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  1. added 2020-04-02
    Is Mathematics Unreasonably Effective?Daniel Waxman - forthcoming - Australasian Journal of Philosophy:1-17.
    Many mathematicians, physicists, and philosophers have suggested that the fact that mathematics—an a priori discipline informed substantially by aesthetic considerations—can be applied to natural s...
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  2. added 2020-02-04
    A Dilemma for Mathematical Constructivism.Samuel Kahn - 2020 - Axiomathes:01-10.
    In this paper I argue that constructivism in mathematics faces a dilemma. In particular, I maintain that constructivism is unable to explain (i) the application of mathematics to nature and (ii) the intersubjectivity of mathematics unless (iii) it is conjoined with two theses that reduce it to a form of mathematical Platonism. The paper is divided into five sections. In the first section of the paper, I explain the difference between mathematical constructivism and mathematical Platonism and I outline my argument. (...)
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  3. added 2019-12-24
    Creating a New Mathematics.Arran Gare - 2016 - In Ronny Desmet (ed.), Intuition in Mathematics and Physics. Anoka, MN, USA: pp. 146-164.
    The focus of this chapter is on efforts to create a new mathematics, with my prime interest being the role of mathematics in comprehending a world consisting first and foremost of processes, and examining what developments in mathematics are required for this. I am particularly interested in developments in mathematics able to do justice to the reality of life. Such mathematics could provide the basis for advancing ecology, human ecology and ecological economics and thereby assist in the transformation of society (...)
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  4. added 2019-12-22
    Revisão de ' Os Limites Exteriores da Razão ' (The Outer Limits of Reason)Por Noson Yanofsky 403p (2013) (Revisão Revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 188-202.
    Eu dou uma revisão detalhada de "os limites exteriores da razão" por Noson Yanofsky de uma perspectiva unificada de Wittgenstein e psicologia evolutiva. Eu indico que a dificuldade com tais questões como paradoxo na linguagem e matemática, incompletude, undecidabilidade, computabilidade, o cérebro eo universo como computadores, etc., todos surgem a partir da falta de olhar atentamente para o nosso uso da linguagem no apropriado contexto e, consequentemente, a falta de separar questões de fato científico a partir de questões de como (...)
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  5. added 2019-12-19
    Aplicabilitatea matematicii ca problema filosofica.Gabriel Târziu - 2013 - Iași, Romania: Institutul European Publishing House.
    In aceasta lucrare, autorul si-a propus sa readuca in discutie problema aplicabilitatii matematicii - atat de importanta pentru Kant, dar care a ajuns sa fie in mare parte neglijata in filosofia contemporana a matematicii - incercand sa argumenteze, plecand de la ea, pentru o viziune empirista in filosofia matematicii. Strategia pe care autorul isi propune sa o urmeze, in linii mari, consta intr-o incercare de a atrage atentia asupra unei probleme care apare atunci cand avem in vedere utilitatea matematicii in (...)
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  6. added 2019-09-24
    Formal Semantics and Applied Mathematics: An Inferential Account.Ryan M. Nefdt - 2020 - Journal of Logic, Language and Information 29 (2):221-253.
    In this paper, I utilise the growing literature on scientific modelling to investigate the nature of formal semantics from the perspective of the philosophy of science. Specifically, I incorporate the inferential framework proposed by Bueno and Colyvan : 345–374, 2011) in the philosophy of applied mathematics to offer an account of how formal semantics explains and models its data. This view produces a picture of formal semantic models as involving an embedded process of inference and representation applying indirectly to linguistic (...)
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  7. added 2019-09-13
    Early Modern Mathematical Principles and Symmetry Arguments.James Franklin - 2017 - In The Idea of Principles in Early Modern Thought Interdisciplinary Perspectives. New York, USA: Routledge. pp. 16-44.
    The leaders of the Scientific Revolution were not Baconian in temperament, in trying to build up theories from data. Their project was that same as in Aristotle's Posterior Analytics: they hoped to find necessary principles that would show why the observations must be as they are. Their use of mathematics to do so expanded the Aristotelian project beyond the qualitative methods used by Aristotle and the scholastics. In many cases they succeeded.
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  8. added 2019-08-31
    Infinity and the Foundations of Linguistics.Ryan 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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  9. added 2019-07-22
    Applicability Problems Generalized.Michele Ginammi - 2018 - In Gabriele Pulcini & Mario Piazza (eds.), Truth, Existence and Explanation. Springer Verlag. pp. 209-224.
