“The Eleatic and the Indispensabilist,” an article by Assistant Professor of Philosophy Russell Marcus, was recently published in the open access journal Theoria. The article focused on the debate over whether we should believe that mathematical objects exist and how that debate connects to the general question of how to determine what we should believe to exist.
Marcus said that “indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist, and so that mathematical objects do not exist.”
He showed that arguments on both sides are not decisive and then sketched a way to capture some of the important intuitions behind both views by adopting a view he calls autonomy Platonism.
Autonomy Platonism and the Indispensability Argument, Marcus’ monograph on this view, was published last summer.
Theoria is an international journal for theory, history and foundations of science published by Spain’s Universidad del Pais Vasco (University of the Basque Country). According to the journal’s website, it is “one of the leading philosophy journals in the Spanish-speaking world.”