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  1. Quine, Putnam, and the ‘Quine–Putnam’ Indispensability Argument.David Liggins - 2008 - Erkenntnis 68 (1):113 - 127.
    Much recent discussion in the philosophy of mathematics has concerned the indispensability argument—an argument which aims to establish the existence of abstract mathematical objects through appealing to the role that mathematics plays in empirical science. The indispensability argument is standardly attributed to W. V. Quine and Hilary Putnam. In this paper, I show that this attribution is mistaken. Quine's argument for the existence of abstract mathematical objects differs from the argument which many philosophers of mathematics ascribe to him. Contrary to (...)
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  • The role of pragmatic considerations during mathematical derivation in the applicability of mathematics.José Antonio Pérez-Escobar - 2024 - Philosophical Investigations 47 (4):543-557.
    The conditions involved in the applicability of mathematics in science are the subject of ongoing debates. One of the best‐received approaches is the inferential account, which involves structural mappings and pragmatic considerations in a three‐step model. According to the inferential account, these pragmatic considerations happen in the immersion and interpretation stages, but not during derivation (symbol‐pushing in a mathematical formalism). In this work, I draw inspiration from the later Wittgenstein and make the case that the applicability of mathematics also rests (...)
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  • Structure and applied mathematics.Travis McKenna - 2022 - Synthese 200 (5):1-31.
    ‘Mapping accounts’ of applied mathematics hold that the application of mathematics in physical science is best understood in terms of ‘mappings’ between mathematical structures and physical structures. In this paper, I suggest that mapping accounts rely on the assumption that the mathematics relevant to any application of mathematics in empirical science can be captured in an appropriate mathematical structure. If we are interested in assessing the plausibility of mapping accounts, we must ask ourselves: how plausible is this assumption as a (...)
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  • The mathematical stance.Alan Baker - 2022 - Synthese 200 (1):1-18.
    Defenders of the enhanced indispensability argument argue that the most effective route to platonism is via the explanatory role of mathematical posits in science. Various compelling cases of mathematical explanation in science have been proposed, but a satisfactory general philosophical account of such explanations is lacking. In this paper, I lay out the framework for such an account based on the notion of “the mathematical stance.” This is developed by analogy with Dennett’s well-known concept of “the intentional stance.” Roughly, adopting (...)
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  • Scientific Models and Political Theory: The Ideal Theory Debate Revisited.Ryan M. Nefdt - 2021 - Theoria 87 (6):1585-1608.
    Political philosophy has traditionally been defined as a normative discipline with a distinctively ideal component, largely informed by moral philosophy. In this paper, I investigate a prominent critique of ideal theory specifically with the goal of resituating the debate within a larger framework in the philosophy of science. I then mount a novel case for how ideal theory should be viewed in terms of scientific modelling. I close with a discussion of how this view can dissolve apparent paradoxes and provide (...)
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  • Models, structures, and the explanatory role of mathematics in empirical science.Mary Leng - 2021 - Synthese 199 (3-4):10415-10440.
    Are there genuine mathematical explanations of physical phenomena, and if so, how can mathematical theories, which are typically thought to concern abstract mathematical objects, explain contingent empirical matters? The answer, I argue, is in seeing an important range of mathematical explanations as structural explanations, where structural explanations explain a phenomenon by showing it to have been an inevitable consequence of the structural features instantiated in the physical system under consideration. Such explanations are best cast as deductive arguments which, by virtue (...)
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  • A New Role for Mathematics in Empirical Sciences.Atoosa Kasirzadeh - 2021 - Philosophy of Science 88 (4):686-706.
    Mathematics is often taken to play one of two roles in the empirical sciences: either it represents empirical phenomena or it explains these phenomena by imposing constraints on them. This article identifies a third and distinct role that has not been fully appreciated in the literature on applicability of mathematics and may be pervasive in scientific practice. I call this the “bridging” role of mathematics, according to which mathematics acts as a connecting scheme in our explanatory reasoning about why and (...)
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  • Can we have mathematical understanding of physical phenomena?Gabriel Târziu - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (1):91-109.
