Mathematics and Metaphysics on the Boundaries of Scientific Ontology

Mr Cristian Soto (University of Melbourne)

This paper examines the boundaries of scientific ontology, that is to say, the problem of which entities are to be granted ontological rights as belonging to our best scientific view of reality. This problem encompasses several issues in metaphysics, philosophy of science, and philosophy of mathematics. I will focus in particular on assessing some aspects of the contribution of both mathematics and metaphysics to the shaping of scientific ontology. The main tenet of my argument is a radically naturalistic one, viz.: philosophers should prefer mathematical theorising rather than metaphysical speculation when it comes to evaluating what ultimately there is according to our best knowledge of objective features of reality. In putting forward my argument, I address questions related to (i) the metaphysics of mathematics, such as whether or not mathematical entities belong to the spatio-temporal causal link; (ii) the applicability of mathematics to the physical realm, as in the case of the formulation of laws in science; (iii) the ontological status of metaphysical presuppositions in science, like those of the nature of time and causation; (iv) the ontological contribution of mathematics and metaphysics to the establishment of the boundaries of scientific ontology at some micro and macro scales; and (v) the general epistemic contribution of mathematics and metaphysics to the progress of scientific knowledge. In short, I attempt to promote the view that mathematics rather than metaphysics is the best grasp that we have of the boundaries of scientific ontology.