Avoiding “Tack-on” Theories of Culture

It is a commonplace that some broad sense of “the social” functions centrally in Wittgenstein’s later writings, including those writings devoted to mathematics. By “the social” I mean a nest of ideas connected to the learning, teaching, and performance environment of symbolic activity. Although there might be disagreement as to precisely how much weight to give them, most commentators would agree that the notion of practice (Praxis) and related notions such as use (Gebrauch), custom (Gepflogenheit), and form of life (Lebensform) are important for understanding Wittgenstein’s later thought. But this widespread agreement about the significance of the social for Wittgenstein’s later thought could obscure a distinguishing feature of that thought. It could lead to a failure to distinguish what I describe below as Wittgenstein’s “anthropological naturalism” from what I will call a “sociological naturalism” of practice, which encourages philosophers to seek answers to problems in, say, the philosophy of mathematics by focusing most of their attention on the practices of working professional mathematicians. After all, if we are told to “look and see” how a term is used if we want to grasp its meaning, what better way to understand the meaning of, say, “number” than to look and see how mathematicians operate with this term. This approach is in line with a widespread and many-decades-old naturalist trend in philosophy of science more generally, wherein one eschews mere “armchair” speculation and takes one’s problems and solutions mainly, if not exclusively, from the activities of experts in the respective fields. Whatever the merits of this trend in the philosophy of the science, in the case of reading Wittgenstein, too much focus on higher cognitive practices such as sophisticated theories, proofs, or even experimental activity risks bypassing what he is often targeting. For it can be very far from obvious how Wittgenstein’s frequent discussions of extremely elementary linguistic and mathematical situations are supposed to shed light on the technical questions that are sometimes taken to be the very stuff of mathematics or logic. Gaining more understanding of these issues will, I hope, clarify how we might read Wittgenstein’s later work as allowing us to avoid “tac-on” theories of culture.