Logical Revolt

Abstract

The last chapter was concerned with explaining and criticising the realist theory of mathematics that Ramsey held in 1925. That theory required a bloated ontology of functions, individuals and propositions, sufficient for a supposed logicism from which the Multiplicative Axiom emerged as a logical truth. By 1929, however, it is clear that Ramsey must have given up this position, having abandoned the Tractarian account of generalisations (at least for infinite domains) in favour of a view on which generalisations are expressions of rules that govern particular judgements. It is clear that once this move is made, something must also be said about the nature of generalisations in mathematical contexts because these too appear to range over infinite domains. Yet each of the arguments that Ramsey gives against the realist construal of generalisations in the empirical case are readily transposable to the mathematical case.