Wittgenstein: Necessity, Imagination, and Metaphilosophy

Prima facie, there seems to be a tension between Wittgenstein's Kantianism in the philosophy of mathematics (especially the view according to which a proposition p is logically necessary if we are not able to conceive of not-p) and Wittgenstein's later use of imagination in philosophy (especially his building logically alien cases, in which certain imaginary people reject what we take to be a logically necessary proposition). This paper investigates the tension just sketched by assessing and criticizing three answers to the question “With what purposes does Wittgenstein build logically alien imaginary cases?”. One of the main reasons why the paper rejects such answers is that they are not compatible with Wittgenstein's later meta-philosophy. The paper also sketches an alternative account, on which the tension between Kantianism and philosophical imagination in Wittgenstein's later philosophy of mathematics is only apparent, and argues that, thus interpreted, Wittgenstein's use of imagination, far from being in contrast with Wittgenstein's meta-philosophical ideas, somewhat derives from them.