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  1. On Specifying Truth-Conditions.Agustín Rayo - 2008 - Philosophical Review 117 (3):385-443.
    This essay is a study of ontological commitment, focused on the special case of arithmetical discourse. It tries to get clear about what would be involved in a defense of the claim that arithmetical assertions are ontologically innocent and about why ontological innocence matters. The essay proceeds by questioning traditional assumptions about the connection between the objects that are used to specify the truth-conditions of a sentence, on the one hand, and the objects whose existence is required in order for (...)
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  • Mathematical Surrealism as an Alternative to Easy-Road Fictionalism.Kenneth Boyce - 2020 - Philosophical Studies 177 (10):2815-2835.
    Easy-road mathematical fictionalists grant for the sake of argument that quantification over mathematical entities is indispensable to some of our best scientific theories and explanations. Even so they maintain we can accept those theories and explanations, without believing their mathematical components, provided we believe the concrete world is intrinsically as it needs to be for those components to be true. Those I refer to as “mathematical surrealists” by contrast appeal to facts about the intrinsic character of the concrete world, not (...)
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  • Infinitesimal Idealization, Easy Road Nominalism, and Fractional Quantum Statistics.Elay Shech - 2019 - Synthese 196 (5):1963-1990.
    It has been recently debated whether there exists a so-called “easy road” to nominalism. In this essay, I attempt to fill a lacuna in the debate by making a connection with the literature on infinite and infinitesimal idealization in science through an example from mathematical physics that has been largely ignored by philosophers. Specifically, by appealing to John Norton’s distinction between idealization and approximation, I argue that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path to (...)
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  • Ontological Realism and Sentential Form.Eileen Nutting - 2018 - Synthese 195 (11):5021-5036.
    The standard argument for the existence of distinctively mathematical objects like numbers has two main premises: some mathematical claims are true, and the truth of those claims requires the existence of distinctively mathematical objects. Most nominalists deny. Those who deny typically reject Quine’s criterion of ontological commitment. I target a different assumption in a standard type of semantic argument for. Benacerraf’s semantic argument, for example, relies on the claim that two sentences, one about numbers and the other about cities, have (...)
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  • Objects and Objectivity : Alternatives to Mathematical Realism.Ebba Gullberg - 2011 - Dissertation, Umeå Universitet
    This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes (...)
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  • What Anti-Realism in Philosophy of Mathematics Must Offer.Feng Ye - 2010 - Synthese 175 (1):13 - 31.
    This article attempts to motivate a new approach to anti-realism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to anti-realism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current anti-realistic philosophies have not yet met these challenges, and that is why they cannot convince realists. Then, I will introduce a research project for a new, truly naturalistic, and completely scientific approach to philosophy of mathematics. It belongs (...)
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  • There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.
    Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not a path for the faint hearted. Indeed, the substantial technical difficulties facing Field's project have led some to explore other, easier options. Recently, Jody Azzouni, Joseph Melia, and Stephen Yablo have argued that it is a mistake to read our ontological commitments simply from what the quantifiers of our best (...)
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  • Replies to Comments on If-Thenism.Stephen Yablo - 2017 - Australasian Philosophical Review 1 (2):212-227.
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  • True Enough.Catherine Z. Elgin - 2004 - Philosophical Issues 14 (1):113–131.
    Truth is standardly considered a requirement on epistemic acceptability. But science and philosophy deploy models, idealizations and thought experiments that prescind from truth to achieve other cognitive ends. I argue that such felicitous falsehoods function as cognitively useful fictions. They are cognitively useful because they exemplify and afford epistemic access to features they share with the relevant facts. They are falsehoods in that they diverge from the facts. Nonetheless, they are true enough to serve their epistemic purposes. Theories that contain (...)
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  • Methodology in the Ontology of Artworks: Exploring Hermeneutic Fictionalism.Elisa Caldarola - 2020 - In Concha Martinez Vidal & José Luis Falguera Lopez (ed.), Abstract Objects: For and Against.
    There is growing debate about what is the correct methodology for research in the ontology of artworks. In the first part of this essay, I introduce my view: I argue that semantic descriptivism is a semantic approach that has an impact on meta-ontological views and can be linked with a hermeneutic fictionalist proposal on the meta-ontology of artworks such as works of music. In the second part, I offer a synthetic presentation of the four main positive meta-ontological views that have (...)
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  • Throwing Spatial Light: On Topological Explanations in Gestalt Psychology.Bartłomiej Skowron & Krzysztof Wójtowicz - 2020 - Phenomenology and the Cognitive Sciences (3):1-22.
    It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is to (...)
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  • Non‐Factualism Versus Nominalism.Matteo Plebani - 2017 - Pacific Philosophical Quarterly 98 (3).
    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, (...)
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  • Fictionalism Versus Deflationism: A New Look.Matteo Plebani - 2018 - Philosophical Studies 175 (2):301-316.
    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 (...)
