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28Predicative subject matterPhilosophical Studies 1-19. forthcoming.The notions of subject matter and aboutness have been objects of considerable attention among philosophers over the last few years. Current theories of subject matter take sentences to be the primary bearers of subject matter: “sentences have aboutness properties if anything has” (Yablo, Aboutness, Princeton University Press, 2014). However, some subsentential expressions can also be thought of as being about something. Moreover, it appears that the subject matters of sentences depend in a syste…Read more
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17The indispensability argument and the nature of mathematical objectsTheoria : 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
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32Truthmakers, Incompatibility, and ModalityAustralasian Journal of Logic 19 (5). 2022.This paper introduces a new framework, based on the notion of compatibility space, obtained by adding a primitive incompatibility relation to a state space in the sense of Fine. The key idea inspiring the framework is to modify Fine's truthmaker semantics by taking the notion of incompatibility as primitive, and use it to define other notions. We discuss some interesting features of the framework and explore its advantages over the standard framework of state spaces. We review some applications …Read more
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29Subject Matter: A Modest ProposalPhilosophical Quarterly 71 (3): 605-622. 2021.The notion of subject matter is a key concern of contemporary philosophy of language and logic. A central task for a theory of subject matter is to characterise the notion of sentential subject matter, that is, to assign to each sentence of a given language a subject matter that may count as its subject matter. In this paper, we elaborate upon David Lewis’ account of subject matter. Lewis’ proposal is simple and elegant but lacks a satisfactory characterisation of sentential subject matter. Draw…Read more
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15Why Aboutness Matters: Meta-Fictionalism as a Case StudyPhilosophia 49 (3): 1177-1186. 2020.Recent work in the philosophy of language attempts to elucidate the elusive notion of aboutness. A natural question concerning such a project has to do with its motivation: why is the notion of aboutness important? Stephen Yablo offers an interesting answer: taking into consideration not only the conditions under which a sentence is true, but also what a sentence is about opens the door to a new style of criticism of certain philosophical analyses. We might criticize the analysis of a given noti…Read more
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21Thin Objects Are Not TransparentTheoria 89 (3): 314-325. 2023.In this short paper, we analyse whether assuming that mathematical objects are “thin” in Linnebo's sense simplifies the epistemology of mathematics. Towards this end, we introduce the notion of transparency and show that not all thin objects are transparent. We end by arguing that, far from being a weakness of thin objects, the lack of transparency of some thin objects is a fruitful characteristic mark of abstract mathematics.
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15Parts of StructuresPhilosophia 50 (3): 1277-1285. 2022.We contribute to the ongoing discussion on mathematical structuralism by focusing on a question that has so far been neglected: when is a structure part of another structure? This paper is a first step towards answering the question. We will show that a certain conception of structures, abstractionism about structures, yields a natural definition of the parthood relation between structures. This answer has many interesting consequences; however, it conflicts with some standard mereological princ…Read more
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23Sosein as Subject MatterAustralasian 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
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14Nominalistic content, grounding, and covering generalizations: Reply to ‘Grounding and the indispensability argument’Synthese 193 (2): 549-558. 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 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
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18Non‐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 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
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16Mathematical platonism meets ontological pluralism?Inquiry: An Interdisciplinary Journal of Philosophy 63 (6): 655-673. 2020.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 plural platonism, the view that results from combining mathematical platonism and ontological pluralism. I will argue that some forms of platonism are in harmony with ontological pluralism, while other forms of platonism are in tension with it. This shows that there are some interesting connections between the…Read more
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16Logic and Philosophy of Mathematics in the Early Husserl - By Stefania Centrone (review)Dialectica 65 (3): 477-482. 2011.
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15Imagine there's no (platonic) heavenThink 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
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32Mathematical 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...
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8IntroductionIn Camposampiero Favaretti & Matteo Plebani (eds.), Existence and Nature: New Perspectives, De Gruyter. pp. 1-8. 2012.
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22Fictionalism versus deflationism: a new lookPhilosophical Studies 175 (2): 301-316. 2018.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 dis…Read more
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417Ontology and Metaontology: A Contemporary GuideBloomsbury Academic. 2015.'Ontology and Metaontology: A Contemporary Guide' is a clear and accessible survey of ontology, focussing on the most recent trends in the discipline. Divided into parts, the first half characterizes metaontology: the discourse on the methodology of ontological inquiry, covering the main concepts, tools, and methods of the discipline, exploring the notions of being and existence, ontological commitment, paraphrase strategies, fictionalist strategies, and other metaontological questions. The sec…Read more
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20Could Everything Be True? Probably NotPhilosophia 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
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22Existence and Nature: New Perspectives (edited book)De Gruyter. 2012.Is all that exists part of the natural world? If there are non-natural entities, what is their difference from natural things? Is the human-independent realm of nature the only paradigm for ontological respectability, as naturalism claims? Can existence be simply explained away by means of formal devices? Philosophers keep struggling with such questions. Still, the two basic notions involved, that of existence and that of nature, have not yet been fully explored. The four essays collected here a…Read more
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18If-Thenism, Arithmetic and RemaindersAustralasian 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.
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21Computability, Finiteness and the Standard Model of ArithmeticIn Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics, Springer International Publishing. 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
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16Caricatures and Prop Oriented Make-BelieveErgo: 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
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18A Naturalistic Paradox: Existence and Nature in the Philosophy of MathematicsIn Camposampiero Favaretti & Matteo Plebani (eds.), Existence and Nature: New Perspectives, De Gruyter. pp. 9-32. 2012.
Matteo Plebani
Università Degli Studi Di Torino
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Università Degli Studi Di TorinoAssociate Professor