevance logic. Reading: Burgess, “No Requirement of Relevance.” Recommended: Anderson and Belnap, Entailment, vol. 1, §§15, 16.1.

Logic and reasoning. Reading: Harman, Change in View, Chapters 1–2.

Relevance logic and inconsistent data. Reading: Lewis, “Logic for Equivocators.” Recommended: Anderson, Belnap, and Dunn, Entailment, vol. 2, §§81–81.2.3.

Subjunctive vs. indicative conditionals. Defense of the material conditional. Reading: Thomson, “In Defense of ‘⊃’”. Unit 3 problems due.

Do conditionals have truth conditions? Reading: Edgington, “Do Conditionals Have Truth-Conditions?”

A modal account of the indicative conditional. Reading: Stalnaker, “Indicative Conditionals.”

A counterexample to Modus Ponens? Reading: McGee, “A Counterexample to Modus Ponens.”

The sorites paradox. Multivalued logics. Reading: Sainsbury, Paradoxes, §§2.1–2.4. Williamson, Vagueness, §§4.1–4.6.

Fuzzy logic. Reading: Williamson, Vagueness, §§4.7–4.14.

Supervaluationism. Reading: Williamson, Vagueness, Chapter 5.

Evans on vagueness in the world. Reading: Evans, “Can There Be Vague Objects?”

Paper due.

Final exam. 3–6 PM, location TBA