Philosophical logic

Basic Information

Course 2017/2018
Genoveva Martí
José Martínez Fernández
Department of Philosophy
Universitat de Barcelona
Module 7. Issues in Contemporary Theoretical and Practical Philosophy


Fridays 10:00 - 13:00
UB, Philosophy Faculty, room 410


Discussions about ways the world might have been, what could or could not have been the case, what is contingent, possible, impossible or necessary, have evident philosophical interest in and of themselves, and play also a crucial role in many areas of Philosophy. Modal Logic provides the foundation for a systematic way of approaching those questions. The goal of this course is to provide an introduction to some of the central themes concerning the logic of necessity and possibility. We will also explore other applications of modal logic to deontic logic (the logic of obligation and permission) and epistemic logic (the logic of knowledge attributions).


Structure and Contents

Students will be expected to have background equivalent to an introductory course in propositional and quantificational Logic.

1.- Introduction

            1.1 Necessity and Possibility. The modal operators.

            1.2 Some history.

            1.3 Possible worlds.

            1.4 Terminological distinctions.

            1.5 Extensions vs alternative logics.


2.- Review of classical propositional logic.


3.- Propositional Modal Logic.

            3.1 Syntax.

           3.2 Semantics: models and possible worlds.

           3.3 A system of derivation.

            3.4 Deontic and epistemic interpretations of modal systems.


4.- Review of classical first-order logic.


5.- Quantificational Modal Logic.

           5.1 Remarks on the derivation system.

           5.2 A generic semantics.

           5.3 The Barcan Formula and its converse.

            5.4 Semantics of type I.


6.- Existence and possible worlds.

            6.1 Varying domains. Semantics of type II and III.

            6.2 The Barcan Formula and its converse again.

            6.3 Free Logic.


7.- Modal operators and quantification over possible worlds.

            7.1 David Lewis's Counterpart Theory.

            7.2 The issue of expressive power.


8.- The operator "actually."


9.- The values of variables.

            9.1 Direct assignments vs possible world relative assignments.

            9.2 Intensional semantics.


Students will read basic texts on the different topics covered. Class will be organized as lectures with time for discussion and practice with some exercises. Other exercises will be given to students as homework assignments.


Students will be given homework assignments practically every week. Some of them will be just for practice and others will count towards the final grade. Participation in class will also contribute to the final grade, according to the following distribution:

Homework assignments - 6 assignments worth 15% each

Participation: 10%


Learning outcomes:


Students should be able to critically understand central texts in logic and philosophy in a way that puts them in a position to develop and apply original ideas. 


Students should be able to communicate their knowledge and their arguments to specialized audiences in a clear and articulate way. 


Students should be able to work both independently and in a team in an international environment. 


Students should be able to identify fallacies and methodological errors in reasoning.


Students should be able to critically engage with the concepts and methods of contemporary modal logics.


Students should be able to identify and critically engage with the current state of a particular philosophical debate, and form a reasoned view, even if provisional, about it.


Students should be able to critically use specialized terminology in the field of logic and the philosophy of the cognitive sciences.


Students should be able to solve basic problems in the field of modal logic.


Students should be able to use different logical systems to represent knowledge. 



Theodore Sider, Logic for Philosophy, Oxford UP, 2010.


Part of the course will be based on notes and handouts made available by the instructors.


Other readings will be assigned in class.