127: Philosophical Logic

Lectures HT20

Rad Hum. Lecture Room, M. 12, weeks 1-8, with two additional lectures, T. 12, weeks 1-2.

These are the core lectures for students taking FHS Paper 127. But they may also be of interest to others who want to learn about the technical details and philosophical applications of extensions to (and deviations from) classical logic.

There will also be two additional lectures in weeks 1 and 2. These deal with the mathematical methods used in the course, and are aimed at students who did not take the second logic paper, Elements of Deductive Logic, for Prelims.

The paper is studied in conjunction with a set textbook, Theodore Sider’s Logic for Philosophy (Oxford University Press). I recommend that you read the indicated sections of the book before attending the lecture each week.


A series of logic exercises and philosophy tasks to accompany the course is available here: 127 exercises [.pdf, new tab]

(I’ve made no substantive changes to the HT19 Exercises.)


The schedule for the main series of lectures is as follows.

Week 1. Classical propositional logic, variations, and deviations

LfP 2.1-2.4 (2.5 non-examinable), 3.1-3.4 (3.5 non-examinable)
Review of syntax and classical semantics for PL; three-valued semantics; supervaluationism
Lecture notes week 1 [.pdf, new tab]
Additional lecture A (first of two additional lectures for non-EDL students)

Week 2. Modal propositional logic: semantics

LfP 6.1-6.3, 7.1-7.3 (7.4 non-examinable)
Syntax of MPL; Kripke semantics for K, D, T, B, S4 and S5. Deontic, epistemic and tense logic.
Lecture notes week 2
Additional lecture B (second of two additional lectures for non-EDL students)

Week 3. Modal propositional logic: proof theory

LfP 2.6, 2.8, 6.4
Axiomatic proofs for PL. Axiomatic proofs for K, D, T, B, S4 and S5.
Lecture notes week 3

Week 4. Modal propositional logic: metatheory

LfP 2.7, 6.5 (Proofs in 2.9, 6.6 non-examinable)
Soundness and Completeness for MPL. (Proof of completeness is non-examinable).
Lecture notes week 4

Week 5. Classical predicate logic, extensions, and deviations.

LfP 4, 5
Review of the syntax and classical semantics of PC. Extensions of PC.
Lecture notes week 5

Week 6. Quantified modal logic: constant domains

LfP 9.1-9.5, 9.7
Semantics and proof theory for SQML.
Lecture notes week 6

Week 7. Quantified modal logic: variable domains, 2D semantics

LfP 9.6, 10
Kripke semantics for variable domain K, D, T, B, S4, and S5. Two-dimensional semantics for @, X and F.
Lecture notes week 7

Week 8. Counterfactuals.

LfP 8
Stalnaker’s and Lewis’s semantics for counterfactuals.
Lecture notes week 8


The exam paper will contain 6 questions. Three questions should be attempted in three hours. Questions may vary as to the amount of technical versus philosophical material, but typical questions are likely to be weighted as follows:

  • Book work (approximately 20%): any of the definitions, theorems and proofs in LfP count as “book work”, as do those given in the lectures (save for those indicated as non-examinable in the schedule above).
  • Logic exercises (approximately 40%): the problem sheets are a good guide to the sort of thing to expect in the problem solving section of the question.
  • Philosophical applications (approximately 40%): in addition to the philosophical material in LfP, these may draw on the readings specified in the lectures, exercise sheets and philosophy tasks. Carefully studying these papers is good preparation for this section.

The full and definitive exam regulations may be found in the grey book: http://www.admin.ox.ac.uk/examregs/

In addition to the past papers available on Oxam, a sample paper is available here. [Note that this paper contains more questions that the actual exam does.]

A collection paper will also be available to sit at the start of TT. Tutors who wish to set this paper should please email me to request a copy. (Arrangements for sitting the collection should be made by individual colleges, as usual.)