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  1. 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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  • 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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  • On Putnam’s Proof of the Impossibility of a Nominalistic Physics.Thomas William Barrett - forthcoming - Erkenntnis:1-28.
    In his book Philosophy of Logic, Putnam presents a short argument which reads like—and indeed, can be reconstructed as—a formal proof that a nominalistic physics is impossible. The aim of this paper is to examine Putnam’s proof and show that it is not compelling. The precise way in which the proof fails yields insight into the relation that a nominalistic physics should bear to standard physics and into Putnam’s indispensability argument.
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  • Why Inference to the Best Explanation Doesn’T Secure Empirical Grounds for Mathematical Platonism.Kenneth Boyce - 2018 - Synthese 198 (1):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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  • 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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  • 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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  • Evidential Holism and Indispensability Arguments.Joe Morrison - 2012 - Erkenntnis 76 (2):263-278.
    The indispensability argument is a method for showing that abstract mathematical objects exist. Various versions of this argument have been proposed. Lately, commentators seem to have agreed that a holistic indispensability argument will not work, and that an explanatory indispensability argument is the best candidate. In this paper I argue that the dominant reasons for rejecting the holistic indispensability argument are mistaken. This is largely due to an overestimation of the consequences that follow from evidential holism. Nevertheless, the holistic indispensability (...)
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  • Putnam’s Indispensability Argument Revisited, Reassessed, Revived.Otávio Bueno - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):201-218.
    Crucial to Hilary Putnam’s realism in the philosophy of mathematics is to maintain the objectivity of mathematics without the commitment to the existence of mathematical objects. Putnam’s indispensability argument was devised as part of this conception. In this paper, I reconstruct and reassess Putnam’s argument for the indispensability of mathematics, and distinguish it from the more familiar, Quinean version of the argument. Although I argue that Putnam’s approach ultimately fails, I develop an alternative way of implementing his form of realism (...)
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  • Putnam and Contemporary Fictionalism.Concha Martínez Vidal - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):165-181.
    Putnam rejects having argued in the terms of the argument known in the literature as “the Quine-Putnam indispensability argument”. He considers that mathematics contribution to physics does not have to be interpreted in platonist terms but in his favorite modal variety. The purpose of this paper is to consider Putnam’s acknowledged argument and philosophical position against contemporary so called in the literature ‘fictionalist’ views about applied mathematics. The conclusion will be that the account of the applicability of mathematics that stems (...)
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  • Indispensability Arguments and Their Quinean Heritage.Jacob Busch & Andrea Sereni - 2012 - Disputatio 4 (32):343 - 360.
    Indispensability arguments for mathematical realism are commonly traced back to Quine. We identify two different Quinean strands in the interpretation of IA, what we label the ‘logical point of view’ and the ‘theory-contribution’ point of view. Focusing on each of the latter, we offer two minimal versions of IA. These both dispense with a number of theoretical assumptions commonly thought to be relevant to IA. We then show that the attribution of both minimal arguments to Quine is controversial, and stress (...)
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  • Towards a Fictionalist Philosophy of Mathematics.Robert Knowles - unknown
    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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  • Introduction.[author unknown] - forthcoming - Introduction 4 (32).
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  • Evidential Holism.Joe Morrison - 2017 - Philosophy Compass 12 (6):e12417.
    Evidential holism begins with something like the claim that “it is only jointly as a theory that scientific statements imply their observable consequences.” This is the holistic claim that Elliott Sober tells us is an “unexceptional observation”. But variations on this “unexceptional” claim feature as a premise in a series of controversial arguments for radical conclusions, such as that there is no analytic or synthetic distinction that the meaning of a sentence cannot be understood without understanding the whole language of (...)
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  • Two Weak Points of the Enhanced Indispensability Argument – Domain of the Argument and Definition of Indispensability.Vladimir Drekalović - 2016 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 23 (3):280-298.
    The contemporary Platonists in the philosophy of mathematics argue that mathematical objects exist. One of the arguments by which they support this standpoint is the so-called Enhanced Indispensability Argument (EIA). This paper aims at pointing out the difficulties inherent to the EIA. The first is contained in the vague formulation of the Argument, which is the reason why not even an approximate scope of the set objects whose existence is stated by the Argument can be established. The second problem is (...)
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  • Putnam and the Indispensability of Mathematics.Otávio Bueno - 2013 - Principia: An International Journal of Epistemology 17 (2):217.
    In this paper, I examine Putnam’s nuanced views in the philosophy of mathematics, distinguishing three proposals: modalism, quasi-empirical realism, and an indispensability view. I argue that, as he shifted through these views, Putnam aimed to preserve a semantic realist account of mathematics that avoids platonism. In the end, however, each of the proposals faces significant difficulties. A form of skepticism then emerges.
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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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  • Mathematical Platonism Meets Ontological Pluralism?Matteo Plebani - 2017 - Inquiry: An Interdisciplinary Journal of Philosophy:1-19.
    Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for...
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  • Introduction.[author unknown] - forthcoming - Introduction 4 (32).
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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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  • Indispensability and Holism.Jacob Busch - 2011 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 42 (1):47-59.
    It is claimed that the indispensability argument for the existence of mathematical entities (IA) works in a way that allows a proponent of mathematical realism to remain agnostic with regard to how we establish that mathematical entities exist. This is supposed to be possible by virtue of the appeal to confirmational holism that enters into the formulation of IA. Holism about confirmation is supposed to be motivated in analogy with holism about falsification. I present an account of how holism about (...)
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