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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 1953Quine 1981Putnam 1975 and Putnam 1971. Further considerations can be found for instance in Parsons 1980Chihara 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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  1. The Eleatic and the Indispensabilist.Russell Marcus - manuscript
    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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  2. Debunking Arguments: Mathematics, Logic, and Modal Security.Justin Clarke-Doane - forthcoming - In Robert Richards and Michael Ruse (ed.), The Cambridge Handbook of Evolutionary Ethics. Cambridge University Press.
    I discuss the structure of genealogical debunking arguments. I argue that they undermine our mathematical beliefs if they undermine our moral beliefs. The contrary appearance stems from a confusion of arithmetic truths with (first-order) logical truths, or from a confusion of reliability with justification. I conclude with a discussion of the cogency of debunking arguments, in light of the above. Their cogency depends on whether information can undermine all of our beliefs of a kind, F, without giving us direct reason (...)
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  3. The Incubus of Inter-Translatability... A Realist’s Nightmare? [REVIEW]Nicholas Danne - forthcoming - Metascience:1-4.
  4. Applied Mathematics Without Numbers.Jack Himelright - forthcoming - Philosophia Mathematica.
    In this paper, I develop a "safety result" for applied mathematics. I show that whenever a theory in natural science entails some non-mathematical conclusion via an application of mathematics, there is a counterpart theory that carries no commitment to mathematical objects, entails the same conclusion, and the claims of which are true if the claims of the original theory are "correct": roughly, true given the assumption that mathematical objects exist. The framework used for proving the safety result has some advantages (...)
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  5. Quantifier Variance, Mathematicians’ Freedom and the Revenge of Quinean Indispensability Worries.Sharon Berry - 2022 - Erkenntnis 87 (5):2201-2218.
    Invoking a form of quantifier variance promises to let us explain mathematicians’ freedom to introduce new kinds of mathematical objects in a way that avoids some problems for standard platonist and nominalist views. In this paper I’ll note that, despite traditional associations between quantifier variance and Carnapian rejection of metaphysics, Siderian realists about metaphysics can naturally be quantifier variantists. Unfortunately a variant on the Quinean indispensability argument concerning grounding seems to pose a problem for philosophers who accept this hybrid. However (...)
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  6. Safety First: Making Property Talk Safe for Nominalists.Jack Himelright - 2022 - Synthese 200 (3):1-26.
    Nominalists are confronted with a grave difficulty: if abstract objects do not exist, what explains the success of theories that invoke them? In this paper, I make headway on this problem. I develop a formal language in which certain platonistic claims about properties and certain nominalistic claims can be expressed, develop a formal language in which only certain nominalistic claims can be expressed, describe a function mapping sentences of the first language to sentences of the second language, and prove some (...)
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  7. Platonic Relations and Mathematical Explanations.Robert Knowles - 2021 - Philosophical Quarterly 71 (3):623-644.
    Some scientific explanations appear to turn on pure mathematical claims. The enhanced indispensability argument appeals to these ‘mathematical explanations’ in support of mathematical platonism. I argue that the success of this argument rests on the claim that mathematical explanations locate pure mathematical facts on which their physical explananda depend, and that any account of mathematical explanation that supports this claim fails to provide an adequate understanding of mathematical explanation.
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  8. What Are Empirical Consequences? On Dispensability and Composite Objects.Alex LeBrun - 2021 - Synthese 199 (5-6):13201-13223.
    Philosophers sometimes give arguments that presuppose the following principle: two theories can fail to be empirically equivalent on the sole basis that they present different “thick” metaphysical pictures of the world. Recently, a version of this principle has been invoked to respond to the argument that composite objects are dispensable to our best scientific theories. This response claims that our empirical evidence distinguishes between ordinary and composite-free theories, and it empirically favors the ordinary ones. In this paper, I ask whether (...)
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  9. 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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  10. Mathematics and Explanatory Generality: Nothing but Cognitive Salience.Juha Saatsi & Robert Knowles - 2021 - Erkenntnis 86 (5):1119-1137.
    We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content to key (...)
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  11. Mathematical Application and the No Confirmation Thesis.Kenneth Boyce - 2020 - Analysis 80 (1):11-20.
    Some proponents of the indispensability argument for mathematical realism maintain that the empirical evidence that confirms our best scientific theories and explanations also confirms their pure mathematical components. I show that the falsity of this view follows from three highly plausible theses, two of which concern the nature of mathematical application and the other the nature of empirical confirmation. The first is that the background mathematical theories suitable for use in science are conservative in the sense outlined by Hartry Field. (...)
