Modal Logic

Practical information

You can find the take-home exam here. Alternatively, you can submit an essay, ca 15 pages long. The deadline for submissions is September 17th. Please submit your answers by email.

Mondays, from 4pm to 6pm (s.t., includes practice sessions), room 021

Office hours by appointment, in room 234, Ludwigstrasse 31, second floor

Textbook: Garson (2013) Modal Logic for Philosophers. You can find it here!

Mode of evaluation: take-home exam (to be uploaded by the end of the semester) or essay (15 pages). Deadline for submission is September 17.

Course description

The course consists in a thorough introduction to modal logic. Modal logics are mainly concerned with the deductive behaviour of modalities. These are primarily the alethic modalities (ways in which a sentence can be true) ‘it is necessary that’ or ‘necessarily’ and ‘it is possible that’ or ‘possibly’, but also include epistemic modalities such as ‘is known that’ and ‘is believed that’, deontic modalities such as ‘it is obligatory that’ and ‘it is permitted that’, tense modalities, and provability modalities, among others.

The first half of the course is devoted to modal propositional logics, their semantics and proof-theory, as well as the presentation of well-known metatheoretic results. This includes a detailed exposition of possible-worlds semantics, an tool ubiquitous tool in mathematical philosophy. The second half of the course focuses on modal predicate logics, their semantics, proof-theory and salient metatheoretic results. Students are introduced to the traditional philosophical issues revolving around the identity relation, predicates of existence, definite descriptions, Barcan formulae, and intensional objects.

Contents (preliminary)

0. Introduction: What is Modal Logic?


Read: Garson's (2013), Introduction: What is Modal Logic?

1. System K: Language and Natural Deduction


Read: Garson's (2013), Chapter 1, except section 1.6.

Exercises: all exercises in the chapter except those in section 1.6 and exercise 1.14.

2. Extensions of K

16/4 - 23/4

Read: Garson's (2013), Chapter 2, except sections 2.2 and 2.8.

Exercises: all exercises in the chapter before section 2.8.

3. Possible-Worlds Semantics


Read: Garson's (2013), Chapter 3.

Exercises: all exercises in the chapter.

4. Trees and Diagrams


Read: Garson's (2013), Chapter 4.

Exercises: all exercises in Chapter 4 except 4.7.

5. The Accessibility Relation


Read: Garson's (2013), Chapter 5, except sec. 5.5, and Chapter 6.

Exercises: 1, 2, 5, 6, 13 of Chapter 5.

6. Soundness, Completeness, and Decidability

28/5 - 11/6

Read: Garson's (2013), Chapters 7 and 8.

Exercises: 2-4, 11-14, 17, 18 (ignore the "simplified"), and 20-22, 24, 26, 28 (ignore (U◻F)) of Chapter 7.

7. Systems of Quantified Modal Logic

A) The Failure of Leibniz Law


Read: Garson's (2013), Chapter 12.1-3; Russell's (1905) "On Denoting".

Exercises: 1-5 of Chapter 12.

B) The Problem of Non-Denoting Terms


Read: Garson's (2013), Chapter 12.4-6; Quine's (1961) "On What there is"; Nelson's (2012) "Existence".

Exercises: 6-13 of Chapter 12.

C) Constant vs Variable Domains - Rigid and Non-Rigid Designators


Read: Garson's (2013), Chapter 12.7-13; Linsky and Zalta's (1994) "In Defense of the Simplest Quantified Modal Logic"; Kripke's (1963) "Semantical Considerations in Modal Logic".

Exercises: 12.15 and 12.21.

8. Semantics for Quantified Modal Logics


Read: Garson's (2013), Chapter 13.1-5.

Exercises: 13.1, 4, 5, 6, 8-10.


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