About this topic
Summary One of the lines of reasoning in support of mathematical platonism employs the fact that mathematical theories find applications in sciences which, at least prima facie, concern themselves with the physical world. From the indispensability of mathematics in science the argument moves to the indispensability of reference to mathematical objects in science. Further on, since we, supposedly, have good reasons to accept the existence of objects our best scientific theories have to refer to, we should accept the existence of such mathematical objects, on a par with the existence of electrons and other invisible entities postulated by such scientific theories. Accordingly, the argument has been attacked on different grounds. Some deny the indispensability of mathematics in science, some claim that indispensability of mathematical theories is not the same as the indispensability of reference to mathematical objects, some insist that this approach doesn't make justice to the difference between a priori mathematical knowledge and a posteriori scientific knowledge, some worry that applied mathematics is only a part of theoretical mathematics and some suggest that best scientific theories don't have to be our guide to metaphysics.
Key works Loci classici are Quine 1961Quine 1981Putnam 1975 and Putnam 1971. Further considerations can be found for instance in Parsons 1979Chihara 1973 and   Maddy 1992. Field 1980 is directed at showing the dispensability of mathematics in science. An extensive defence of the indispensability argument have been mounted by Colyvan 2001.
Introductions Start with Colyvan 2008 (and references therein).
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221 found
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  1. added 2019-02-01
    An Introduction to the Philosophy of Mathematics, by Colyvan Mark: Cambridge: Cambridge University Press, 2012, Pp. X+ 188, AU $46.95 (Paperback). [REVIEW]Zach Weber - 2013 - Australasian Journal of Philosophy 91 (4):828-828.
  2. added 2019-02-01
    Quine's Weak and Strong Indispensability Argument.Lieven Decock - 2002 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 33 (2):231-250.
    Quine's views on indispensability arguments in mathematics are scrutinised. A weak indispensability argument is distinguished from a strong indispensability thesis. The weak argument is the combination of the criterion of ontological commitment, holism and a mild naturalism. It is used to refute nominalism. Quine's strong indispensability thesis claims that one should consider all and only the mathematical entities that are really indispensable. Quine has little support for this thesis. This is even clearer if one takes into account Maddy's critique of (...)
  3. added 2019-01-10
    Quine and the Incoherence of the Indispensability Argument.Michael Shaffer - forthcoming - Logos and Episteme.
    It is an under-appreciated fact that Quine's rejection of the analytic/synthetic distinction, when coupled with some other plausible and related views, implies that there are serious difficulties in demarcating empirical theories from pure mathematical theories within the Quinean framework. This is a serious problem because there seems to be a principled difference between the two disciplines that cannot apparently be captured in the orthodox Quienan framework. For the purpose of simplicity let us call this Quine's problem of demarcation. In this (...)
  4. added 2018-10-25
    Infinitesimal Idealization, Easy Road Nominalism, and Fractional Quantum Statistics.Elay Shech - forthcoming - Synthese 1.
    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 (...)
  5. added 2018-10-09
    Response to Colyvan.Joseph Melia - 2002 - Mind 111 (441):75-80.
  6. added 2018-09-06
    Confirmational Holism and its Mathematical Holes.Anthony Peressini - 2008 - Studies in History and Philosophy of Science Part A 39 (1):102-111.
    I critically examine confirmational holism as it pertains to the indispensability arguments for mathematical Platonism. I employ a distinction between pure and applied mathematics that grows out of the often overlooked symbiotic relationship between mathematics and science. I argue that this distinction undercuts the notion that mathematical theories fall under the holistic scope of the confirmation of our scientific theories.Keywords: Confirmational holism; Indispensability argument; Mathematics; Application; Science.
  7. added 2018-08-06
    Clarificando o Suporte do Argumento Melhorado da Indispensabilidade Matemática.Eduardo Castro - 2017 - Argumentos 17 (9):57-71.
