**PHIL40013: Uncertainty, Vagueness and Paradox** is a University of Melbourne honours seminar subject for fourth-year students. Our aim in the Honours program is to introduce students to current work in research in philosophical logic.

In 2017, we’re covering the connections between proof theory and philosophy. Here’s the reading list, if you’re interested in following along.

*Introduction and Overview, Background**Introduction to Inferentialism*- Robert Brandom,
*Articulating Reasons: an introduction to inferentialism*, Harvard University Press, 2000. Introduction and Chapter 1 “Semantic Inferentialism and Logical Expressivism.”

- Robert Brandom,
*The Tonk Debate*- Arthur Prior, “The Runabout Inference-Ticket”,
*Analysis*21:2 (1960) 38–39. - J. T. Stevenson, “Roundabout the Runabout Inference-Ticket”,
*Analysis*21:6 (1961) 124–128. - Nuel D. Belnap, “Tonk, Plonk and Plink”,
*Analysis*22:6 (1962) 130–134.

- Arthur Prior, “The Runabout Inference-Ticket”,
*Natural Deduction and Normalisation*- Greg Restall,
*Proof Theory and Philosophy*Draft, Chapter 1. - Dag Prawitz,
*Natural Deduction: A Proof Theoretical Study*, Almqvist and Wiksell, 1965. Chapters 1-4.

- Greg Restall,
*Harmony and Meaning*- Prawitz “On the Idea of a General Proof Theory”, Synthese 27 (1974) 63–77.
- Michael Dummett:
*The Logical Basis of Metaphysics*, Harvard University Press, 1991. Chapter 9 “Circularity, Consistency and Harmony” - Gillian Russell, “The Justification of the Basic Laws of Logic,”
*Journal of Philosophical Logic*44:6 (2015) 793–803.

*Sequent Calculus and Cut Elimination*- Greg Restall,
*Proof Theory and Philosophy*Draft, Chapter 2 - Michael Kremer, “Logic and Meaning: The Philosophical Significance of the Sequent Calculus“,
*Mind*97 (1998), 50–72. - Francesca Poggiolesi,
*Gentzen Calculi for Modal Propositional Logic*, Springer, 2011. Chapter 1 “What Is a Good Sequent Calculus?”

- Greg Restall,
*Assertion and Denial*- P. T. Geach, “Assertion”,
*The Philosophical Review*, 74:4 (1965), 449–465. - Robert Brandom, “Asserting”,
*Noûs*, 17:4 (1983), 637–650. - Huw Price, “Why ‘Not’?”,
*Mind*, 99:394 (1990), 221–238. - Ian Rumfitt, “‘Yes’ and ‘No’”,
*Mind*109:436 (2000), 781–823.

- P. T. Geach, “Assertion”,
*Multiple Conclusions*- Greg Restall, “Multiple Conclusions”, pp 189–205 in
*Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress*, edited by Petr Hájek, Luis Valdés-Villanueva and Dag Westerståhl, KCL Publications, 2005. - Florian Steinberger, “Why Conclusions Should Remain Single,”
*Journal of Philosophical Logic*40 (2011), 333–355.

- Greg Restall, “Multiple Conclusions”, pp 189–205 in
*Truth Values and Proof Theory*- Greg Restall, “Truth Values and Proof Theory,”
*Studia Logica*, 92:2 (2009) 241–264. - Dave Ripley, “Bilateralism, Coherence and Warrant,” pp. 307–324 in
*Act-Based Conceptions of Propositional Content*, edited by Friederike Moltmann and Mark Textor, Oxford University Press, 2017.

- Greg Restall, “Truth Values and Proof Theory,”
*Beyond Declaratives*- Nuel Belnap, “Declaratives are Not Enough”,
*Philosophical Studies*, 59 (1990), 1–30.

- Nuel Belnap, “Declaratives are Not Enough”,

For further information, contact me. To participate, check the handbook.

← PHIL30043: The Power and Limits of Logic | Class Archive | PHIL20030: Meaning, Possibility and Paradox →

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.

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