    In this paper, I will do preparatory work for a generalized account of applicability, that is, for an account which works for math-to-physics, math-to-math, and physics-to-math application. I am going to present and discuss some examples of these three kinds of application, and I will confront them in order to see whether it is possible to find analogies among them and whether they can be ultimately considered as instantiations of a unique pattern. I will argue that these analogies can be (...)
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  10. added 2019-07-22
    The Applicability of Mathematics and the Indispensability Arguments.Michele Ginammi - 2016 - Lato Sensu, Revue de la Société de Philosophie des Sciences 3 (1).
    In this paper I will take into examination the relevance of the main indispensability arguments for the comprehension of the applicability of mathematics. I will conclude not only that none of these indispensability arguments are of any help for understanding mathematical applicability, but also that these arguments rather require a preliminary analysis of the problems raised by the applicability of mathematics in order to avoid some tricky difficulties in their formulations. As a consequence, we cannot any longer consider the applicability (...)
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  11. added 2019-07-22
    The Unreasonable Effectiveness. The Philosophical Problem of the Applicability of Mathematics.Michele Ginammi - 2011 - Rivista Italiana di Filosofia Analitica Junior 2 (2):26-40.
    In this article I will sketch a general introduction to the problem of the applicability of mathematics as it is conceived in contemporary philosophy of mathematics. After some brief considerations concerning the historical reason why this problem was dismissed by the philosophical analysis during the first half of 20th century, I will expound Wigner’s puzzle, and I will make some theoretical considerations about it. In particular, I will show that the problem of applicability is independent from the ontological framework we (...)
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  12. added 2019-06-06
    Daniel J. Cohen, Equations From God: Pure Mathematics and Victorian Faith. Baltimore: Johns Hopkins University Press, 2007. Pp. X+242. ISBN 978-0-8018-8553-2. £33.50. [REVIEW]Judith Grabiner - 2008 - British Journal for the History of Science 41 (2):298-300.
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  13. added 2019-06-06
    Steiner on the Applicability of Mathematics and Naturalism.Sorin Bangu - 2006 - Philosophia Mathematica 14 (1):26-43.
    Steiner defines naturalism in opposition to anthropocentrism, the doctrine that the human mind holds a privileged place in the universe. He assumes the anthropocentric nature of mathematics and argues that physicists' employment of mathematically guided strategies in the discovery of quantum mechanics challenges scientists' naturalism. In this paper I show that Steiner's assumption about the anthropocentric character of mathematics is questionable. I draw attention to mathematicians' rejection of what Maddy calls ‘definabilism’, a methodological maxim governing the development of mathematics. I (...)
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  14. added 2019-06-06
    Discussion. Applied Constructive Mathematics: On Hellman's 'Mathematical Constructivism in Spacetime'.H. Billinge - 2000 - British Journal for the Philosophy of Science 51 (2):299-318.
    claims that constructive mathematics is inadequate for spacetime physics and hence that constructive mathematics cannot be considered as an alternative to classical mathematics. He also argues that the contructivist must be guilty of a form of a priorism unless she adopts a strong form of anti-realism for science. Here I want to dispute both claims. First, even if there are non-constructive results in physics this does not show that adequate constructive alternatives could not be formulated. Secondly, the constructivist adopts a (...)
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  15. added 2019-06-06
    Review of Discipline and Experience: The Mathematical Way in the Scientific Revolution by Peter Dear. [REVIEW]Lorraine Daston - 1997 - Philosophy of Science 64 (3):519-521.
  16. added 2019-06-06
    The Role of Mathematics in Modern Physical Theory: Some Philosophical Aspects of Contemporary Science.Alexander William Stern - 1929 - The Monist 39 (2):263-272.
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  17. added 2019-04-28
    Mathematical Engineering and Mathematical Change.Jean‐Pierre Marquis - 1999 - International Studies in the Philosophy of Science 13 (3):245 – 259.
    In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathematics has important consequences on our conception (...)
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  18. added 2019-04-26
    Reconstruction in Philosophy of Mathematics.Davide Rizza - 2018 - Dewey Studies 2 (2):31-53.
    Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...)
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  19. added 2019-04-26
    Divergent Mathematical Treatments in Utility Theory.Davide Rizza - 2016 - Erkenntnis 81 (6):1287-1303.
    In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection (...)
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  20. added 2019-04-26
    Nonstandard Utilities for Lexicographically Decomposable Orderings.Davide Rizza - 2015 - Journal of Mathematical Economics 1 (60):105-109.
