Aesthetics, Mathematics and Philosophical Method: Wittgenstein on the ‘Queer Resemblance’ between an Aesthetic Investigation and a Philosophical Investigation in Mathematics

Among Wittgenstein’s remarks we also find scattered reflections on the nature of philosophy and its methods. These remarks, which frequently take the form of comparisons or analogies, often seem either trivial or incomprehensible if taken out of their context. This essay deals with one such remark, in which Wittgenstein wants to draw attention to “the queer resemblance between a philosophical investigation (especially in mathematics) and one in aesthetics”. By placing this analogy in its context, I want to show how it can shed light on some key features of Wittgenstein’s philosophical work (especially his lectures on aesthetics and the foundations of mathematics) and his conception of philosophy. I argue that the “methodological” similarity that the analogy alludes to has to do especially with the idea of “a synopsis of trivialities” or a “perspicuous representation”, i.e. the Darstellungsform that is fundamental to Wittgenstein’s later philosophical work. In this connection, I will address Wittgenstein’s controversial criticism of set theory, and show how it can be seen as an example of a “philosophical investigation in mathematics” that can be clarified by the analogy with an “aesthetic investigation”.

Keywords: esthetics, Cantor, mathematics, method, perspicuous representation, Wittgenstein.