| Topic | Readings |
|---|---|
| Course introduction, general examples |
• Makinson, David C. The Paradox of the Preface, Analysis 25.6 (1965): 205–207. • Lewis Carroll, What the Tortoise said to Achilles, Mind 4(14), 1895, p.278-280. • William G. Lycan, What, Exactly, Is a Paradox? Analysis 70(4) (2010): 615–622. |
| Simple paradoxes about space, time, change, and movement |
• R. M. Sainsbury, Paradoxes, Ch. 1 (pp. 4–21). • P. Łukowski, Paradoxes, Ch. 5.2. • J. F. Thomson, Tasks and Super-Tasks, Analysis 15(1) (1954): 1–13. • See also: SEP: Supertasks, and SEP: Spacetime-supertasks. |
| Vagueness and Sorites Paradoxes |
• R. M. Sainsbury, Paradoxes, Ch. 3 (pp. 40–66). • P. Łukowski, Paradoxes, Ch. 5.1. • J. Robert G. Williams, “Vagueness.” See also: SEP: Vagueness. • Gareth Evans, “Can There Be Vague Objects?” Analysis 38.4 (1978): 208–212. • Delia Graff Fara, Shifting Sands, Philosophical Topics 28(1) (2000): 45–82 (focus on §§1, 4, 6). • See also: SEP: Sorites Paradox. |
| Liar |
• R. M. Sainsbury, Paradoxes, Ch. 6. • P. Łukowski, Paradoxes, §4.2.1. • Glanzberg and Beall, The Liar Paradox (SEP). • Stephen Yablo, Paradox Without Self-Reference, Analysis 53(4) (1993): 251–252. • See also: Self reference and paradox (SEP) |
| Sets, logic, maths |
General topics: Russell’s Paradox, Cantor’s Paradox, Burali–Forti Paradox, Skolem’s Paradox, Richard’s & Berry’s Paradoxes,
Grelling–Nelson (Heterological) Paradox Infinity: Hilbert’s Hotel, Banach–Tarski Paradox, Vitali Set, Borel’s Paradox, Gabriel’s Horn • Bertrand Russell, Letter to Frege, 16 June 1902. • Cantini, Paradoxes and Contemporary Logic (SEP). • John Stillwell, Mathematics and Its History (3rd ed.), Springer, 2010 – chapter on set-theoretic paradoxes. • Russell, On Some Difficulties in the Theory of Transfinite Numbers and Order Types, Proceedings of the London Mathematical Society 4 (1906): 29–53. • Rucker, Rudy, Infinity and the Mind: The Science and Philosophy of the Infinite, Princeton University Press, 2004. • Ramsey, The Foundations of Mathematics, Proceedings of the London Mathematical Society 25 (1926): 338–384. • Timothy Bays, SEP: Skolem’s Paradox. • Joel David Hamkins, Skolem’s Paradox (blog essay). • Ulrich Meyer, The Banach–Tarski Paradox. • Donald Gillies, “The Axiom of Choice and the Banach–Tarski Paradox,” British Journal for the Philosophy of Science 43(2) (1992): 143–153. • Penelope Maddy, “Believing the Axioms I & II,” Journal of Symbolic Logic 53 (1988). • See also: SEP: Axiom of Choice, SEP: Banach–Tarski Paradox. Curry paradox Russell paradox |
| Probability and social choice paradoxes |
• Gábor Székely, Paradoxes in Probability Theory and Mathematical Statistics, Ch. 1: “Classics” • Gehrlein, Condorcet’s Paradox, Social Choice and Welfare 1 (1984): 225–241. • SEP: Voting Methods. • SEP: Simpson’s Paradox. • See also: SEP: Decision Theory • R. M. Sainsbury, Paradoxes, Ch. 4 (pp. 69–89). • Robert Nozick, “Newcomb’s Problem and Two Principles of Choice,” Essays in Honor of Carl G. Hempel, 1969. • Bar-Hillel and Margalit, Newcomb’s Paradox Revisited, British Journal for the Philosophy of Science 24 (1973): 295–304. • Broome, The Two-Envelope Paradox, Analysis 54.1 (1994): 6–11. • See also: SEP: Newcomb’s Paradox. |
| Time |
• Sider, Theodore. “Time.” In Earl Conee and Ted Sider, Riddles of Existence: A Guided Tour of Metaphysics, Oxford University Press, 2007. • McTaggart, J. Ellis, “The Unreality of Time,” Mind 17.4 (1908): 457–474. • Arthur N. Prior, “Some Free Thinking About Time,” in Logic and Reality: Essays on the Legacy of Arthur Prior (1996): 47–51. • D. H. Mellor, “The Unreality of Tense,” in The Philosophy of Time (1993): 47–59. • David Lewis, “The Paradoxes of Time Travel,” American Philosophical Quarterly 13.2 (1976): 145–152. • See also: SEP: Time, SEP: Time Travel. |