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  • Inscrutability and Ontological Commitment.Berit Brogaard - 2008 - Philosophical Studies 141 (1):21 - 42.
    There are two doctrines for which Quine is particularly well known: the doctrine of ontological commitment and the inscrutability thesis—the thesis that reference and quantification are inscrutable. At first glance, the two doctrines are squarely at odds. If there is no fact of the matter as to what our expressions refer to, then it would appear that no determinate commitments can be read off of our best theories. We argue here that the appearance of a clash between the two doctrines (...)
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  • A Truthmaker Indispensability Argument.Sam Baron - 2013 - Synthese 190 (12):2413-2427.
    Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of (...)
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  • Nominalistic Content, Grounding, and Covering Generalizations: Reply to ‘Grounding and the Indispensability Argument’.Matteo Plebani - 2016 - Synthese 193 (2):549-558.
    ‘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 willing to (...)
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  • Abstract Expressionism and the Communication Problem.David Liggins - 2014 - British Journal for the Philosophy of Science 65 (3):599-620.
    Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and (...)
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  • The Return of Moral Fictionalism.Nadeem J. Z. Hussain - 2004 - Philosophical Perspectives 18 (1):149–188.
    Fictionalism has recently returned as a standard response to ontologically problematic domains. This article assesses moral fictionalism. It argues (i) that a correct understanding of the dialectical situation in contemporary metaethics shows that fictionalism is only an interesting new alternative if it can provide a new account of normative content: what is it that I am thinking or saying when I think or say that I ought to do something; and (ii) that fictionalism, qua fictionalism, does not provide us with (...)
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  • Representational Indispensability and Ontological Commitment.John Heron - 2020 - Thought: A Journal of Philosophy 9 (2):105-114.
    Thought: A Journal of Philosophy, EarlyView.
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  • Quinean Worlds: Possibilist Ontology in an Extenionalist Framework.Pedro Santos - 2014 - Grazer Philosophische Studien 89 (1):205-230.
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  • Can Indispensability-Driven Platonists Be (Serious) Presentists?Sam Baron - 2014 - Theoria 80 (2):153-173.
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  • The Myth of Seven.Stephen Yablo - 2005 - In Mark Eli Kalderon (ed.), Fictionalism in Metaphysics. Clarendon Press. pp. 88--115.
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  • Are There Genuine Physical Explanations of Mathematical Phenomena?Bradford Skow - 2015 - British Journal for the Philosophy of Science 66 (1):69-93.
    There are lots of arguments for, or justifications of, mathematical theorems that make use of principles from physics. Do any of these constitute explanations? On the one hand, physical principles do not seem like they should be explanatorily relevant; on the other, some particular examples of physical justifications do look explanatory. In this article, I defend the idea that physical justifications can and do explain mathematical facts. 1 Physical Arguments for Mathematical Truths2 Preview3 Mathematical Facts4 Purity5 Doubts about Purity: I6 (...)
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  • The Indispensability Argument and the Nature of Mathematical Objects.Matteo Plebani - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):249-263.
    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 position. The conclusion is that the metaphysical commitments (...)
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  • Mathematics and the World: Explanation and Representation.John-Hamish Heron - 2017 - Dissertation, King’s College London
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  • Go Figure: A Path Through Fictionalism.Stephen Yablo - 2001 - Midwest Studies in Philosophy 25 (1):72–102.
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  • Fictionalism in Metaphysics.Frederick Kroon - 2011 - Philosophy Compass 6 (11):786-803.
    This is a survey of contemporary work on ‘fictionalism in metaphysics’, a term that is taken to signify both the place of fictionalism as a distinctive anti‐realist metaphysics in which usefulness rather than truth is the norm of acceptance, and the fact that philosophers have given fictionalist treatments of a range of specifically metaphysical notions.
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  • Figurative Language in Explanation.Inga Nayding - 2013 - Disputatio 5 (35):2013.
    Yablo argued that some metaphors are representationally essential: they enable us to express contents that we would not be able to express without them. He defended a fictionalist view of mathematical language by making the case that it similarly serves as a representational aid. Against this, Colyvan argued that metaphorical/figurative language can never play an essential role in explanation and that mathematical language often does, hence concluding that Yablo’s fictionalism is untenable. I show that Colyvan’s thesis about explanation is highly (...)
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  • Names of Attitudes and Norms for Attitudes.Inga Nayding - 2015 - Disputatio 7 (40):1-24.
    Fictionalists claim that instead of believing certain controversial propositions they accept them nonseriously, as useful make-believe. In this way they present themselves as having an austere ontology despite the apparent ontological commitments of their discourse. Some philosophers object that this plays on a distinction without a difference: the fictionalist’s would-be nonserious acceptance is the most we can do for the relevant content acceptance-wise, hence such acceptance is no different from what we ordinarily call ‘belief’ and should be so called. They (...)
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  • Fictionalism.Fiora Salis - 2015 - Online Companion to Problems in Analytic Philosophy.