    Using a basic theorem from mathematical logic, I show that there are field-extensions ofRon which a class of orderings that do not admit any real-valued utility functions can be represented by uncountably large families of utility functions. These are the lexicographically decomposable orderings studied in Beardon et al. (2002a). A corollary to this result yields an uncountably large family of very simple utility functions for the lexicographic ordering of the real Cartesian plane. I generalise these results to the lexicographic ordering (...)
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  21. added 2019-04-26
    Resolving Paradoxes In Judgment Aggregation.Davide Rizza - 2012 - Philosophical Quarterly 62 (247):337-354.
    When a law court makes a decision based on the individual deliberation of each judge, a case of judgment aggregation occurs. The possibility that the aggregation's outcome be logically inconsistent, even though it is based on consistent individual judgments, arises relatively easily and has been the subject of several investigations. In this paper I show that this paradoxical behaviour is the effect of decision procedures that are unable to discriminate between logically consistent and logically inconsistent individual judgments. The paradoxes can (...)
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  22. added 2019-04-26
    Magicicada, Mathematical Explanation and Mathematical Realism.Davide Rizza - 2011 - Erkenntnis 74 (1):101-114.
    Baker claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects and thus (...)
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  23. added 2019-04-26
    Mathematical Nominalism and Measurement.Davide Rizza - 2010 - Philosophia Mathematica 18 (1):53-73.
    In this paper I defend mathematical nominalism by arguing that any reasonable account of scientific theories and scientific practice must make explicit the empirical non-mathematical grounds on which the application of mathematics is based. Once this is done, references to mathematical entities may be eliminated or explained away in terms of underlying empirical conditions. I provide evidence for this conclusion by presenting a detailed study of the applicability of mathematics to measurement. This study shows that mathematical nominalism may be regarded (...)
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  24. added 2019-03-28
    Scientific Explanation, Unifying Mathematics, and Indispensability Arguments.Patrick Dieveney - forthcoming - Synthese:1-21.
    Indispensability arguments occupy a prominent role in discussions of mathematical realism. While different versions of these arguments are discussed in the literature, their general structure remains the same. These arguments contend that insofar as reference to mathematical objects is indispensable to science, we are committed to the existence of these ‘objects’. Unsurprisingly, much of the debate concerning indispensability arguments focuses on the crucial contention that mathematical objects are indispensable to science. For these arguments to provide support for mathematical realism, what (...)
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  25. added 2019-03-28
    Mathematical Spandrels.Alan Baker - 2017 - Australasian Journal of Philosophy 95 (4):779-793.
    The aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these penumbral properties, and focus on (...)
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  26. added 2019-03-28
    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 (...)
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  27. added 2019-03-28
    Abstract Explanations in Science.Christopher Pincock - 2015 - British Journal for the Philosophy of Science 66 (4):857-882.
    This article focuses on a case that expert practitioners count as an explanation: a mathematical account of Plateau’s laws for soap films. I argue that this example falls into a class of explanations that I call abstract explanations.explanations involve an appeal to a more abstract entity than the state of affairs being explained. I show that the abstract entity need not be causally relevant to the explanandum for its features to be explanatorily relevant. However, it remains unclear how to unify (...)
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  28. added 2019-03-28
    Science and Mathematics: The Scope and Limits of Mathematical Fictionalism: Mary Leng: Mathematics and Reality. Oxford: Oxford University Press, 2010, X+278pp, £39.00 HB. [REVIEW]Christopher Pincock, Alan Baker, Alexander Paseau & Mary Leng - 2012 - Metascience 21 (2):269-294.
    Science and mathematics: the scope and limits of mathematical fictionalism Content Type Journal Article Category Book Symposium Pages 1-26 DOI 10.1007/s11016-011-9640-3 Authors Christopher Pincock, University of Missouri, 438 Strickland Hall, Columbia, MO 65211-4160, USA Alan Baker, Department of Philosophy, Swarthmore College, Swarthmore, PA 19081, USA Alexander Paseau, Wadham College, Oxford, OX1 3PN UK Mary Leng, Department of Philosophy, University of York, Heslington, York, YO10 5DD UK Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  29. added 2019-03-28
    Mathematical Explanations Of Empirical Facts, And Mathematical Realism.Aidan Lyon - 2012 - Australasian Journal of Philosophy 90 (3):559-578.
    A main thread of the debate over mathematical realism has come down to whether mathematics does explanatory work of its own in some of our best scientific explanations of empirical facts. Realists argue that it does; anti-realists argue that it doesn't. Part of this debate depends on how mathematics might be able to do explanatory work in an explanation. Everyone agrees that it's not enough that there merely be some mathematics in the explanation. Anti-realists claim there is nothing mathematics can (...)
