Non‐factualism Versus Nominalism

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 (about mathematical objects), 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.     

Nominalistic content,grounding, and covering generalizations: Reply to ‘Grounding and the indispensability argument’

‘Grounding and the indispensability argument’ presents a number of ways in which nominalists can use the notion of grounding to rebut the indispensability argument for the existence of mathematical objects. I will begin by considering the strategy that puts grounding to the service of easy-road nominalists (“Nominalistic content meets grounding” section). I will give some support to this strategy by addressing a worry some may have about it (“A misguided worry about the grounding strategy” section). I will then consider a problem for the fast-lane strategy (“Grounding and generality: a problem for the fast lane” section) and a problem for easy-road nominalists willing to accept Liggins’ grounding strategy (“More on the grounding strategy and easy-road nominalism” section). Both are related to the problem of formulating nominalistic explanations at the right level of generality. I will then consider a problem that Liggins only hints at (“Mathematics and covering generalizations” section). This problem has to do with mathematics’ function of providing the sort of covering generalizations we need in scientific explanations.     

Fictionalism versus deflationism: a new look

In the recent literature there has been some debate between advocates of deflationist and fictionalist positions in metaontology. The purpose of this paper is to advance the debate by reconsidering one objection presented by Amie Thomasson against fictionalist strategies in metaontology. The objection can be reconstructed in the following way. Fictionalists need to distinguish between the literal and the real content of sentences belonging to certain areas of discourse. In order to make that distinction, they need to assign different truth-conditions to the real and the literal content. But it is hard to see what more is required for the literal content to be true than for the real content to be true. So, fictionalism is an unsatisfactory position. Here I offer a novel reply to Thomasson’s challenge. I argue that the literal and the real content need not be distinguished in terms of their truth-conditions; rather, they can be distinguished in terms of their different subject-matters, leaving it open whether their truth-conditions coincide or not. I explain how replying to Thomasson’s objection is crucial for deepening our understanding of fictionalist strategies in metaontology.     

Why Aboutness Matters: Meta-Fictionalism as a Case Study

Philosophia - Recent work in the philosophy of language attempts to elucidate the elusive notion of aboutness (Berto 2018; Lewis 1988; Fine 2017a, b; Hawke 2017; Moltmann 2018; Yablo 2014). A...