Can Nonexistent Mathematical Objects Make a Difference? Meinongianism, indispensability argument and mathematical entanglement

Abstract

One of the arguments that most influence the debate on the existence of mathematical objects is undoubtedly the indispensability argument. Central to this argument is the Quinean ontic thesis that we are committed to the existence of all the entities we (indispensably) quantify over in our best scientific theories. But what if a different meta-ontological paradigm is adopted? In this paper, I propose a Meinongian interpretation of the indispensability argument. The new reading of the indispensability argument, in accordance with heavy duty platonism, allows me to introduce a new notion of metaphysical dependence that goes by the name of mathematical entanglement, and to conclude that nonexistent mathematical objects make a difference to the concrete, physical world.