Gillian Russell

Philosophy Professor at UNC Chapel Hill

Phil 4051 : Philosophy of Logic (Fall 2008)

Class Times: Mondays and Wednesdays, 2.30-4pm
Instructor: Gillian Russell
Location: Wilson Hall, Seminar Room
My office: 209 Wilson Hall
Office hours: Wednesdays 4.15-5.15pm or by appointment
Email: grussell – at – wustl – dot – edu
E-reserves site for this course:
Course Website:

This course surveys some central issues in the philosophy of logic. We begin with some foundational issues in classical logic, including the relation of logic to psychological reasoning and Tarski’s definition of logical consequence. We will go on to consider the motivations for, and status of, well-known extensions (sometimes regarded as ‘neo-classical’ logics) including modal and counterfactual logics. We will also examine some outright challengers to classical logic, including relevant and many-vaued logics. After evaluating the arguments for and against these challengers, we’ll examine one recent, controversial view—logical pluralism—which suggests that we might not need to choose a single logic from among the rival systems after all.

Many of the readings for this course are classics of contemporary philosophy, and the subject is likely to be of especial interest to students who have interests in logic, and in the philosophy and foundations of mathematics and language.

Some of the important ideas in the course presuppose at least a basic acquaintance with formal logic, and hence either Phil 100 or Phil 301 (or permission of the instructor) are prequisites.

The main textbook for the course is Graham Priest’s Introduction to Non-classical Logic, but many of the readings will be from elsewhere and these will eventually all be up on e-res, or be linked to from this webpage.

Readings and Topics

Readings with a "*” after them are especially difficult.

Week 1 – Wednesday 27th August – What is logic?

No pre-assigned reading, but we’ll look at excerpts from Aristotle, Kant, and Frege in class.

Week 2 – Wednesday 3rd September

Is logic the study of reasoning? Reading: Chapters 1 and 2 of Change in View by Gilbert Harman, MIT Press, (Cambridge, 1986) (on e-res)

Week 3 – Monday 8th and Wednesday 10th Septermber

Monday and Wednesday: A reminder of some of the basics of classical logic. Reading: chapter 1 of Priest: Classical Logic and the material conditional.

Week 4 – Monday 15th and Wednesday 17th September

Logical Consequence:

Monday: the standard conception. Reading: “On the Concept of Logical Consequence”*, Alfred Tarski in Blackwell Anthology of the
Philosophy of Logic, ed. Dale Jacquette, Blackwell, (Oxford, 2005)

Wednesday: Criticisms of the standard conception: Reading: Selections from The Concept of Logical Consequence, John Etchemendy, CLSI (Stanford, 1999).

Friday 19th September: Problem set 1 due.

Week 5 – 22nd and 24th September

The Material Conditional: sections 1-4 from chapter 1 of Entailment: The Logic of Relevance and Necessity, volume 1, Alan Ross Anderson and Nuel Belnap. (on e-res)

Wednesday: Pragmatic approaches to the material conditional. Reading: "Logic and Conversation" – H.P. Grice (on e-res).

Week 6 – 29th September and 1st October

Monday: Chapter 2 of Priest’s Introduction to Non-Classical Logic: Basic modal logic
Wednesday: Chapter 3 of Priest’s Introduction to Non-classical Logic: Normal modal logics
Recommended extra reading: chapter 4: Non-normal modal logics; strict conditionals.

Week 7 – 6th and 8th October

Monday: Excerpt from The Pluarality of Worlds – David Lewis (on e-res)

Wednesday: "Possible Worlds" – Robert Stalnaker, on J-stor:

Friday 10th October – problem set 2 due.

Week 8 – 13th and 15nd October

Monday: “Three Grades of Modal Involvement”, W.V.O.Quine in From a Logical Point of View. (on e-res)

Wednesday: "Reference and Modality", W. V. O. Quine in From a Logical Point of View. (on e-res)

Week 9 – 20th and 22nd October

Monday: "Quinus ab Omni Naevo Vindicatus", J. P. Burgess in Meaning and Reference, suppl. vol. Canadian Journal of Philosophy, vol. 25 1997. (on e-res)

Wednesday: Modal logic without the necessity? (no assigned reading)

Week 10 – 27th and 29th October

Monday: Vagueness and The Sorites Paradox. Reading: "Vagueness", Bertrand Russell in Vagueness: A Reader edited by Rosanna Keefe and Peter Smith, MIT Press 1997 (on e-res)
Wednesday: Three-valued logics. Reading: Priest pages 120-124.

Friday 31st October: short paper due.

Week 11 – 3rd and 5th November

Monday: Super-valuationism: Priest pages 133-140.

Wednesday: Class cancelled.

Week 12 – 10th and 12th November

Monday: Kit Fine’s "Vagueness, Truth and Logic"* in Vagueness: A Reader edited by Rosanna Keefe and Peter Smith, MIT Press 1997 (on e-res)

Wednesday: Epistemic approaches to vaguesness: "Vagueness and Ignorance", Timothy Williamson, in Vagueness: A Reader edited by Rosanna Keefe and Peter Smith, MIT Press 1997 (on e-res)

Week 13 – 17th and 19th November

Monday: "Can there be vague objects?" – Gareth Evans on J-stor:
"Vague Identity: Evans Misunderstood" – David Lewis on J-stor:

Wednesday: Introduction to the Liar paradox: Reading: "The Semantic Conception of Truth, Alfred Tarski on J-stor:

Reading: "Outline of a Theory of Truth"*, Saul Kripke, in Recent Essays on Truth and the Liar Paradox, ed. Robert Martin, (Oxford, 1984.)es)

Friday 21st November: Problem set 3 due.

Week 14 – 24th November

Monday: Dialethesim: Chapter 1 of In Contradiction Graham Priest (on e-res)

Wednesday: Thanksgiving Break

Week 15 – 1st and 3rd December

Monday: Getting straight on LP: Reading: Chapter 9 of Priest.

N. Denyer, ‘Dialetheism and Trivialisation’, Mind 98 (1989), 259-63, on j-stor:

Wednesday: "Logical Pluralism", Greg Restall and J.C. Beall, Australasian Journal of Philosophy, 78:475-493 (2000) – copy available here


Monday 8th December

No assigned reading.


Assessment for undergraudates is by way of three problem sets (one on classical logic, one on modal logic, and one on many-valued logics) , one short paper (400 words) and one long paper, of about 2000 words. Assessment for graduate students is the same, except that the long paper should be about 3000 words. The due dates for the problem sets and short paper are listed in the syllabus and the long paper is due on the last day of classes. I will be saying a lot more about what I expect from the papers in class, but you should meet with me to discuss your topic before beginning to write the long paper. The problem sets are worth 30% of your grade, the short papers 20% and the long papers 50%. There is no exam for this course.

I prefer papers to be double-spaced, and for each page to be marked with your name and page numbers. Please clip the pages together with a paper clip rather than a staple. Papers can be turned in by placing them in the appropriate drawer in the "turn in" filing cabinet in the philosophy department by 3.30pm on the day on which they are due. (The office closes at 4pm and we try to discourage students from knocking on the door at 4pm when the staff are trying to go home.)


Any cases of suspected plagiarism, or other problems with academic integrity, will be reported to the Dean in his role as head of the academic integrity committee.

Pass/Fail Option

Students taking the course pass/fail will need an overall grade of C- for a pass.