    The enhanced mathematical indispensability argument, proposed by Alan Baker (2005), argues that we must commit to mathematical entities, because mathematical entities play an indispensable explanatory role in our best scientific theories. This article clarifies the doctrines that support this argument, namely, the doctrines of naturalism and confirmational holism.
  8. added 2018-02-17
    Platonism, Naturalism, and Mathematical Knowledge.James Robert Brown - 2011 - Routledge.
    This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does (...)
  9. added 2018-02-16
    Are There Genuine Physical Explanations of Mathematical Phenomena?Brdford 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 (...)
  10. added 2017-11-28
    What We Talk About When We Talk About Numbers.Richard Pettigrew - manuscript
    In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism.
  11. added 2017-11-20
    Autonomy Platonism and the Indispensability Argument. By Russell Marcus. Lanham, Md.: Lexington Books, 2015. Pp. Xii + 247. [REVIEW]Nicholas Danne - 2017 - Metaphilosophy 48 (4):591-594.
  12. added 2017-10-05
    Rejecting Mathematical Realism While Accepting Interactive Realism.Seungbae Park - 2018 - Analysis and Metaphysics 17:7-21.
    Indispensablists contend that accepting scientific realism while rejecting mathematical realism involves a double standard. I refute this contention by developing an enhanced version of scientific realism, which I call interactive realism. It holds that interactively successful theories are typically approximately true, and that the interactive unobservable entities posited by them are likely to exist. It is immune to the pessimistic induction while mathematical realism is susceptible to it.
  13. added 2017-06-17
    Optimal Representations and the Enhanced Indispensability Argument.Manuel Barrantes - 2017 - Synthese:1-17.
    The Enhanced Indispensability Argument (EIA) appeals to the existence of Mathematical Explanations of Physical Phenomena (MEPPs) to justify mathematical Platonism, following the principle of Inference to the Best Explanation. In this paper, I examine one example of a MEPP —the explanation of the 13-year and 17-year life cycle of magicicadas— and argue that this case cannot be used to justify mathematical Platonism. I then generalize my analysis of the cicada case to other MEPPs, and show that these explanations rely on (...)
  14. added 2017-03-11
    In Defense of Mathematical Inferentialism.Seungbae Park - 2017 - Analysis and Metaphysics 16:70-83.
    I defend a new position in philosophy of mathematics that I call mathematical inferentialism. It holds that a mathematical sentence can perform the function of facilitating deductive inferences from some concrete sentences to other concrete sentences, that a mathematical sentence is true if and only if all of its concrete consequences are true, that the abstract world does not exist, and that we acquire mathematical knowledge by confirming concrete sentences. Mathematical inferentialism has several advantages over mathematical realism and fictionalism.
  15. added 2017-02-14
    Liu Hui's Theories of Mathematics.R. Mei - 1996 - Boston Studies in the Philosophy of Science 179:243-254.
  16. added 2017-02-13
    Practice, Constraint, and Mathematical Concepts.Mark C. R. Smith - 2012 - Philosophia Scientiae 16 (1):15-28.
    Dans cet article je propose d'exprimer et de défendre une conception des pratiques et du domaine de discours mathématiques qui soit sensible, d'une part, au pluralisme des relations entre pratiques inférentielles et intérêts, et d'autre part, à la structure objective et déterminante des concepts mathématiques. J'ébauche tout d'abord une caractérisation générale des pratiques, pour ensuite préciser certains phénomènes propres aux pratiques mathématiques. Suit un recensement des idées qui se dégagent des arguments pluralistes, et de celles qui sont à retenir. Mais (...)
  17. added 2017-02-13
    The Pure and the Applied: Bourbakism Comes to Mathematical Economics.E. Roy Weintraub & Philip Mirowski - 1994 - Science in Context 7 (2).
  18. added 2017-02-13
    Perennial Philosophy: Evidence From the Mathematical and Physical Sciences.Alan M. Laibelman - 1992 - Ultimate Reality and Meaning 15:216.
