A truthmaker-free approach to arithmetical truth

Abstract

Truthmaking is usually defined as a relationship of ontological dependence that holds between propositions (the truthbearers) and worldly objects (the truthmakers). But is this accurate? If we have reasons to answer this question in the negative, then we can either allow other kinds of objects as truthmakers or we can go further and state that truthmaking does not require a supposition that any particular kinds of objects are truthmakers, leading to a sort of ontological deflationism about truthmaking. These answers have already been raised in the literature as genuine possibilities. Still, none of them has been substantiated by anything more elementary and fundamental than truthmaking, which might render such responses ad hoc. In this paper, it will be shown that by relying on grounding, we can support both approaches. To demonstrate this, we will use arithmetical truth as the backbone of the paper, showing that we have independent reasons both to allow abstract objects to be truthmakers for arithmetical statements and to dispense altogether with the reliance on truthmakers to explain their truth.