Logic I

Aims and contents

Mastery of contemporary modal logic is vital not only for logicians, but also for philosophers of language, metaphysicians, philosophers of mind, epistemologists, and political philosophers: such notions as meaning, content, intension, supervenience, reduction, causation, knowledge, belief, moral duty, and of course nomic, physical, metaphysical, logical and temporal necessity, can all be defined in the framework of modal logic.

The single feature of modal logic allowing it to perform all these philosophical tasks, is its semantics, phrased in terms of the Leibnizian notion of possible world. A possible world is a way things might be or have been, in some respects similar to the real world, in some others, different. Possible worlds semantics raises many philosophical questions, from the metaphysical status of worlds (Do possible worlds different from actuality really exist? If so, what are these things?), to the meaningfulness of quantification over non- actual individuals.

This course introduces both to the logical techniques of, and to the philosophical issues raised by, first- order modal logic, which combines the language of first order-logic with quantifiers, identity, names and descriptions, with modal operators. We will explore such topics as: The metaphysics of possible worlds, possibilia, and fictional objects; The behaviour of identity in modal contexts; The differences between constant and variable domain semantics, actualist and possibilist quantification; The Barcan formulas; Lambda-abstraction; Rigid and non-rigid designation; Empty terms; Formal accounts of descriptions.

We will also look at the burgeoning topic of non-normal worlds: worlds where logical laws may fail. These anarchic worlds have proved useful to model phenomena of great interest for philosophers and logicians, from doxastic logics for non-logically-omniscient agents, to counterpossible conditionals, to hyperintensional phenomena. They also allow a smooth semantic treatment of non-classical alternatives to mainstream logic, such as non-normal modal logics and relevant logics.

Coursework

The course consists of a series of lectures intertwined with disputationes: debates with objections and replies around the topics discussed in the lectures. The students will also be asked take a final written exam.

Assessment methods

30% of the final grade will be determined collectively by the outcome of the disputationes. 70% of the final grade will be determined by the final closed book exam.

Final Exam
This will take place on Wednesday 13 November, in the last lecture of the course. The exam will consist of four open questions requiring short answers, to be chosen out of a menu of six. You will have two hours.

Readings*

- M. Fitting, R.L. Mendelsohn [1998], First-Order Modal Logic, Kluwer, Dordrecht (only some parts).
- F. Berto, M. Plebani [2015], Ontology and Metaontology: A Contemporary Guide, Bloomsbury, London, Ch. 11: Possible Worlds.
- F. Berto [2013], “Impossible Worlds”, The Stanford Encyclopedia of Philosophy, CSLI, Stanford, CA http://plato.stanford.edu/entries/impossible-worlds
- E. Mares [2012], “Relevance Logic”, The Stanford Encyclopedia of Philosophy, CSLI, Stanford, CA http://plato.stanford.edu/entries/logic-relevance/.

* All texts will be made available to all students in .pdf.