  19. added 2017-02-11
    Mathematics Without Truth (a Reply to Maddy).H. Field - 1990 - Pacific Philosophical Quarterly 71 (3):206-222.
    This paper elaborates on the fictionalist conception of mathematics, and on how it accommodates the obvious fact that mathematical claims are important in application to the physical world. It also replies to Maddy's argument that fictionalism does not have the epistemological advantage over Platonism that it appears to have; the reply involves a discussion of whether mathematics should be regarded as conservative over second order physical theories as well as first order ones.
  20. added 2017-02-10
    Naturalising Mathematics: A Critical Look at the Quine-Maddy Debate.Marianna Antonutti Marfori - 2012 - Disputatio 4 (32):323-342.
    This paper considers Maddy’s strategy for naturalising mathematics in the context of Quine’s scientific naturalism. The aim of this proposal is to account for the acceptability of mathematics on scientific grounds without committing to revisionism about mathematical practice entailed by the Quine-Putnam indispensability argument. It has been argued that Maddy’s mathematical naturalism makes inconsistent assumptions on the role of mathematics in scientific explanations to the effect that it cannot distinguish mathematics from pseudo-science. I shall clarify Maddy’s arguments and show that (...)
  21. added 2017-02-02
    Practical Reason and Mathematical Argument.J. O'Neill - 1998 - Studies in History and Philosophy of Science Part A 29 (2):195-205.
  22. added 2017-02-01
    Margaret Morrison, Critical Discussion of Unifying Scientific Theories. Physical Concepts and Mathematical Structures.F. A. Muller - 2001 - Erkenntnis 55 (1):132-143.
  23. added 2017-01-29
    Parsimony and Inference to the Best Mathematical Explanation.Alan Baker - 2016 - Synthese 193 (2).
    Indispensability-based arguments for mathematical platonism are typically motivated by drawing an analogy between abstract mathematical objects and concrete scientific posits. In this paper, I argue that mathematics can sometimes help to reduce our concrete ontological, ideological, and structural commitments. My focus is on optimization explanations, and in particular the case study involving periodical cicadas. I argue that in this case, stronger mathematical apparatus yields explanations that have fewer concrete commitments. The nominalist cannot accept these more parsimonious explanations without embracing the (...)
  24. added 2017-01-27
    Revealing the Face of Isis.J. L. Usó-Doménech & J. Nescolarde-Selva - 2014 - Foundations of Science 19 (3):311-318.
    This reply to Gash’s (Found Sci 2014) commentary on Nescolarde-Selva and Usó-Doménech (Found Sci 2014b) answers the questions raised and at the same time opens up new questions.
  25. added 2017-01-27
    Is Indispensability Still a Problem for Fictionalism?Susan Vineberg - 2008 - ProtoSociology 25:128-142.
    For quite some time the indispensability arguments of Quine and Putnam were considered a formidable obstacle to anyone who would reject the existence of mathematical objects.1 Various attempts to respond to the indispensability arguments were developed, most notably by Chihara and Field.2 Field tried to defend mathematical fictionalism, according to which the existential assertions of mathematics are false, by showing that the mathematics used in applications is in fact dispensable. Chihara suggested, on the other hand, that mathematics makes true existential (...)
  26. added 2017-01-27
    Mathematics in Science: The Role of the History of Science in Communicating the Significance of Mathematical Formalism in Science.Kevin C. de Berg - 1992 - Science & Education 1 (1):77-87.
  27. added 2017-01-27
    The Mathematical Science of Christopher Wren. [REVIEW]John Hendry - 1983 - British Journal for the History of Science 16 (3):291-292.
  28. added 2017-01-26
    Reviewed Work(S): An Introduction to the Philosophy of Mathematics by Mark Colyvan.Review by: Richard Pettigrew - 2013 - Bulletin of Symbolic Logic 19 (3):396-397,.
  29. added 2017-01-26
    On Tins and Tin-Openers.Michael Liston - 2009 - In Henk W. de Regt (ed.), Epsa Philosophy of Science: Amsterdam 2009. Springer. pp. 151--160.
