•  32
    Sosein as Subject Matter
    Australasian Journal of Logic 15 (2): 77-94. 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
  •  1
    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
  •  16
    If-Thenism, Arithmetic and Remainders
    Australasian Philosophical Review 1 (2): 196-201. 2017.
    ABSTRACTThe target article presents a new version of if-thenism: call it IF-thenism. In this commentary I discuss whether IF-thenism can solve a problem that besets classic if-thenism. The answer will be that it can, on certain assumptions. I will briefly examine the tenability of these assumptions.
  •  32
    The indispensability argument and the nature of mathematical objects
    Theoria : An International Journal for Theory, History and Fundations of Science 33 (2): 249-263. 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
  •  57
    Mathematical platonism meets ontological pluralism?
    Inquiry: An Interdisciplinary Journal of Philosophy 1-19. 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...
  •  29
    Caricatures and Prop Oriented Make-Believe
    Ergo: 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
  •  62
    Imagine there's no (platonic) heaven
    Think 14 (39): 73-75. 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
  •  46
    Could Everything Be True? Probably Not
    Philosophia 43 (2): 499-504. 2015.
    Trivialism is the doctrine that everything is true. Almost nobody believes it, but, as Priest shows, finding a non-question-begging 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
  •  93
    ‘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. 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 fast-lane strategy and a problem for easy-road nominalists willi…Read more
  •  70
    Non‐Factualism Versus Nominalism
    Pacific 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 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 tha…Read more