    In this entry I will offer a survey of the contemporary debate on fic- tionalism, which is a distinctive anti-realist view about certain regions of discourse that are valued for their usefulness rather than their truth.
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  • What is a Second Order Theory Committed To?Charles Sayward - 1983 - Erkenntnis 20 (1):79 - 91.
    The paper argues that no second order theory is ontologically commited to anything beyond what its individual variables range over.
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  • Nominalism, Trivialism, Logicism.Agustín Rayo - 2015 - Philosophia Mathematica 23 (1):nku013.
    This paper extracts some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases. Although much of the material in this paper is drawn from the book — and from an earlier paper — I hope the present (...)
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  • Hofweber's Philosophy of Mathematics.AgustÍn Rayo - 2017 - Philosophy and Phenomenological Research 94 (2):474-480.
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  • Two Criticisms Against Mathematical Realism.Seungbae Park - 2017 - Diametros 52:96-106.
    Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a tricle is true or false. A tricle is an (...)
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  • On Specifying Truth-Conditions.Jason M. Byron - manuscript
    I develop a technique for specifying truth-conditions.
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  • Realismo/Anti-Realismo.Eduardo Castro - 2014 - Compêndio Em Linha de Problemas de Filosofia Analítica.
    State of the art paper on the topic realism/anti-realism. The first part of the paper elucidates the notions of existence and independence of the metaphysical characterization of the realism/anti-realism dispute. The second part of the paper presents a critical taxonomy of the most important positions and doctrines in the contemporary literature on the domains of science and mathematics: scientific realism, scientific anti-realism, constructive empiricism, structural realism, mathematical Platonism, mathematical indispensability, mathematical empiricism, intuitionism, mathematical fictionalism and second philosophy.
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  • Indispensability Argument and Anti-Realism in Philosophy of Mathematics.Feng Ye - 2007 - Frontiers of Philosophy in China 2 (4):614-628.
    The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical (...)
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  • Indispensability Argument and Anti-Realism in Philosophy of Mathematics.Y. E. Feng - 2007 - Frontiers of Philosophy in China 2 (4):614-628.
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  • If-Thenism, Arithmetic and Remainders.Matteo Plebani - 2017 - Australasian Philosophical Review 1 (2):196-201.
    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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  • No Objects, No Problem?Matthew McGrath - 2005 - Australasian Journal of Philosophy 83 (4):457 – 486.
    One familiar form of argument for rejecting entities of a certain kind is that, by rejecting them, we avoid certain difficult problems associated with them. Such problem-avoidance arguments backfire if the problems cited survive the elimination of the rejected entities. In particular, we examine one way problems can survive: a question for the realist about which of a set of inconsistent statements is false may give way to an equally difficult question for the eliminativist about which of a set of (...)
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  • Good Weasel Hunting.Robert Knowles & David Liggins - 2015 - Synthese 192 (10):3397-3412.
    The ‘indispensability argument’ for the existence of mathematical objects appeals to the role mathematics plays in science. In a series of publications, Joseph Melia has offered a distinctive reply to the indispensability argument. The purpose of this paper is to clarify Melia’s response to the indispensability argument and to advise Melia and his critics on how best to carry forward the debate. We will begin by presenting Melia’s response and diagnosing some recent misunderstandings of it. Then we will discuss four (...)
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  • A Role for Mathematics in the Physical Sciences.Chris Pincock - 2007 - Noûs 41 (2):253-275.
    Conflicting accounts of the role of mathematics in our physical theories can be traced to two principles. Mathematics appears to be both (1) theoretically indispensable, as we have no acceptable non-mathematical versions of our theories, and (2) metaphysically dispensable, as mathematical entities, if they existed, would lack a relevant causal role in the physical world. I offer a new account of a role for mathematics in the physical sciences that emphasizes the epistemic benefits of having mathematics around when we do (...)
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  • Katharina Felka, Talking About Numbers: Easy Arguments for Mathematical Realism, Studies in Theoretical Philosophy, Vol. 3, Frankfurt Am Main: Vittorio Klostermann Verlag, 2016, 188 Pp., €49.00. ISBN 978‐3‐465‐03879‐5. [REVIEW]Matteo Plebani - 2018 - Dialectica 72 (3):473-479.
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  • Essential Properties and the Right to Life: A Response to Lee.Dean Stretton - 2004 - Bioethics 18 (3):264–282.
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  • Types and Tokens.Linda Wetzel - 2008 - Stanford Encyclopedia of Philosophy.
    The distinction between a type and its tokens is a useful metaphysical distinction. In §1 it is explained what it is, and what it is not. Its importance and wide applicability in linguistics, philosophy, science and everyday life are briefly surveyed in §2. Whether types are universals is discussed in §3. §4 discusses some other suggestions for what types are, both generally and specifically. Is a type the sets of its tokens? What exactly is a word, a symphony, a species? (...)
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