This course aims to extend students' prior knowledge of propositional and predicate logic to the exciting and powerful domain of modal logic. Traditionally, modal logic is a branch of formal logic that studies sentences containing the logical phrases it is necessary that p and it is possible that p and complex combinations of them that occur in famous philosophical arguments in metaphysics. As such, modal logic allows us to examine the logic intrinsic to philosophical practice at a deeper level.
However, modern modal logic is not only the logic of necessity and possibility (which is now called alethic logic). Rather, it is a family of logics that deal with other modal concepts related to knowledge, belief, time, norms and laws, scientific laws, and various other aspects of language and cognition. In this course, students will be introduced to modal logic in a general fashion that includes alethic logic, tense logic, epistemic logic (x knows that p), doxastic logic (x believes that p), deontic logic (p is permissible, p is forbidden), and counterfactual logic (if it were the case that p, then q would be the case). Additional topics might include conditionals, multivalued logics, intuitionistic logic, paraconsistent logic, and multimodal systems.%infinitary logic, and second-order logic.
The course will focus on propositiona} modal logic, which contains the main methodological ideas that will help students in their studies and research in philosophy. The course will focus on natural deduction, on trees, and on the more abstract Kripke semantics based on the notions of possible world and accessibility relation. The basic metatheory (soundness and completeness proofs) of each system will also be covered. Because of the simplicity and generality of the methods used in modal logic, students successfully completing this course should expect to be able to utilize the notions studied in most fields of philosophy.