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. (shrink)

ABSTRACTA ‘sceptical’ approach to easy arguments involves reducing our confidence in the supposedly uncontroversial premise with which the arguments begin. Here I address the question: if we accept Yablo's new version of a sceptical proposal, what difference might that make for the relevant meta-ontological debates? I argue that serious difficulties remain for even this ‘best’ version of a sceptical approach. Noting these difficulties might motivate us to look again at the alternative strategy—of reading the uncontroversial premise straightforwardly and thinking that (...) doubts about the conclusion were based on artificial inflation or confusion. (shrink)