Wittgenstein on Counting in Political Economy

This paper follows Ludwig Wittgenstein’s Remarks on the Foundations of Mathematics to investigate the source of the purported necessity delineated in mathematical statements and proofs. It suggests that this “normativity” has a similar structure to that underlying promising, contracting, and political obligation. Whereas many philosophers have abdicated the project of defending that empirical science can yield necessary truths or universal laws,1 still it is typical that mathematical truths are conceived to be necessary. Therefore the philosopher W.V .O. Quine, although a thorough-going empiricist who attempted to defend mathematics on the grounds of sensory perception, still faced the burden of explaining “why mathematics was (and is) thought to be necessary, certain, and knowable a priori.”2 If we understand “normativity” to convey some sort of structural indispensability that may guide judgment and action, then mathematical knowledge represents perhaps the paradigmatic case of a codified, law-like system that embodies non- negotiable relations and claims, that may be intuited by the human intellect.