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Deflating Existential Consequence: A Case for Nominalism

Oxford, England: Oup Usa (2004)

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  1. Explanatory Indispensability Arguments in Metaethics and Philosophy of Mathematics.Debbie Roberts - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford, England: Oxford University Press UK.
  • Why so Serious? Non-serious Presentism and the Problem of Cross-temporal Relations.Ross Inman - 2012 - Metaphysica 13 (1):55-63.
    It is a common assumption in the metaphysics of time that a commitment to presentism entails a commitment to serious presentism, the view that objects can exemplify properties or stand in relations only at times at which they exist. As a result, non-serious presentism is widely thought to be beyond the bounds for the card-carrying presentist in response to the problem of cross-temporal relations. In this paper, I challenge this general consensus by examining one common argument in favor of the (...)
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  • Dummett on abstract objects.George Duke - 2012 - New York: Palgrave-Macmillan.
    This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.
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  • Platonism and Intra-mathematical Explanation.Sam Baron - forthcoming - Philosophical Quarterly.
    I introduce an argument for Platonism based on intra-mathematical explanation: the explanation of one mathematical fact by another. The argument is important for two reasons. First, if the argument succeeds then it provides a basis for Platonism that does not proceed via standard indispensability considerations. Second, if the argument fails it can only do so for one of three reasons: either because there are no intra-mathematical explanations, or because not all explanations are backed by dependence relations, or because some form (...)
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  • Fictionalism in the philosophy of mathematics.Mark Colyvan - 1998 - In Edward Craig (ed.), The Routledge Encyclopedia of Philosophy. Routledge.
    Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘π is irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities, and according to fictionalists there are no such entities. Fictionalism is a nominalist (or anti-realist) account of mathematics in that it denies the existence of a realm of abstract (...)
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  • Ontological Commitment and Quantifiers.T. Parent - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. New York, NY: Routledge.
    This is a slightly opinionated review of three main factions in metaontology: Quineans, Carnapians, and Meinongians. Emphasis is given to the last camp, as the metaontological aspect of Meinongianism has been underappreciated. The final section then offers some general remarks about the legitimacy of ontology, touching on ideas I have developed in other publications.
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  • Natural Language Ontology (SEP entry).Moltmann Friederike - 2022 - Stanford Encyclopedia of Philosophy.
  • Wigner’s Puzzle for Mathematical Naturalism.Sorin Bangu - 2009 - International Studies in the Philosophy of Science 23 (3):245-263.
    I argue that a recent version of the doctrine of mathematical naturalism faces difficulties arising in connection with Wigner's old puzzle about the applicability of mathematics to natural science. I discuss the strategies to solve the puzzle and I show that they may not be available to the naturalist.
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  • Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism.Jared Warren - 2020 - New York, USA: Oxford University Press.
    What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...)
  • Fundamental and Derivative Truths.J. R. G. Williams - 2010 - Mind 119 (473):103 - 141.
    This article investigates the claim that some truths are fundamentally or really true — and that other truths are not. Such a distinction can help us reconcile radically minimal metaphysical views with the verities of common sense. I develop an understanding of the distinction whereby Fundamentality is not itself a metaphysical distinction, but rather a device that must be presupposed to express metaphysical distinctions. Drawing on recent work by Rayo on anti-Quinean theories of ontological commitments, I formulate a rigourous theory (...)
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  • Importance and Explanatory Relevance: The Case of Mathematical Explanations.Gabriel Târziu - 2018 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (3):393-412.
    A way to argue that something plays an explanatory role in science is by linking explanatory relevance with importance in the context of an explanation. The idea is deceptively simple: a part of an explanation is an explanatorily relevant part of that explanation if removing it affects the explanation either by destroying it or by diminishing its explanatory power, i.e. an important part is an explanatorily relevant part. This can be very useful in many ontological debates. My aim in this (...)
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  • Existence questions.Amie L. Thomasson - 2008 - Philosophical Studies 141 (1):63 - 78.
    I argue that thinking of existence questions as deep questions to be resolved by a distinctively philosophical discipline of ontology is misguided. I begin by examining how to understand the truth-conditions of existence claims, by way of understanding the rules of use for ‘exists’ and for general noun terms. This yields a straightforward method for resolving existence questions by a combination of conceptual analysis and empirical enquiry. It also provides a blueprint for arguing against most common proposals for uniform substantive (...)
