First-Order Modal Logic and Its Metaphysics
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.
The course also features a part in which we will go through the completeness of propositional and first-order non-modal logic; understanding how completeness proofs work is an important part of philosophy students’ logical education.
Students will be evaluated based on a final written exam.