The platonism/nominalism debate in the philosophy of mathematics concerns the question whether numbers and other mathematical objects exist. Platonists believe the answer to be in the positive, nominalists in the negative. According to non-factualists, the question is ‘moot’, in the sense that it lacks a correct answer. Elaborating on ideas from Stephen Yablo, this article articulates a non-factualist position in the philosophy of mathematics and shows how the case for non-factualism entails that standard arguments for rival positions fail. In particular, (...) showing how and why non-factualists reject nominalism illuminates the originality and interest of their position. (shrink)

The paper discusses an objection, put forward by - among others - John McDowell, to Kripke’s Wittgenstein’s non-factualist and relativist view of semantic discourse. The objection goes roughly as follows: while it is usually possible to be a relativist about a given domain of discourse without being a relativist about anything else, relativism about semantic discourse entails global relativism, which in turn entails subjective idealism, which we can reasonably assume to be false. The paper’s first section sketches Kripke’s Wittgenstein’s ideas (...) about semantic discourse and gives a fully explicit formulation of the objection. The second section describes and briefly discusses the formal apparatus needed to evaluate the objection - which is basically equivalent to John MacFarlane’s recent development of David Kaplan’s classic semantic framework. Finally, the third section explains in detail why the objection fails. I show that even though relativism about semantic discourse does entail a form of global relativism, the relativism in question does not entail anything like Berkeleyan or Fichtean idealism. This particular kind of relativism holds that which character (in Kaplan’s sense) is associated to a given utterance depends on what MacFarlane calls “the context of assessment”. (shrink)

Jody Azzouni 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. (shrink)