    Can mathematics contribute to our understanding of physical phenomena? One way to try to answer this question is by getting involved in the recent philosophical dispute about the existence of mathematical explanations of physical phenomena. If there is such a thing, given the relation between explanation and understanding, we can say that there is an affirmative answer to our question. But what if we do not agree that mathematics can play an explanatory role in science? Can we still consider that (...)
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  • Fundamentality, Effectiveness, and Objectivity of Gauge Symmetries.Aldo Filomeno - 2016 - International Studies in the Philosophy of Science 30 (1):19-37.
    Much recent philosophy of physics has investigated the process of symmetry breaking. Here, I critically assess the alleged symmetry restoration at the fundamental scale. I draw attention to the contingency that gauge symmetries exhibit, that is, the fact that they have been chosen from an infinite space of possibilities. I appeal to this feature of group theory to argue that any metaphysical account of fundamental laws that expects symmetry restoration up to the fundamental level is not fully satisfactory. This is (...)
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  • The Applicability of Mathematics to Physical Modality.Nora Berenstain - 2017 - Synthese 194 (9):3361-3377.
    This paper argues that scientific realism commits us to a metaphysical determination relation between the mathematical entities that are indispensible to scientific explanation and the modal structure of the empirical phenomena those entities explain. The argument presupposes that scientific realism commits us to the indispensability argument. The viewpresented here is that the indispensability of mathematics commits us not only to the existence of mathematical structures and entities but to a metaphysical determination relation between those entities and the modal structure of (...)
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  • Towards a Fictionalist Philosophy of Mathematics.Robert Knowles - 2015 - Dissertation, University of Manchester
    In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content that does not imply the existence of mathematical objects. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward assertions. In Part I, I argue that the role played by (...)
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  • Outline of a dynamical inferential conception of the application of mathematics.Tim Räz & Tilman Sauer - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 49:57-72.
    We outline a framework for analyzing episodes from the history of science in which the application of mathematics plays a constitutive role in the conceptual development of empirical sciences. Our starting point is the inferential conception of the application of mathematics, recently advanced by Bueno and Colyvan. We identify and discuss some systematic problems of this approach. We propose refinements of the inferential conception based on theoretical considerations and on the basis of a historical case study. We demonstrate the usefulness (...)
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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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  • 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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  • How Not to Enhance the Indispensability Argument.Russell Marcus - 2014 - Philosophia Mathematica 22 (3):345-360.
    The new explanatory or enhanced indispensability argument alleges that our mathematical beliefs are justified by their indispensable appearances in scientific explanations. This argument differs from the standard indispensability argument which focuses on the uses of mathematics in scientific theories. I argue that the new argument depends for its plausibility on an equivocation between two senses of explanation. On one sense the new argument is an oblique restatement of the standard argument. On the other sense, it is vulnerable to an instrumentalist (...)
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  • Mathematics, Science, and Confirmation Theory.Christopher Pincock - 2010 - Philosophy of Science 77 (5):959-970.
    This paper begins by distinguishing intrinsic and extrinsic contributions of mathematics to scientific representation. This leads to two investigations into how these different sorts of contributions relate to confirmation. I present a way of accommodating both contributions that complicates the traditional assumptions of confirmation theory. In particular, I argue that subjective Bayesianism does best accounting for extrinsic contributions, while objective Bayesianism is more promising for intrinsic contributions.
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  • An Inferential Conception of the Application of Mathematics.Otávio Bueno & Mark Colyvan - 2011 - Noûs 45 (2):345-374.
    A number of people have recently argued for a structural approach to accounting for the applications of mathematics. Such an approach has been called "the mapping account". According to this view, the applicability of mathematics is fully accounted for by appreciating the relevant structural similarities between the empirical system under study and the mathematics used in the investigation ofthat system. This account of applications requires the truth of applied mathematical assertions, but it does not require the existence of mathematical objects. (...)
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  • The Honest Weasel A Guide for Successful Weaseling.Patrick Dieveney - 2020 - Disputatio 12 (56):41-69.