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  • The Epistemic Indispensability Argument.Cristian Soto - 2019 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 50 (1):145-161.
    This article elaborates the epistemic indispensability argument, which fully embraces the epistemic contribution of mathematics to science, but rejects the contention that such a contribution is a reason for granting reality to mathematicalia. Section 1 introduces the distinction between ontological and epistemic readings of the indispensability argument. Section 2 outlines some of the main flaws of the first premise of the ontological reading. Section 3 advances the epistemic indispensability argument in view of both applied and pure mathematics. And Sect. 4 (...)
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  • The ‘Space’ at the Intersection of Platonism and Nominalism.Edward Slowik - 2015 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 46 (2):393-408.
    This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but it (...)
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  • Spacetime, Ontology, and Structural Realism.Edward Slowik - 2005 - International Studies in the Philosophy of Science 19 (2):147 – 166.
    This essay explores the possibility of constructing a structural realist interpretation of spacetime theories that can resolve the ontological debate between substantivalists and relationists. Drawing on various structuralist approaches in the philosophy of mathematics, as well as on the theoretical complexities of general relativity, our investigation will reveal that a structuralist approach can be beneficial to the spacetime theorist as a means of deflating some of the ontological disputes regarding similarly structured spacetimes.
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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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  • Frege, Indispensability, and the Compatibilist Heresy.Andrea Sereni - 2015 - Philosophia Mathematica 23 (1):11-30.
    In Grundgesetze, Vol. II, §91, Frege argues that ‘it is applicability alone which elevates arithmetic from a game to the rank of a science’. Many view this as an in nuce statement of the indispensability argument later championed by Quine. Garavaso has questioned this attribution. I argue that even though Frege's applicability argument is not a version of ia, it facilitates acceptance of suitable formulations of ia. The prospects for making the empiricist ia compatible with a rationalist Fregean framework appear (...)
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  • Steps Towards a Minimalist Account of Numbers.Thomas Schindler - 2021 - Mind 131 (523):863-891.
    This paper outlines an account of numbers based on the numerical equivalence schema, which consists of all sentences of the form ‘#x.Fx=n if and only if ∃nx Fx’, where # is the number-of operator and ∃n is defined in standard Russellian fashion. In the first part of the paper, I point out some analogies between the NES and the T-schema for truth. In light of these analogies, I formulate a minimalist account of numbers, based on the NES, which strongly parallels (...)
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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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  • Scientific Models and Metalinguistic Negotiation.Mirco Sambrotta - 2019 - Theoria. An International Journal for Theory, History and Foundations of Science 34 (2):277.
    The aim of this paper is to explore the possibility that, at least, some metaphysical debates are ‘metalinguistic negotiations’. I will take the dispute between the dominant approaches of realism and the anti-realism ones about the ontological status of scientific models as a case-study. I will argue that such a debate may be better understood as a disagreement, at bottom normatively, motivated, insofar as a normative and non-factual question may be involved in it: how the relevant piece of language ought (...)
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  • Heidegger and Analytic Philosophy: Together at Last?Jon Robson - 2014 - International Journal of Philosophical Studies 22 (3):482-487.
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  • Ontological commitment.Agustín Rayo - 2007 - Philosophy Compass 2 (3):428–444.
    I propose a way of thinking aboout content, and a related way of thinking about ontological commitment. (This is part of a series of four closely related papers. The other three are ‘On Specifying Truth-Conditions’, ‘An Actualist’s Guide to Quantifying In’ and ‘An Account of Possibility’.).
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  • The facticity of explanation and its consequences.Yvonne Raley - 2007 - International Studies in the Philosophy of Science 21 (2):123 – 135.
    This paper argues that, contrary to the views of Nancy Cartwright and Brian Ellis, explanations are factive: if a statement is taken to be an explanation, it also has to be accepted as true. Taking explanations to be true, in turn, seems to imply that all the entities posited in explanations are real. But this is precisely what some philosophers, such as Cartwright and Ellis, want to deny. What these philosophers do not want to deny, however, is that such statements (...)
