This course will introduce a variety of logical systems beyond first-order predicate logic that are commonly used in philosophy. We will spend the most time with modal logic (the logic of necessity and possibility). We will, however, begin with ordinary propositional/senential logic, so as to develop its semantics and proof theory in a more rigorous way than is common in beginning logic courses. We will show that these ?match? in a certain sense. More precisely, we will introduce a proof system for propositional logic, and show that every theorem of this system is valid (this result is called ?soundness?), and we will also sketch a proof that every valid sentence can be deducted within this system (?completeness?). We will then turn to modal logic. We will consider the proof theory and semantics of several systems of modal logic, and the soundness and completeness of those systems. Depending on time, we will discuss some of the following: tense logic, deontic logic, counterfactual conditionals, first-order predicate logic, modal first-order predicate logic, and definite descriptions.
Required work: Approximately fourteen homework assignments, and approximately three exams. The last exam will occur during the final exams period.
Pre-requisite, strictly enforced: PHI 215 (Symbolic Logic) at UB or instructor permission. Students who have not taken PHI 215 at UB, but who believe that they have taken an equivalent course, must contact the instructor before enrolling. |