Paradoxes (Phil 579.01/679.02)

Official Outline and Syllabus


An investigation of paradoxes and their philosophical relevance in areas such as vagueness, sets and properties, rational action, probabilistic and inductive reasoning.  The first half of the course will dealwith a collection of “classic” paradoxes mainly having to do with logic and semantics: the paradox of theheap (aka, the Sorites paradox), semantic paradoxes (such as the Liar Paradox, Grelling’s Paradox, and Yablo’s Paradox), Russell’s Paradox in set theory, and their proposed solutions. In the second half of the course we will look at paradoxes arising in other areas: inductive reasoning (Hempel’s Raven Paradox and Goodman’s Grue Paradox); conditional reasoning and epistemic paradoxes (such as the Surprise Examination Paradox); paradoxes of probabilistic reasoning (the Sleeping Beauty Problem); andparadoxes of decision theory (Newcomb’s Problem and the Two Envelope Paradox).

Prerequisites and preparation

Logic I (PHIL 279) or Elementary Formal Logic (PHIL 377) is a prerequisite for this course.





1 Introduction Quine, “Paradoxes
Bolander, “Self reference
2 Vagueness :
Sorites Paradox
Hyde, “Sorites paradox
Dummett, “Wang’s Paradox
Fine, “Vagueness, truth, and logic
Fara, “Shifting Sands
3 Truth :
Liar Paradox
Tarski, “The semantic conception of truth
Glanzberg and Beall, “The liar paradox
Yablo, “ Paradox without self-reference
4 Kripke, “Outline of a Theory of Truth
5 Sets and Properties :
Russell’s Paradox
Grelling’s Paradox
Berry’s Paradox
Burali-Forti Paradox
Cantini, “Paradoxes and contemporary logic
Russell, “On some difficulties in the theory of transfinite numbers and order types
Ramsey, “The Foundations of Mathematics
6 Assessments of Semantic Paradoxes Parsons, “Liar paradox
Burge, “Semantical paradox
Glanzberg, “The liar in context
Russell, “What is semantic dialetheism?”
7 Induction :
The Raven
Hempel, “Studies in the Logic of Confirmation
Goodman, “New Riddle of Induction
8 Deontic Logic (guest lecture: Gillman Payette)
Conditional Reasoning :
Henry V Paradox
Dreier, “Practical Conditionals”
9 McGee’s Paradoxes
The Surprise Exam
McGee, “A Counterexample to Modus Ponens
Sorensen, “Epistemic paradoxes
Scriven, “Paradoxical Announcements
10 The Dogmatism Paradox Sorensen, “Dogmatism, Junk Knowledge, and Conditionals
Intro to Probability Theory (guest lecture: Bengt Autzen)
Gillies, “The Logical Theory”, Chapter 3 of Gillies’ Philosophical Theories of Probability, London: Routledge, 2000.
Mikkelson, “Dissolving the wine/water paradox”
11 Self-locating Belief :
Sleeping Beauty
The Shooting Room
Elga, “Self-locating Belief and the Sleepin Beauty Problem
Leslie, “Testing the Doomsday Argument
12 Decision Theory :
Newcomb’s Problem
Two Envelope Paradox
Nozick, “Newcomb’s Problem and two principles of choice
Bar-Hillel and Margalit, “Newcomb’s Paradox Revisited
Broome, “The Two-Envelope Paradox
13 Student presentations

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