127. Philosophical Logic

This topic is a second course in logic. It follows on from the first logic course provided by The Logic Manual in Prelims.

This topic exposes you to logical systems that extend and enrich--or challenge and deviate from--classical logic, the standard propositional and predicate logic familiar from Prelims. Why depart from classical logic? Here's one example: classical logic has exactly two truth-values, true and false. How, then, are we to deal with sentences such as Hamlet has blood type O', which appear to defy classification with either? One systematic answer is provided by three-valued logics which deviate from classical logic by permitting their sentences to be neither truth nor false. Another example: classical logic only has truth-functional connectives. How, then, are we to deal with connectives like It must be the case that...' whose semantics cannot be captured with a truth-table? One systematic answer is provided by modal logic, which extends classical logic by allowing its connectives to be non-truth-functional.

This topic has two principal aims. The first is to give you the technical competence to work with, and prove things about, a number of logical systems which have come to play a central role across philosophy. These include non-classical propositional logics, such as three-valued and intuitionistic systems, and extensions of classical logic, such as propositional and predicate modal logic, as well as systems for counterfactual conditionals and `two-dimensional' logic. The second principal aim is for you to come to appreciate the diverse philosophical applications of these systems. The logic studied in this topic has important connections to the metaphysics of time and existence, a priori knowledge, obligation, vagueness, and conditionals, amongst many other issues, and is often presupposed in the contemporary literature on these topics. Competence with the logic in this topic unlocks a wide range of fascinating work across philosophy.

Consequently, this topic calls for some technical ability but is considerably less mathematically demanding than the Logic and Set Theory paper (B1), studied in mathematics.