PY4601: Paradoxes

January 2023

at the University of St Andrews

py4601: Paradoxes is an honours Philosophy module at the University of St Andrews. It’s coordinated by my colleague, Patrick Greenough, and I’m teaching a small slice at the end on the liar paradox.

If you’d like to see what I am covering, you can see some slides and notes here.

Here’s what we’re covering in the whole module: A paradox is a plausible argument for an absurd conclusion. Better still: a paradox is an apparently plausible argument, with apparently plausible premises, which leads to an apparently absurd conclusion using apparently valid reasoning. In this module, we are going to look at three groups of paradoxes (and the connections between them):

  1. Epistemological Paradoxes (e.g. various forms of Scepticism, Lottery Paradox, Dogmatism Paradox).
  2. Paradoxes of Vagueness and Indeterminacy (The Sorites Paradoxes, The Problem of the Many, The Open Future, The Ship of Theseus, The Chicken and Egg Paradox).
  3. Semantic Paradoxes (The Liar Paradox, The Truth-Teller, Postcard Paradox, The No-No Paradox, The Prover Paradox, Curry’s Paradox, Yablo’s Paradox).

This module is a mixture of meta-philosophy (the philosophy of the nature of philosophical problems and the methods we can or should use to address these problems) plus first-order philosophy (what is the best solution to, e.g., the Sorites Paradox?).

Some Philosophical Questions to be addressed:

  1. How should we treat some particular paradox?
  2. Will context and Contextualism help?
  3. Will some kind of relativist or perspectivalist view help?
  4. Can and should we revise logic? In what way?
  5. Can we bite the bullet and accept true contradictions?

Some Meta-Philosophical Questions to be addressed:

  1. Why do paradoxes arise? What is their source? What is their nature?
  2. What is the scope of paradox? Do they occur outside of philosophy? (Visual Paradoxes)
  3. Do paradoxes show that our concepts are inconsistent or incomplete or indeterminate?
  4. Are some paradoxes unsolvable? If so, why?
  5. What do intractable paradoxes have in common? Could there be a common treatment?
  6. Have some paradoxes been solved? (Best Candidates: Zeno’s Paradoxes.)
  7. Can we make philosophical progress with paradoxes?
  8. What is philosophical progress?
  9. Does progress call for some kind of Pluralism via many acceptable solutions/treatments?
  10. Will some kind of quietism (“homeopathy”) help? (Cf. Horwich.)
  11. Can there be effective neutral treatments? (Neutralism.)
  12. Can paradoxes help us to understand deep, internecine conflict? (Applied Philosophy Issues.)

The module lies at the intersection of meta-philosophy with the philosophy of language, logic, the philosophy of logic, metaphysics, epistemology.


I’m Greg Restall, and this is my personal website. I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.


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