    Most science requires applied mathematics. This truism underlies the Quine-Putnam indispensability argument: we cannot be mathematical nominalists without rejecting whole swaths of good science that are seamlessly linked with mathematics. One style of response accepts the challenge head-on and attempts to show how to do science without mathematics. There is some consensus that the response fails because the nominalistic apparatus deployed either is not extendible to all of mathematical physics or is merely a deft reconstrual equivalent to standard mathematics. A (...)
  30. added 2017-01-26
    Reply to Colyvan.Joseph Melia - 2002 - Mind 111:75-9.
  31. added 2017-01-26
    The Mystery of the Commons: On the Indispensability of Civic Rhetoric.Manfred Stanley - 1983 - Social Research 50.
  32. added 2017-01-25
    Quine's Master Argument.John F. Fox - 2010 - Logique Et Analyse 53 (212):429-447.
  33. added 2017-01-24
    The Applicability of Mathematics in Science: Indispensability and Ontology.Penelope Rush - 2013 - International Studies in the Philosophy of Science 27 (2):219-222.
  34. added 2017-01-23
    Remarks on Mark Colyvan on Mathematical Explanation.Fabrice Pataut - unknown
  35. added 2017-01-22
    Rething Mathematical Necessity.Hilary Putnam - 1992 - In ¸ Iteputnam:Wl. pp. 245--63.
  36. added 2017-01-22
    Symposium: The Relation Between the Mathematical and the Physical.Léon Brunschvicg - 1923 - Aristotelian Society Supplementary Volume 3 (1):42 - 55.
  37. added 2017-01-21
    Naturalism and Abstract Entities.Feng Ye - 2010 - International Studies in the Philosophy of Science 24 (2):129-146.
    I argue that the most popular versions of naturalism imply nominalism in philosophy of mathematics. In particular, there is a conflict in Quine's philosophy between naturalism and realism in mathematics. The argument starts from a consequence of naturalism on the nature of human cognitive subjects, physicalism about cognitive subjects, and concludes that this implies a version of nominalism, which I will carefully characterize. The indispensability of classical mathematics for the sciences and semantic/confirmation holism does not affect the argument. The disquotational (...)
  38. added 2017-01-21
    Unifying Scientific Theories: Physical Concepts and Mathematical Structures.Talel A. Debs - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (1):151-153.
  39. added 2017-01-21
    Critical Notice of Margaret Morrison Unifying Scientific Theories: Physical Concepts and Mathematical Structures.Andrew Wayne - 2002 - Canadian Journal of Philosophy 32 (1):117-137.
  40. added 2017-01-19
    Confirmational Holism and its Mathematical (W)Holes.Anthony F. Peressini - 2008 - Studies in History and Philosophy of Science Part A 39 (1):102-111.
    I critically examine confirmational holism as it pertains to the indispensability arguments for mathematical Platonism. I employ a distinction between pure and applied mathematics that grows out of the often overlooked symbiotic relationship between mathematics and science. I argue that this distinction undercuts the notion that mathematical theories fall under the holistic scope of the confirmation of our scientific theories.Keywords: Confirmational holism; Indispensability argument; Mathematics; Application; Science.
  41. added 2017-01-19
    Living in Harmony: Nominalism and the Explanationist Argument for Realism.Juha T. Saatsi - 2007 - International Studies in the Philosophy of Science 21 (1):19 – 33.
    According to the indispensability argument, scientific realists ought to believe in the existence of mathematical entities, due to their indispensable role in theorising. Arguably the crucial sense of indispensability can be understood in terms of the contribution that mathematics sometimes makes to the super-empirical virtues of a theory. Moreover, the way in which the scientific realist values such virtues, in general, and draws on explanatory virtues, in particular, ought to make the realist ontologically committed to abstracta. This paper shows that (...)
