Reasoning Under a Presupposition and the Export Problem: The Case of Applied Mathematics

ABSTRACT‘expressionist’ accounts of applied mathematics seek to avoid the apparent Platonistic commitments of our scientific theories by holding that we ought only to believe their mathematics-free nominalistic content. The notion of ‘nominalistic content’ is, however, notoriously slippery. Yablo's account of non-catastrophic presupposition failure offers a way of pinning down this notion. However, I argue, its reliance on possible worlds machinery begs key questions against Platonism. I propose instead that abstract expressionists follow Geoffrey Hellman's lead in taking the assertoric content of empirical science to be irreducibly modal, using the ‘non-interference’ of mathematical objects as justification for detaching nominalistic consequences.