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  30. added 2019-03-28
    Science-Driven Mathematical Explanation.Alan Baker - 2012 - Mind 121 (482):243-267.
    Philosophers of mathematics have become increasingly interested in the explanatory role of mathematics in empirical science, in the context of new versions of the Quinean ‘Indispensability Argument’ which employ inference to the best explanation for the existence of abstract mathematical objects. However, little attention has been paid to analysing the nature of the explanatory relation involved in these mathematical explanations in science (MES). In this paper, I attack the only articulated account of MES in the literature (an account sketched by (...)
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  31. added 2019-03-28
    Modeling Reality.Christopher Pincock - 2011 - Synthese 180 (1):19 - 32.
    My aim in this paper is to articulate an account of scientific modeling that reconciles pluralism about modeling with a modest form of scientific realism. The central claim of this approach is that the models of a given physical phenomenon can present different aspects of the phenomenon. This allows us, in certain special circumstances, to be confident that we are capturing genuine features of the world, even when our modeling occurs independently of a wholly theoretical motivation. This framework is illustrated (...)
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  32. added 2019-03-28
    Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
    Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss (...)
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  33. added 2019-03-28
    Mathematical Explanation and Indispensability Arguments.Simon Langford Chris Daly - 2009 - Philosophical Quarterly 59 (237):641-658.
    We defend Joseph Melia's thesis that the role of mathematics in scientific theory is to ‘index’ quantities, and that even if mathematics is indispensable to scientific explanations of concrete phenomena, it does not explain any of those phenomena. This thesis is defended against objections by Mark Colyvan and Alan Baker.
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  34. added 2019-03-28
    The Explanatory Power of Phase Spaces.Aidan Lyon & Mark Colyvan - 2008 - Philosophia Mathematica 16 (2):227-243.
    David Malament argued that Hartry Field's nominalisation program is unlikely to be able to deal with non-space-time theories such as phase-space theories. We give a specific example of such a phase-space theory and argue that this presentation of the theory delivers explanations that are not available in the classical presentation of the theory. This suggests that even if phase-space theories can be nominalised, the resulting theory will not have the explanatory power of the original. Phase-space theories thus raise problems for (...)
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  35. added 2019-03-28
    Mathematical Idealization.Chris Pincock - 2007 - Philosophy of Science 74 (5):957-967.
    Mathematical idealizations are scientific representations that result from assumptions that are believed to be false, and where mathematics plays a crucial role. I propose a two stage account of how to rank mathematical idealizations that is largely inspired by the semantic view of scientific theories. The paper concludes by considering how this approach to idealization allows for a limited form of scientific realism. ‡I would like to thank Robert Batterman, Gabriele Contessa, Eric Hiddleston, Nicholaos Jones, and Susan Vineberg for helpful (...)
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  36. added 2019-03-28
    A Revealing Flaw in Colyvan's Indispensability Argument.Christopher Pincock - 2004 - Philosophy of Science 71 (1):61-79.
    Mark Colyvan uses applications of mathematics to argue that mathematical entities exist. I claim that his argument is invalid based on the assumption that a certain way of thinking about applications, called `the mapping account,' is correct. My main contention is that successful applications depend only on there being appropriate structural relations between physical situations and the mathematical domain. As a variety of non-realist interpretations of mathematics deliver these structural relations, indispensability arguments are invalid.
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  37. added 2019-03-22
    The ‘Miracle’ of Applicability? The Curious Case of the Simple Harmonic Oscillator.Sorin Bangu & Robert H. C. Moir - 2018 - Foundations of Physics 48 (5):507-525.
    The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner’s famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of (...)
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  38. added 2019-02-24
    Mathematical Necessity and Reality.James Franklin - 1989 - Australasian Journal of Philosophy 67 (3):286 – 294.
    Einstein, like most philosophers, thought that there cannot be mathematical truths which are both necessary and about reality. The article argues against this, starting with prima facie examples such as "It is impossible to tile my bathroom floor with regular pentagonal tiles." Replies are given to objections based on the supposedly purely logical or hypothetical nature of mathematics.
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  39. added 2019-02-20
    Supertasks and Arithmetical Truth.Jared Warren & Daniel Waxman - 2020 - Philosophical Studies 177 (5):1275-1282.
    This paper discusses the relevance of supertask computation for the determinacy of arithmetic. Recent work in the philosophy of physics has made plausible the possibility of supertask computers, capable of running through infinitely many individual computations in a finite time. A natural thought is that, if supertask computers are possible, this implies that arithmetical truth is determinate. In this paper we argue, via a careful analysis of putative arguments from supertask computations to determinacy, that this natural thought is mistaken: supertasks (...)
