Why metaphysics is not like mathematics

Source abstract

Abstract In the recent literature, moderate naturalistic metaphysicians have been attempting to justify the existence of ‘free range’ analytic metaphysics by employing an analogy with pure mathematics: just as pure mathematics is justified by its potential applications to science, so too, they argue, is analytic metaphysics justified by its potential applications in philosophy of science. Employing standard textbook logical tools to evaluate analogies, we argue that the analogy doesn’t hold: there are relevant dissimilarities between the two disciplines. The grounds and domain of application of metaphysics and mathematics to science are ultimately different, and arguments intended to justify the epistemic value of metaphysics for science often presuppose its value rather than demonstrate it. This is why metaphysics is not like mathematics.