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.
Structure and content
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.
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: 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.
5.1 Semantics
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.