  42. added 2017-01-19
    Kognitive Mobilität. Eine Makroskopische Untersuchung der Wanderung Von Wissenschaftlern Zwischen Forschungsgebieten Am Beispiel der Mathematik.Roland Wagner-Döbler - 1998 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 29 (2):265-287.
    Cognitive Mobility, a Macroscopic Investigation of Migration of Scientists between Research Fields Studied by Example of Mathematics. — In history of science, scientific migrations of famous scientists are well-known. Nothing is known, however, about the total of migrations between fields of science, despite the importance of scientific mobility for information transfer and exchange. In the present investigation all migrations between the major 39 subdisciplines of mathematics from 1959 through 1975 are studied in a macroscopic manner. The quantitative importance of migration (...)
  43. added 2017-01-19
    Explanation, Independence and Realism in Mathematics.Michael D. Resnik & David Kushner - 1987 - British Journal for the Philosophy of Science 38 (2):141-158.
  44. added 2017-01-18
    On Representing the Relationship Between the Mathematical and the Empirical.Otávio Bueno, Steven French & James Ladyman - 2002 - Philosophy of Science 69 (3):497-518.
    We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London's analysis of the superfluid behavior of liquid helium in terms of Bose‐Einstein (...)
  45. added 2017-01-18
    Weaseling Away the Indispensability Argument.J. Melia - 2000 - Mind 109 (435):455-480.
    According to the indispensability argument, the fact that we quantify over numbers, sets and functions in our best scientific theories gives us reason for believing that such objects exist. I examine a strategy to dispense with such quantification by simply replacing any given platonistic theory by the set of sentences in the nominalist vocabulary it logically entails. I argue that, as a strategy, this response fails: for there is no guarantee that the nominalist world that go beyond the set of (...)
  46. added 2017-01-18
    Science Nominalized.Terence Horgan - 1984 - Philosophy of Science 51 (4):529-549.
    I propose a way of formulating scientific laws and magnitude attributions which eliminates ontological commitment to mathematical entities. I argue that science only requires quantitative sentences as thus formulated, and hence that we ought to deny the existence of sets and numbers. I argue that my approach cannot plausibly be extended to the concrete "theoretical" entities of science.
  47. added 2017-01-17
    Mathematics and Explanatory Generality.Alan Baker - 2017 - Philosophia Mathematica 25 (2):194-209.
    According to one popular nominalist picture, even when mathematics features indispensably in scientific explanations, this mathematics plays only a purely representational role: physical facts are represented, and these exclusively carry the explanatory load. I think that this view is mistaken, and that there are cases where mathematics itself plays an explanatory role. I distinguish two kinds of explanatory generality: scope generality and topic generality. Using the well-known periodical-cicada example, and also a new case study involving bicycle gears, I argue that (...)
  48. added 2017-01-17
    The Indispensability Argument for Induction.Lukáš Bielik - 2015 - Balkan Journal of Philosophy 7 (1):45-54.
    Developing the ideas presented in Jacquette, the paper presents an indispensability argument aimed at justification of induction. First, Hume’s problem of induction is introduced via slightly different reconstructions. Second, several traditional attempts to solve Hume’s problem are presented. Finally, Jacquette’s proposal to justify induction by an indispensability argument is developed. I conclude with presenting a kind of indispensability argument for induction.
  49. added 2017-01-17
    Altruism and the Indispensability of Motives.Mark S. Peacock, Michael Schefczyk & Peter Schaber - 2005 - Analyse & Kritik 27 (1):188-196.
  50. added 2017-01-16
    The Philosophy of Mathematics: A Study of Indispensability and Inconsistency.Hannah C. Thornhill - unknown
    This thesis examines possible philosophies to account for the practice of mathematics, exploring the metaphysical, ontological, and epistemological outcomes of each possible theory. Through a study of the two most probable ideas, mathematical platonism and fictionalism, I focus on the compelling argument for platonism given by an appeal to the sciences. The Indispensability Argument establishes the power of explanation seen in the relationship between mathematics and empirical science. Cases of this explanatory power illustrate how we might have reason to believe (...)
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