Grounding Concepts: The Problem of Composition

In a recent book C.S. Jenkins proposes a theory of arithmetical knowledge which reconciles realism about arithmetic with the a priori character of our knowledge of it. Her basic idea is that arithmetical concepts are grounded in experience and it is through experience that they are connected to reality. I argue that the account fails because Jenkins’s central concept, the concept for grounding, is inadequate. Grounding as she defines it does not suffice for realism, and by revising the definition we would abandon the idea that grounding is experiential. Her account falls prey to a problem of which Locke, whom she regards as a source of inspiration was aware and which he avoided by choosing anti-realism about mathematics.