Philosophical Logic

A second pass through logic, building on the basic propositional and predicate logic of Introduction to Logic.

This topic exposes you to logical systems that extend and enrich, or challenge and deviate from, classical logic. 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 true 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.

The topic has two 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: 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 aim is for you to come to appreciate the diverse philosophical applications of these systems. The logic studied here 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 this logic unlocks a wide range of work across philosophy.

The topic calls for some technical ability but is considerably less mathematically demanding than a comparable treatment in mathematics.