
93Nominalistic content, grounding, and covering generalizations: Reply to ‘Grounding and the indispensability argument’Synthese 193 (2): 549558. 2016.‘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 easyroad nominalists. I will give some support to this strategy by addressing a worry some may have about it. I will then consider a problem for the fastlane strategy and a problem for easyroad nominalists willi…Read more

70Non‐Factualism Versus NominalismPacific Philosophical Quarterly 98 (3). 2017.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 nonfactualists, the question is ‘moot’, in the sense that it lacks a correct answer. Elaborating on ideas from Stephen Yablo, this article articulates a nonfactualist position in the philosophy of mathematics and shows how the case for nonfactualism entails tha…Read more

62Imagine there's no (platonic) heavenThink 14 (39): 7375. 2015.Some people think that numbers and other mathematical entities exist. They believe in a platonic heaven of ideal mathematical objects, as some people like to put it. This may seem a very strange thing to believe in: after all, we cannot see numbers, nor touch them, nor smell them. So why should one believe that they exist? Because, as Putnam and Quine used to say, numbers are indispensable to science: it seems almost impossible to state our best scientific theories without mentioning numbers or …Read more

57Mathematical platonism meets ontological pluralism?Inquiry: An Interdisciplinary Journal of Philosophy 119. 2017.Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for...

46Could Everything Be True? Probably NotPhilosophia 43 (2): 499504. 2015.Trivialism is the doctrine that everything is true. Almost nobody believes it, but, as Priest shows, finding a nonquestionbegging argument against it turns out to be a difficult task. In this paper, I propose a statistical argument against trivialism, developing a strategy different from those presented in Priest

32The indispensability argument and the nature of mathematical objectsTheoria : An International Journal for Theory, History and Fundations of Science 33 (2): 249263. 2018.I will contrast two conceptions of the nature of mathematical objects: the conception of mathematical objects as preconceived objects, and heavy duty platonism. I will argue that friends of the indispensability argument are committed to some metaphysical theses and that one promising way to motivate such theses is to adopt heavy duty platonism. On the other hand, combining the indispensability argument with the conception of mathematical objects as preconceived objects yields an unstable positio…Read more

32Sosein as Subject MatterAustralasian Journal of Logic 15 (2): 7794. 2018.Meinongians in general, and Routley in particular, subscribe to the principle of the independence of Sosein from Sein. In this paper, I put forward an interpretation of the independence principle that philosophers working outside the Meinongian tradition can accept. Drawing on recent work by Stephen Yablo and others on the notion of subject matter, I offer a new account of the notion of Sosein as a subject matter and argue that in some cases Sosein might be independent from Sein. The question wh…Read more

29Caricatures and Prop Oriented MakeBelieveErgo: An Open Access Journal of Philosophy 3. 2016.A caricature can reveal an aspect of its subject that a more faithful representation would fail to render: by depicting a slow and clumsy person as a monkey one can point out such qualities of the depicted subject, and by depicting a person with quite big ears as a person with enormous ears one can point out that the depicted person has rather big ears. How can a form of representation that is by definition inaccurate be so representationally powerful? Figurative language raises a similar puzzle…Read more

16IfThenism, Arithmetic and RemaindersAustralasian Philosophical Review 1 (2): 196201. 2017.ABSTRACTThe target article presents a new version of ifthenism: call it IFthenism. In this commentary I discuss whether IFthenism can solve a problem that besets classic ifthenism. The answer will be that it can, on certain assumptions. I will briefly examine the tenability of these assumptions.

1Computability, Finiteness and the Standard Model of ArithmeticIn Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. Filmat Studies in the Philosophy of Mathematics, Springer Verlag. 2016.This paper investigates the question of how we manage to single out the natural number structure as the intended interpretation of our arithmetical language. Horsten submits that the reference of our arithmetical vocabulary is determined by our knowledge of some principles of arithmetic on the one hand, and by our computational abilities on the other. We argue against such a view and we submit an alternative answer. We single out the structure of natural numbers through our intuition of the abso…Read more
Areas of Interest
Metaphysics 
Logic and Philosophy of Logic 
Philosophy of Mathematics 