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  12. Mathematical Surrealism as an Alternative to Easy-Road Fictionalism.Kenneth Boyce - 2020 - Philosophical Studies 177 (10):2815-2835.
    Easy-road mathematical fictionalists grant for the sake of argument that quantification over mathematical entities is indispensable to some of our best scientific theories and explanations. Even so they maintain we can accept those theories and explanations, without believing their mathematical components, provided we believe the concrete world is intrinsically as it needs to be for those components to be true. Those I refer to as “mathematical surrealists” by contrast appeal to facts about the intrinsic character of the concrete world, not (...)
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  13. Morality and Mathematics.Justin Clarke-Doane - 2020 - Oxford, England: Oxford University Press.
    To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to (...)
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  14. Representational Indispensability and Ontological Commitment.John Heron - 2020 - Thought: A Journal of Philosophy 9 (2):105-114.
    Recent debates about mathematical ontology are guided by the view that Platonism's prospects depend on mathematics' explanatory role in science. If mathematics plays an explanatory role, and in the right kind of way, this carries ontological commitment to mathematical objects. Conversely, the assumption goes, if mathematics merely plays a representational role then our world-oriented uses of mathematics fail to commit us to mathematical objects. I argue that it is a mistake to think that mathematical representation is necessarily ontologically innocent and (...)
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  15. Infinite Lies and Explanatory Ties: Idealization in Phase Transitions.Sam Baron - 2019 - Synthese 196 (5):1939-1961.
    Infinite idealizations appear in our best scientific explanations of phase transitions. This is thought by some to be paradoxical. In this paper I connect the existing literature on the phase transition paradox to work on the concept of indispensability, which arises in discussions of realism and anti-realism within the philosophy of science and the philosophy of mathematics. I formulate a version of the phase transition paradox based on the idea that infinite idealizations are explanatorily indispensable to our best science, and (...)
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  16. Optimal Representations and the Enhanced Indispensability Argument.Manuel Barrantes - 2019 - Synthese 196 (1):247-263.
    The Enhanced Indispensability Argument appeals to the existence of Mathematical Explanations of Physical Phenomena 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 defend the EIA. I then generalize my analysis of the cicada case to other MEPPs, and show that these explanations rely on what I will call ‘optimal (...)
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  17. The Enhanced Indispensability Argument, the Circularity Problem, and the Interpretability Strategy.Jan Heylen & Lars Arthur Tump - 2019 - Synthese 198 (4):3033-3045.
    Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (...)
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  18. Quine and the Incoherence of the Indispensability Argument.Michael J. Shaffer - 2019 - Logos and Episteme 10 (2):207-213.
    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 (...)
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  19. 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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  20. Indispensability, Causation and Explanation.Sorin Bangu - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):219-232.
    When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists’ endorsement of this causal mathematical nominalism is in tension with another position some of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend to tip the balance in favor of a rival (...)
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  21. 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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  22. 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.
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  23. What We Talk About When We Talk About Numbers.Richard Pettigrew - 2018 - Annals of Pure and Applied Logic 169 (12):1437-1456.
    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.
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  24. 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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  25. Importance and Explanatory Relevance: The Case of Mathematical Explanations.Gabriel Târziu - 2018 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (3):393-412.
    A way to argue that something plays an explanatory role in science is by linking explanatory relevance with importance in the context of an explanation. The idea is deceptively simple: a part of an explanation is an explanatorily relevant part of that explanation if removing it affects the explanation either by destroying it or by diminishing its explanatory power, i.e. an important part is an explanatorily relevant part. This can be very useful in many ontological debates. My aim in this (...)
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  26. Mathematical Explanations and the Piecemeal Approach to Thinking About Explanation.Gabriel Târziu - 2018 - Logique Et Analyse 61 (244):457-487.
    A new trend in the philosophical literature on scientific explanation is that of starting from a case that has been somehow identified as an explanation and then proceed to bringing to light its characteristic features and to constructing an account for the type of explanation it exemplifies. A type of this approach to thinking about explanation – the piecemeal approach, as I will call it – is used, among others, by Lange (2013) and Pincock (2015) in the context of their (...)
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  27. 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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  28. How Mathematics Can Make a Difference.Sam Baron, Mark Colyvan & David Ripley - 2017 - Philosophers' Imprint 17.
    Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.
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  29. 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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  30. 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.
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  31. 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.
  32. 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.
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  33. Dynamical Systems Theory and Explanatory Indispensability.Juha Saatsi - 2017 - Philosophy of Science 84 (5):892-904.