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  • Deflating existence away? A critique of Azzouni's nominalism.Yvonne Raley - 2009 - Philosophia Mathematica 17 (1):73-83.
    Yet, he also says that it is philosophically indeterminate which criterion for what exists is correct. Nominalism is the view that certain objects ( i.e ., abstract objects) do not exist, and not the view that it is philosophically indeterminate whether or not they do. I resolve the dilemma that Azzouni's claims pose: Azzouni is a non-factualist about what exists, but he is a factualist about which criterion for what exists our community of speakers has adopted. It is in the (...)
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  • How to avoid inconsistent idealizations.Christopher Pincock - 2014 - Synthese 191 (13):2957-2972.
    Idealized scientific representations result from employing claims that we take to be false. It is not surprising, then, that idealizations are a prime example of allegedly inconsistent scientific representations. I argue that the claim that an idealization requires inconsistent beliefs is often incorrect and that it turns out that a more mathematical perspective allows us to understand how the idealization can be interpreted consistently. The main example discussed is the claim that models of ocean waves typically involve the false assumption (...)
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  • Ontology: minimalism and truth-conditions.Juan José Lara Peñaranda - 2013 - Philosophical Studies 162 (3):683-696.
    In this paper, I develop a criticism to a method for metaontology, namely, the idea that a discourse’s or theory’s ontological commitments can be read off its sentences’ truth- conditions. Firstly, I will put forward this idea’s basis and, secondly, I will present the way Quine subscribed to it. However, I distinguish between two readings of Quine’s famous ontological criterion, and I center the focus on the one currently dubbed “ontological minimalism”, a kind of modern Ockhamism applied to the mentioned (...)
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  • Sellars, Second-order Quantification, and Ontological Commitment.Andrew Parisi - 2018 - History and Philosophy of Logic 40 (1):81-97.
    Sellars [1960, ‘Grammar and existence: A preface to ontology’] argues that the truth of a second-order sentence does not incur commitment to there being any sort of abstract entity. This paper begins by exploring the arguments that Sellars offers for the above claim. It then develops those arguments by pointing out places where Sellars has been unclear or ought to have said more. In particular, Sellars's arguments rely on there being a means by which language users could come to understand (...)
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  • Ontic terms and metaontology, or: on what there actually is.T. Parent - 2014 - Philosophical Studies 170 (2):199-214.
    Terms such as ‘exist’, ‘actual’, etc., (hereafter, “ontic terms”) are recognized as having uses that are not ontologically committing, in addition to the usual commissive uses. (Consider, e.g., the Platonic and the neutral readings of ‘There is an even prime’.) In this paper, I identify five different noncommissive uses for ontic terms, and (by a kind of via negativa) attempt to define the commissive use, focusing on ‘actual’ as my example. The problem, however, is that the resulting definiens for the (...)
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  • Content Externalism and Quine’s Criterion are Incompatible.T. Parent - 2017 - Erkenntnis 82 (3):625-639.
    Externalism holds that the content of our utterances and thoughts are determined partly by the environment. Here, I offer an argument which suggests that externalism is incompatible with a natural view about ontological commitment--namely, the Quinean view that such commitments are fixed by the range of the variables in your theory. The idea in brief is that if Oscar mistakenly believes that water = XYZ, the externalist ontologically commits Oscar to two waterish kinds, whereas the Quinean commits him to one (...)
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  • Ontological realism and sentential form.Eileen S. 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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  • Benacerraf, Field, and the agreement of mathematicians.Eileen S. Nutting - 2020 - Synthese 197 (5):2095-2110.
    Hartry Field’s epistemological challenge to the mathematical platonist is often cast as an improvement on Paul Benacerraf’s original epistemological challenge. I disagree. While Field’s challenge is more difficult for the platonist to address than Benacerraf’s, I argue that this is because Field’s version is a special case of what I call the ‘sociological challenge’. The sociological challenge applies equally to platonists and fictionalists, and addressing it requires a serious examination of mathematical practice. I argue that the non-sociological part of Field’s (...)
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  • Infinity and the foundations of linguistics.Ryan M. Nefdt - 2019 - Synthese 196 (5):1671-1711.
