Existence, Mathematical Nominalism, and Meta-Ontology: An Objection to Azzouni on Criteria for Existence – Philosophia Mathematica
Abstract: Jody Azzouni (2004, 2010) argues that whilst it is indeterminate what the criteria for existence are, there is a criterion that has been collectively adopted to use ‘exist’ that we can employ to argue for positions in ontology. I raise and defend a novel objection to Azzouni: his view has the counterintuitive consequence that the facts regarding what exists can and will change when users of the word ‘exist’ change what criteria they associate with its usage. Considering three responses, I argue Azzouni has best reason to take one that ultimately renders unsuccessful his arguments against mathematical abstracta.
I have a broad range of philosophical research interests. My primary research interests are in: i) metaphysics and meta-metaphysics/meta-ontology (existence, methodology in metaphysics, and the implications of meta-metaphysical and meta-ontological disputes to first-order metaphysics and ontology), and ii) moral philosophy and the philosophy of normativity (meta-normativity and the metaphysics of normativity, normative reasons, and normative ethics). Some of my primary research interests fall in the intersections between these areas of research.
My other philosophical research interests lie in: iii) applied ethics (defensive harm and war, personal relationships, suicide), iv) meta-philosophy (intuitions in philosophy, philosophical methodology, philosophical progress), v) epistemology (epistemic normativity, reasons for belief, epistemic rationality), vi) philosophy of mind (non-reductive physicalism, mental causation), and vii) philosophy of cognitive science (brain-based mindreading, format of mental representations).