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Road Work Ahead: Heavy Machinery on the Easy Road

Mind 121 (484):1031-1046 (2012)

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  1. Indispensability and Explanation: An Overview and Introduction.Daniele Molinini, Fabrice Pataut & Andrea Sereni - 2016 - Synthese 193 (2):317-332.
  • Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
    Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...)
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  • Hartry Field. Science Without Numbers: A Defense of Nominalism 2nd Ed. [REVIEW]Geoffrey Hellman & Mary Leng - 2019 - Philosophia Mathematica 27 (1):139-148.
    FieldHartry. Science Without Numbers: A Defense of Nominalism 2nd ed.Oxford University Press, 2016. ISBN 978-0-19-877792-2. Pp. vi + 56 + vi + 111.
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  • Explanation and Explanationism in Science and Metaphysics.Juha Saatsi - forthcoming - In Matthew Slater & Zanja Yudell (eds.), Metaphysics and the Philosophy of Science: New Essays. Oxford University Press.
    This chapter examines the status of inference to the best explanation in naturalistic metaphysics. The methodology of inference to the best explanation in metaphysics is studied from the perspective of contemporary views on scientific explanation and explanatory inferences in the history and philosophy of science. This reveals serious shortcomings in prevalent attempts to vindicate metaphysical "explanationism" by reference to similarities between science and naturalistic metaphysics. This critique is brought out by considering a common gambit of methodological unity: (1) Both metaphysics (...)
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  • Should Scientific Realists Be Platonists?Jacob Busch & Joe Morrison - 2016 - Synthese 193 (2):435-449.
    Enhanced indispensability arguments claim that Scientific Realists are committed to the existence of mathematical entities due to their reliance on Inference to the best explanation. Our central question concerns this purported parity of reasoning: do people who defend the EIA make an appropriate use of the resources of Scientific Realism to achieve platonism? We argue that just because a variety of different inferential strategies can be employed by Scientific Realists does not mean that ontological conclusions concerning which things we should (...)
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  • True Nominalism: Referring Versus Coding.Jody Azzouni & Otávio Bueno - 2016 - British Journal for the Philosophy of Science 67 (3):781-816.
    One major motivation for nominalism, at least according to Hartry Field, is the desirability of intrinsic explanations: explanations that don’t invoke objects that are causally irrelevant to the phenomena being explained. There is something right about the search for such explanations. But that search must be carefully implemented. Nothing is gained if, to avoid a certain class of objects, one only introduces other objects and relations that are just as nominalistically questionable. We will argue that this is the case for (...)
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  • Realism and the Limits of Explanatory Reasoning.Juha Saatsi - 2018 - In The Routledge Handbook of Scientific Realism. London: Routledge. pp. 200-211.
    This chapter examines issues surrounding inference to the best explanation, its justification, and its role in different arguments for scientific realism, as well as more general issues concerning explanations’ ontological commitments. Defending the reliability of inference to the best explanation has been a central plank in various realist arguments, and realists have drawn various ontological conclusions from the premise that a given scientific explanation best explains some phenomenon. This chapter stresses the importance of thinking carefully about the nature of explanation (...)
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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 ‘Indispensable Explanatory Role’ of Mathematics.Juha Saatsi - 2016 - Mind 125 (500):1045-1070.
    The literature on the indispensability argument for mathematical realism often refers to the ‘indispensable explanatory role’ of mathematics. I argue that we should examine the notion of explanatory indispensability from the point of view of specific conceptions of scientific explanation. The reason is that explanatory indispensability in and of itself turns out to be insufficient for justifying the ontological conclusions at stake. To show this I introduce a distinction between different kinds of explanatory roles—some ‘thick’ and ontologically committing, others ‘thin’ (...)
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  • The Limits of Subtraction.Mark Colyvan - 2017 - Australasian Philosophical Review 1 (2):168-172.
    ABSTRACTIn the target article ‘If-Thenism’, Stephen Yablo develops a novel form of if-thenism, that appeals to the notion of logical subtraction. In this commentary, I explore the limits of Yablo's proposed subtraction procedure, by leaning on an analogy with photographic subtraction. In particular, I will argue that there will be cases when there's nothing interesting left after the subtraction and, as a consequence, there are serious limits to the applicability of the subtraction procedure.
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  • The Eleatic and the Indispensabilist.Russell Marcus - 2015 - Theoria : An International Journal for Theory, History and Fundations of Science 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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  • 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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  • 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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  • Non-Naturalistic Moral Explanation.Samuel Baron, Mark Colyvan, Kristie Miller & Michael Rubin - forthcoming - Synthese.
    This paper focuses on a particular kind of non-naturalism: moral non-naturalism. Our primary aim is to argue that the moral non-naturalist places herself in an invidious position if she simply accepts that the non-natural moral facts that she posits are not explanatory. This has, hitherto, been the route that moral non-naturalists have taken. They have attempted to make their position more palatable by pointing out that there is reason to be suspicious of the explanatory criterion of ontological commitment. That is (...)
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  • The Explanatory Dispensability of Idealizations.Sam Baron - 2016 - Synthese 193 (2):365-386.
    Enhanced indispensability arguments seek to establish realism about mathematics based on the explanatory role that mathematics plays in science. Idealizations pose a problem for such arguments. Idealizations, in a similar way to mathematics, boost the explanatory credentials of our best scientific theories. And yet, idealizations are not the sorts of things that are supposed to attract a realist attitude. I argue that the explanatory symmetry between idealizations and mathematics can potentially be broken as follows: although idealizations contribute to the explanatory (...)
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  • Which Explanatory Role for Mathematics in Scientific Models? Reply to “The Explanatory Dispensability of Idealizations”.Silvia De Bianchi - 2016 - Synthese 193 (2):387-401.
    In The Explanatory Dispensability of Idealizations, Sam Baron suggests a possible strategy enabling the indispensability argument to break the symmetry between mathematical claims and idealization assumptions in scientific models. Baron’s distinction between mathematical and non-mathematical idealization, I claim, is in need of a more compelling criterion, because in scientific models idealization assumptions are expressed through mathematical claims. In this paper I argue that this mutual dependence of idealization and mathematics cannot be read in terms of symmetry and that Baron’s non-causal (...)
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  • Grounding and the Indispensability Argument.David Liggins - 2016 - Synthese 193 (2):531-548.
    There has been much discussion of the indispensability argument for the existence of mathematical objects. In this paper I reconsider the debate by using the notion of grounding, or non-causal dependence. First of all, I investigate what proponents of the indispensability argument should say about the grounding of relations between physical objects and mathematical ones. This reveals some resources which nominalists are entitled to use. Making use of these resources, I present a neglected but promising response to the indispensability argument—a (...)
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  • Why Inference to the Best Explanation Doesn’T Secure Empirical Grounds for Mathematical Platonism.Kenneth Boyce - 2018 - Synthese:1-13.
    Proponents of the explanatory indispensability argument for mathematical platonism maintain that claims about mathematical entities play an essential explanatory role in some of our best scientific explanations. They infer that the existence of mathematical entities is supported by way of inference to the best explanation from empirical phenomena and therefore that there are the same sort of empirical grounds for believing in mathematical entities as there are for believing in concrete unobservables such as quarks. I object that this inference depends (...)
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  • Indispensability Arguments in the Philosophy of Mathematics.Mark Colyvan - 2008 - Stanford Encyclopedia of Philosophy.
    One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It's not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these theories is also varied. (...)
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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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