    The concept of linguistic infinity has had a central role to play in foundational debates within theoretical linguistics since its more formal inception in the mid-twentieth century. The conceptualist tradition, marshalled in by Chomsky and others, holds that infinity is a core explanandum and a link to the formal sciences. Realism/Platonism takes this further to argue that linguistics is in fact a formal science with an abstract ontology. In this paper, I argue that a central misconstrual of formal apparatus of (...)
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  • An encoding approach to Ante Rem structuralism.T. G. Murphy - 2019 - Synthese 198 (7):5953-5976.
    While ante rem structuralism offers a promising account of mathematical truth and mathematical ontology, several of the most prominent formulations of the view seem to be subject to significant difficulties involving the identity conditions of the objects they posit. In this paper I argue that those difficulties can be overcome by adopting encoding structuralism, a version of realism about mathematical objects developed by Bernard Linsky, Uri Nodelman and Edward Zalta.
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  • Introduction (to the special issue on ontological commitment).Luca Moretti & Huw Price - 2008 - Philosophical Studies 141 (1):1-5.
  • Indispensability and explanation: an overview and introduction.Daniele Molinini, Fabrice Pataut & Andrea Sereni - 2016 - Synthese 193 (2):317-332.
  • The holistic presumptions of the indispensability argument.Russell Marcus - 2014 - Synthese 191 (15):3575-3594.
    The indispensability argument is sometimes seen as weakened by its reliance on a controversial premise of confirmation holism. Recently, some philosophers working on the indispensability argument have developed versions of the argument which, they claim, do not rely on holism. Some of these writers even claim to have strengthened the argument by eliminating the controversial premise. I argue that the apparent removal of holism leaves a lacuna in the argument. Without the holistic premise, or some other premise which facilitates the (...)
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  • The Eleatic and the Indispensabilist.Russell Marcus - 2015 - Theoria 30 (3):415-429.
    The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument against some contemporary eleatics attempt to provide reasons to favor the indispensabilist’s criterion. I show that Colyvan’s argument is not (...)
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  • Intrinsic Explanation and Field’s Dispensabilist Strategy.Russell Marcus - 2013 - International Journal of Philosophical Studies 21 (2):163-183.
    Philosophy of mathematics for the last half-century has been dominated in one way or another by Quine’s indispensability argument. The argument alleges that our best scientific theory quantifies over, and thus commits us to, mathematical objects. In this paper, I present new considerations which undermine the most serious challenge to Quine’s argument, Hartry Field’s reformulation of Newtonian Gravitational Theory.
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  • Existence Is Not Relativistically Invariant—Part 1: Meta-ontology.Florian Marion - 2024 - Acta Analytica 39:1-25.
    Metaphysicians who are aware of modern physics usually follow Putnam (1967) in arguing that Special Theory of Relativity is incompatible with the view that what exists is only what exists now or presently. Partisans of presentism (the motto ‘only present things exist’) had very difficult times since, and no presentist theory of time seems to have been able to satisfactorily counter the objection raised from Special Relativity. One of the strategies offered to the presentist consists in relativizing existence to inertial (...)
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  • Weaseling and the Content of Science.David Liggins - 2012 - Mind 121 (484):997-1005.
    I defend Joseph Melia’s nominalist account of mathematics from an objection raised by Mark Colyvan.
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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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  • Deflationary Nominalism and Puzzle Avoidance.David Mark Kovacs - 2019 - Philosophia Mathematica 27 (1):88-104.
    In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...)
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  • On the Indispensability of the Distinctively Mathematical.C. Juhl - 2012 - Philosophia Mathematica 20 (3):324-338.
    Indispensability arguments purport to show that empirical data provide evidence for the existence of mathematical entities. In this paper we argue that indispensability arguments fail to show that empirical data bears on the mathematical. In order to show this we attempt to clarify what it is to be mathematical , and separate the question whether abstracta in general exist from whether distinctively mathematical abstracta exist. We introduce the notion of an ‘agnostified’ empirical theory as a heuristic device for clarifying the (...)
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  • Committing to an individual: ontological commitment, reference and epistemology.Frederique Janssen-Lauret - 2016 - Synthese 193 (2):583-604.
