# 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?

9/4

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

1. System K: Language and Natural Deduction

16/4

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

30/4

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

Exercises: all exercises in the chapter.

4. Trees and Diagrams

7/5

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

Exercises: all exercises in Chapter 4 except 4.7.

5. The Accessibility Relation

14/5

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

18/6

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

25/6

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

2/7

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

9/7

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

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

Bibliography

- Barcan (Marcus), R. 1967 “Essentialism in Modal Logic,” Noûs, 1: 91-96.
- Bencivenga, E., 1986, “Free Logics,” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, III.6, Dordrecht: D. Reidel, 373-426.
- Blackburn, P., with M. de Rijke and Y. Venema, 2001, Modal Logic, Cambridge: Cambridge University Press.
- Blackburn, P., with J. van Bentham and F. Wolter, 2007, Handbook of Modal Logic, Amsterdam: Elsevier.
- Bull, R. and K. Segerberg, 1984, “Basic Modal Logic,” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, II.1, Dordrecht: D. Reidel, 1-88.
- Carnap, R., 1947, Meaning and Necessity, Chicago: U. Chicago Press.
- Chagrov, A. and M. Zakharyaschev, 1997, Modal Logic, Oxford: Oxford University Press.
- Chellas, B., 1980, Modal Logic: An Introduction, Cambridge: Cambridge University Press.
- Cresswell, M. J., 2001, “Modal Logic”, in L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Oxford: Blackwell, 136-158.
- –––, 1991, “In Defence of the Barcan Formula,” Logique et Analyse, 135-136: 271-282.
- –––, 1995, “Incompleteness and the Barcan formula”, Journal of Philosophical Logic, 24: 379-403.
- Cocchiarella, N. and M. Freund, 2008, Modal Logic An Introduction to its Syntax and Semantics, New York: Oxford.
- Fitting, M. and R. Mendelsohn, 1998, First Order Modal Logic, Dordrecht: Kluwer.
- Garson, J., 2001, “Quantification in Modal Logic,” in D. Gabbay and F. Guenthner (eds.) Handbook of Philosophical Logic, second edition, volume 3, Dordrecht: D. Reidel, 267-323.
- –––, 2005, “Unifying Quantified Modal Logic,” Journal of Philosophical Logic, 34: 621-649.
- –––, 2013, Modal Logic for Philosophers, Second Edition, Cambridge: Cambridge University Press.
- Hughes, G. & Cresswell, M. (1996),
*A New Introduction to Modal Logic*, Routledge. - Kaplan, D., 1989, “Demonstratives”, in Themes from Kaplan, Oxford: Oxford University Press.
- Kripke, S., 1963, “Semantical Considerations on Modal Logic”, Acta Philosophica Fennica, 16: 83-94.
- –––, 1980, Naming and Necessity, Cambridge, MA: Harvard University Press.
- Konyndik, K., 1986, Introductory Modal Logic, Notre Dame: University of Notre Dame Press.
- Lemmon, E. and D. Scott, 1977, An Introduction to Modal Logic, Oxford: Blackwell.
- Lewis, D., 1968, “Counterpart theory and quantified modal logic”,
*Journal of Philosophy*, 65: 113-126. - ---, 1986, On the Plurality of Worlds, Oxford: Blackwell.
- Linsky, B. and E. Zalta, 1994, “In Defense of the Simplest Quantified Modal Logic,” Philosophical Perspectives, (Logic and Language), 8: 431-458.
- Mints, G. 1992, A Short Introduction to Modal Logic, Chicago: University of Chicago Press.
- Nelson, M. (2012) "Existence",
*The Stanford Encyclopedia of Philosophy*(Winter 2016 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2016/entries/existence/>. - Ponse, A., with M. de Rijke, and Y. Venema, 1995, Modal Logic and Process Algebra, A Bisimulation Perspective, Stanford: CSLI Publications.
- Popkorn, S., 1995, First Steps in Modal Logic, Cambridge: Cambridge University Press.
- Quine, W. V. O., 1951, “Two dogmas of empiricism”,
*Philosophical Review*, 60: 20-43. - ---, 1953, “Reference and Modality”, in From a Logical Point of View, Cambridge, MA: Harvard University Press. 139-159.
- ---, 1960, Word and Object. Cambridge, Mass.: M.I.T. Press.
- ---, 1961, “On What There Is”, in From a Logical Point of View, Harper & Row, chapter 1, 1-19.
- ---, 1969, “Foreword to Lewis 1969”.
- Russell, B. 1905, "On Denoting", Mind 14: 479-493.
- Zeman, J., 1973, Modal Logic, The Lewis-Modal Systems, Oxford: Oxford University Press.

- Prior, A. N., 1957, Time and Modality, Oxford: Clarendon Press.

- Williamson, T., 2013, Modal Logic as Metaphysics. Oxford: Oxford University Press.