Worlds, Sentences and Measures

a.k.a. Formal Methods in Philosophy (PHIL3085/PHILGA84/PHILG085)

Daniel Rothschild

Time and place:

Autumn 2016, Tuesdays 2-4PM, 19 Gordon Square, UCL, seminar room, first floor.

The module will follow the standard UCL academic calendar for term 1: the first session is on Friday, 7 October 2016 and the last is on Friday, 16 December 2016 (there is no session during reading week on 11 November)


This course is a survey of some mathematics and logic commonly used across contemporary philosophy. This will include some set theory, metatheory, modal logic, probability theory, and other topics of interest. The aim is to equip you to be able to read and understand contemporary articles, while this class is sometimes at a high level it is specifically geared, as well, for students without a strong technical background.


Basic knowledge of propositional and predicate logic will be assumed, though we will not rely explicitly on any previous content. For those wishing to do some background reading they may find David Papineau's Philosophical Devices helpful.

Practical information:

All our welcome as auditors and should feel free to come to any sessions (and may pick and choose according to interest).

There will be weekly problem sets (9 in total), on which collaboration is encouraged. For undergraduates there is a final exam (Problem sets are worth 60% and exam is worth 40%.) Graduate students are not graded by exam but are required to answer more and more difficult problems.


Readings will be provided on moodle with the exception of the one textbook, Sider, Logic for Philosophy

John Burgess's book Philosophical Logic, covers some of the topics covered in the course.


Set Theory

Week 1 - Lecture notes

For readings see Moodle, or email me for dropbox link.

Problem set 1

Week 2 - Lecture notes

Problem set 2

Propositional logic (and meta theory)

Week 3 - Lecture notes

Problem set 3

Non-classical logic

Week 4 - Lecture notes

Problem set 4

Axiomatic proof notes

Week 5 - Lecture notes

No problem set! (please look over Sider)

Week 6 - Lecture notes

Problem set 5


Week 7 - Lecture notes

Problem set 6


Week 8 - Lecture notes

Problem set 7

Week 9 - Lecture notes

Problem set 8


This chapter is the main reading, for background you will also need to read up to the bit about SQML (up to page 292) in the previous chapter

Lecture notes

Problem set 9

Final exam

Previous year's exam