    Indispensability arguments are among the strongest arguments in support of mathematical realism. Given the controversial nature of their conclusions, it is not surprising that critics have supplied a number of rejoinders to these arguments. In this paper, I focus on one such rejoinder, Melia’s ‘Weasel Response’. The weasel is someone who accepts that scientific theories imply that there are mathematical objects, but then proceeds to ‘take back’ this commitment. While weaseling seems improper, accounts supplied in the literature have failed to (...)
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  • Is the Indispensability Argument Dispensable?Jacob Busch - 2011 - Theoria 77 (2):139-158.
    When the indispensability argument for mathematical entities (IA) is spelled out, it would appear confirmational holism is needed for the argument to work. It has been argued that confirmational holism is a dispensable premise in the argument if a construal of naturalism, according to which it is denied that we can take different epistemic attitudes towards different parts of our scientific theories, is adopted. I argue that the suggested variety of naturalism will only appeal to a limited number of philosophers. (...)
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  • Evidence, explanation and enhanced indispensability.Daniele Molinini - 2016 - Synthese 193 (2):403-422.
    In this paper I shall adopt a possible reading of the notions of ‘explanatory indispensability’ and ‘genuine mathematical explanation in science’ on which the Enhanced Indispensability Argument proposed by Alan Baker is based. Furthermore, I shall propose two examples of mathematical explanation in science and I shall show that, whether the EIA-partisans accept the reading I suggest, they are easily caught in a dilemma. To escape this dilemma they need to adopt some account of explanation and offer a plausible answer (...)
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  • Toward the Applicability of Statistics: A Representational View.Mahdi Ashoori & S. Mahmoud Taheri - 2019 - Principia: An International Journal of Epistemology 23 (1):113-129.
    The problem of understanding how statistical inference is, and can be, applied in empirical sciences is important for the methodology of science. It is the objective of this paper to gain a better understanding of the role of statistical methods in scientific modeling. The important question of whether the applicability reduces to the representational properties of statistical models is discussed. It will be shown that while the answer to this question is positive, representation in statistical models is not purely structural. (...)
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  • Emergence and Fundamentality in a Pancomputationalist Universe.Mark Pexton - 2015 - Minds and Machines 25 (4):301-320.
    The aim of this work is to apply information theoretic ideas to the notion of fundamentality. I will argue that if one adopts pancomputationalism as a metaphysics for the universe, then there are higher-level structures which are just as fundamental for computation as anything from microphysics.
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  • Van Inwagen and the Quine-Putnam indispensability argument.Mitchell O. Stokes - 2007 - Erkenntnis 67 (3):439 - 453.
    In this paper I do two things: (1) I support the claim that there is still some confusion about just what the Quine-Putnam indispensability argument is and the way it employs Quinean meta-ontology and (2) I try to dispel some of this confusion by presenting the argument in a way which reveals its important meta-ontological features, and include these features explicitly as premises. As a means to these ends, I compare Peter van Inwagen’s argument for the existence of properties with (...)
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  • Equivalent explanations and mathematical realism. Reply to “Evidence, Explanation, and Enhanced Indispensability”.Andrea Sereni - 2016 - Synthese 193 (2):423-434.
    The author of “Evidence, Explanation, Enhanced Indispensability” advances a criticism to the Enhanced Indispensability Argument and the use of Inference to the Best Explanation in order to draw ontological conclusions from mathematical explanations in science. His argument relies on the availability of equivalent though competing explanations, and a pluralist stance on explanation. I discuss whether pluralism emerges as a stable position, and focus here on two main points: whether cases of equivalent explanations have been actually offered, and which ontological consequences (...)
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  • Can the new indispensability argument be saved from Euclidean rescues?Jacob Busch - 2012 - Synthese 187 (2):489-508.
    The traditional formulation of the indispensability argument for the existence of mathematical entities (IA) has been criticised due to its reliance on confirmational holism. Recently a formulation of IA that works without appeal to confirmational holism has been defended. This recent formulation is meant to be superior to the traditional formulation in virtue of it not being subject to the kind of criticism that pertains to confirmational holism. I shall argue that a proponent of the version of IA that works (...)
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