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), epistemic logic (the logic of knowledge attributions) and intuitionistic logic.
Students will be expected to have background equivalent to an introductory course in propositional and quantificational Logic.
Structure and Contents
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.
3.2 Semantics: models and possible worlds.
3.3 A system of derivation: semantic tableaux.
3.4 Normal modal logics.
3.5 Non-normal modal logics.
3.6 Intuitionistic logic
4.- Review of classical first-order logic.
5.- Quantificational Modal Logic.
5.2 The Barcan Formula and its converse.
6.- Existence and possible worlds.
6.1 Varying domains.
6.2 The Barcan Formula and its converse again.
7.- Intensional Semantics.
8.- Modal operators and quantification over possible worlds. David Lewis’s Counterpart Theory.
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.
The topics discussed in this course are abstract and somewhat technical. We incorporate the gender perspective by ensuring that the bibliography to be consulted by students contains a substantial number of works written by women.
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.
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. The final grade with be calculated according to the following distribution:
Homework assignments - 6 assignments worth 15% each
Extra exercises: 10%
Graham Priest, An Introduction to Non-Classical Logic. From If to Is, Cambridge UP, 2ed. 2008.
Ruth Barcan Marcus (1961): Modalities and Intensional Languages. Synthese 13 (4):303-322.
Ruth Barcan Marcus (1946): A functional calculus of first order based on strict implication. The Journal of Symbolic Logic 11 (1): 1-16.
Sonia Roca (2011): Essential Properties and Individual Essences. Philosophy Compass 6/1: 65-77
Part of the course will be based on notes and handouts made available by the instructors.
Other readings will be assigned in class.