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  40. added 2018-09-19
    The Principle of Equivalence as a Criterion of Identity.Ryan Samaroo - forthcoming - Synthese:1-25.
    In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...)
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  41. added 2018-08-14
    Zeno of Elea' Paradoxes (The Dialectic of Stability and Motion from a Contemporary Mathematical View) مفارقات زينون: جدل الثبات والحركة من منظور رياضي معاصر.Salah Osman - 2004 - Menoufia University, Faculty of Arts Journal, Egypt 58:99 - 139.
    لا شك أن مفارقات زينون في الحركة قد تم تناولها – تحليلاً ونقدًا – في كثيرٍ من أدبيات العلم والفلسفة قديمًا وحديثًا، حتى لقد ساد الظن بأن ملف المفارقات قد أغُلق تمامًا، لاسيما بعد أن نجح الحساب التحليلي في التعامل منطقيًا مع صعوبات الأعداد اللامتناهية، لكن الفرض الأساسي لهذا البحث يزعم عكس ذلك؛ أعني أن الملف مازال مفتوحًا وبقوة – خصوصًا على المستوى الرياضي الفيزيائي – وأن إغلاقه النهائي قد لا يتم في المستقبل القريب. من جهة أخرى، إذا كانت فكرة (...)
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  42. added 2018-03-29
    Research Habits in Financial Modelling: The Case of Non-Normativity of Market Returns in the 1970s and the 1980s.Boudewijn De Bruin & Christian Walter - 2017 - In Emiliano Ippoliti & Ping Chen (eds.), Methods and Finance: A Unifying View on Finance, Mathematics, and Philosophy. Cham: Springer. pp. 73-93.
    In this chapter, one considers finance at its very foundations, namely, at the place where assumptions are being made about the ways to measure the two key ingredients of finance: risk and return. It is well known that returns for a large class of assets display a number of stylized facts that cannot be squared with the traditional views of 1960s financial economics (normality and continuity assumptions, i.e. Brownian representation of market dynamics). Despite the empirical counterevidence, normality and continuity assumptions (...)
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  43. added 2018-02-17
    Measurement-Theoretic Observations on Field’s Instrumentalism and the Applicability of Mathematics.Davide Rizza - 2006 - Abstracta 2 (2):148-171.
    In this paper I examine Field’s account of the applicability of mathematics from a measurementtheoretic perspective. Within this context, I object to Field’s instrumentalism, arguing that it depends on an incomplete analysis of applicability. I show in particular that, once the missing piece of analysis is provided, the role played by numerical entities in basic empirical theories must be revised: such revision implies that instrumentalism should be rejected and mathematical entities be regarded not merely as useful tools but also as (...)
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  44. added 2018-02-17
    The Reasonable Effectiveness of Mathematics: Partial Structures and the Application of Group Theory to Physics.Steven French - 2000 - Synthese 125 (1):103-120.
    Wigner famously referred to the 'unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics. I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.
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  45. 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 (...)
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  46. added 2018-02-16
    Mathematical Formalisms in Scientific Practice: From Denotation to Model-Based Representation.Axel Gelfert - 2011 - Studies in History and Philosophy of Science Part A 42 (2):272-286.
    The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible with successful (...)
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  47. added 2018-02-16
    Overmathematisation in Game Theory: Pitting the Nash Equilibrium Refinement Programme Against the Epistemic Programme.Boudewijn de Bruin - 2009 - Studies in History and Philosophy of Science Part A 40 (3):290-300.
    The paper argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme. The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains this in terms (...)
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  48. added 2018-02-16
    Reifying Mathematics? Prediction and Symmetry Classification.Sorin Bangu - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2):239-258.
    In this paper I reconstruct and critically examine the reasoning leading to the famous prediction of the ‘omega minus’ particle by M. Gell-Mann and Y. Ne’eman (in 1962) on the basis of a symmetry classification scheme. While the peculiarity of this prediction has occasionally been noticed in the literature, a detailed treatment of the methodological problems it poses has not been offered yet. By spelling out the characteristics of this type of prediction, I aim to underscore the challenges raised by (...)
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  49. added 2018-01-10
    The Intelligibility of the Universe.Mary Cosmas Hughes - 1946 - Washington: the Catholic University of America Press.
  50. added 2017-12-25
    The Necessity of Mathematics.Juhani Yli‐Vakkuri & John Hawthorne - 2018 - Noûs 52.
    Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.
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