    When we use a directly referential expression to denote an object, do we incur an ontological commitment to that object, as Russell and Barcan Marcus held? Not according to Quine, whose regimented language has only variables as denoting expressions, but no constants to model direct reference. I make a case for a more liberal conception of ontological commitment—more wide-ranging than Quine’s—which allows for commitment to individuals, with an improved logical language of regimentation. The reason for Quine’s prohibition on commitment to (...)
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  • Content Extraction, Ontological Mootness and Nominalism: Difficulties on the Easy Road.Andrej Jandrić - 2020 - Erkenntnis:1-13.
    In his latest book Aboutness, Stephen Yablo has proposed a new ‘easy road’ nominalist strategy: instead of engaging in the hard work of paraphrasing a scientific theory which presupposes numbers in a nominalistically acceptable way, nominalists are, according to Yablo, entitled to accept the theory as true, while rejecting the existence of numbers, if from the theory’s content the presupposition that there are numbers can be subtracted away, yielding thus a number-free content remainder. Perfect extricability, i.e. extricability in every possible (...)
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  • The physics and metaphysics of identity and individuality: Steven French and Décio Krause: Identity in physics: A historical, philosophical, and formal analysis. Oxford: Clarendon Press, 2006, 440 pp, £68.00 HB.Don Howard, Bas C. van Fraassen, Otávio Bueno, Elena Castellani, Laura Crosilla, Steven French & Décio Krause - 2010 - Metascience 20 (2):225-251.
    The physics and metaphysics of identity and individuality Content Type Journal Article DOI 10.1007/s11016-010-9463-7 Authors Don Howard, Department of Philosophy and Graduate Program in History and Philosophy of Science, University of Notre Dame, Notre Dame, IN 46556, USA Bas C. van Fraassen, Philosophy Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA Otávio Bueno, Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA Elena Castellani, Department of Philosophy, University of Florence, Via Bolognese 52, 50139 (...)
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  • Intergenerational Rights and the Problem of Cross-Temporal Relations.Aaron M. Griffith - 2018 - Erkenntnis 83 (4):693-710.
    This paper considers the prospects for a theory of intergenerational rights in light of certain ontologies of time. It is argued that the attempt to attribute rights to future persons or obligations to present persons towards future persons, faces serious difficulties if the existence of the future is denied. The difficulty of attributing rights to non-existent future persons is diagnosed as a particularly intractable version of the ‘problem of cross-temporal relations’ that plagues No-Futurist views like presentism. I develop a version (...)
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  • On the definition of observation as justified true perception.Alessio Gava - 2015 - Scientiae Studia 13 (1):123-141.
    The primacy of the act of observation, one of the hallmarks of empiricism, found new life in the centrality of the distinction, made in Bas van Fraassen's constructive empiricism, between observable and unobservable. As Elliott Sober have pointed out, however, it is not clear what van Fraassen understands by observing an object. Worse, the Dutch philosopher does not seem to consider that a clarification of this point is necessary. This, of course, represents an important lacuna in a position generally considered (...)
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  • Fictionalism and Meinongianism.Nathaniel Gan - 2021 - Theoria : An International Journal for Theory, History and Fundations of Science 36 (1):49-62.
    Fictionalism about a kind of disputed object is often motivated by the fact that the view interprets discourse about those objects literally without an ontological commitment to them. This paper argues that this motivation is inadequate because some viable alternatives to fictionalism have similar attractions. Meinongianism—the view that there are true statements about non-existent objects—is one such view. Meinongianism bears significant similarity to fictionalism, so intuitive doubts about its viability are difficult to sustain for fictionalists. Moreover, Meinongianism avoids some of (...)
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  • Fictional characters.Stacie Friend - 2007 - Philosophy Compass 2 (2):141–156.
    If there are no fictional characters, how do we explain thought and discourse apparently about them? If there are, what are they like? A growing number of philosophers claim that fictional characters are abstract objects akin to novels or plots. They argue that postulating characters provides the most straightforward explanation of our literary practices as well as a uniform account of discourse and thought about fiction. Anti-realists counter that postulation is neither necessary nor straightforward, and that the invocation of pretense (...)
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