    I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces (Lyon and Colyvan 2007). Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The take-home message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine platonist arguments from explanatory indispensability.
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  34. Mathematical Explanation and the Biological Optimality Fallacy.Samantha Wakil & James Justus - 2017 - Philosophy of Science 84 (5):916-930.
    Pure mathematics can play an indispensable role explaining empirical phenomena if recent accounts of insect evolution are correct. In particular, the prime life cycles of cicadas and the geometric structure of honeycombs are taken to undergird an inference to the best explanation about mathematical entities. Neither example supports this inference or the mathematical realism it is intended to establish. Both incorrectly assume that facts about mathematical optimality drove selection for the respective traits and explain why they exist. We show how (...)
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  35. 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 (...)
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  36. Russell Marcus. Autonomy Platonism and the Indispensability Argument.Alan Baker - 2016 - Philosophia Mathematica 24 (3):422-424.
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  37. The Current Epistemic Status of the Indispensability Arguments in the Philosophy of Science.Catalin Barboianu - 2016 - Analele Universitatii Din Craiova 36 (2):108-132.
    The predisposition of the Indispensability Argument to objections, rephrasing and versions associated with the various views in philosophy of mathematics grants it a special status of a “blueprint” type rather than a debatable theme in the philosophy of science. From this point of view, it follows that the Argument has more an epistemic character than ontological.
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  38. Mathematical Explanation and Epistemology: Please Mind the Gap.Sam Baron - 2016 - Ratio 29 (2):149-167.
    This paper draws together two strands in the debate over the existence of mathematical objects. The first strand concerns the notion of extra-mathematical explanation: the explanation of physical facts, in part, by facts about mathematical objects. The second strand concerns the access problem for platonism: the problem of how to account for knowledge of mathematical objects. I argue for the following conditional: if there are extra-mathematical explanations, then the core thesis of the access problem is false. This has implications for (...)
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  39. Time Enough for Explanation.Sam Baron & Mark Colyvan - 2016 - Journal of Philosophy 113 (2):61-88.
    The present paper advances an analogy between cases of extra-mathematical explanation and cases of what might be termed ‘extra-logical explanation’: the explanation of a physical fact by a logical fact. A particular case of extra-logical explanation is identified that arises in the philosophical literature on time travel. This instance of extra-logical explanation is subsequently shown to be of a piece with cases of extra-mathematical explanation. Using this analogy, we argue extra-mathematical explanation is part of a broader class of non-causal explanation. (...)
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  40. 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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  41. Naturalizing Indispensability: A Rejoinder to ‘The Varieties of Indispensability Arguments’.Henri Galinon - 2016 - Synthese 193 (2).
    In ‘The varieties of indispensability arguments’ Marco Panza and Andrea Sereni argue that, for any clear notion of indispensability, either there is no conclusive argument for the thesis that mathematics is indispensable to science, or the notion of indispensability at hand does not support mathematical realism. In this paper, I shall not object to this main thesis directly. I shall instead try to assess in a naturalistic spirit a family of objections the authors make along the way to the use (...)
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  42. 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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  43. Indispensability and the Problem of Compatible Explanations: A Reply to ‘Should Scientific Realists Be Platonists?’.Josh Hunt - 2016 - Synthese 193 (2):451-467.
    Alan Baker’s enhanced indispensability argument supports mathematical platonism through the explanatory role of mathematics in science. Busch and Morrison defend nominalism by denying that scientific realists use inference to the best explanation to directly establish ontological claims. In response to Busch and Morrison, I argue that nominalists can rebut the EIA while still accepting Baker’s form of IBE. Nominalists can plausibly require that defenders of the EIA establish the indispensability of a particular mathematical entity. Next, I argue that IBE cannot (...)
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  44. Explanation in Ethics and Mathematics: Debunking and Dispensability.Uri D. Leibowitz & Neil Sinclair (eds.) - 2016 - Oxford, England: Oxford University Press UK.
    How far should our realism extend? For many years philosophers of mathematics and philosophers of ethics have worked independently to address the question of how best to understand the entities apparently referred to by mathematical and ethical talk. But the similarities between their endeavours are not often emphasised. This book provides that emphasis. In particular, it focuses on two types of argumentative strategies that have been deployed in both areas. The first—debunking arguments—aims to put pressure on realism by emphasising the (...)
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  45. 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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  46. Multiple Realization and Expressive Power in Mathematics and Ethics.David Liggins - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford University Press.
    According to a popular ‘explanationist’ argument for moral or mathematical realism the best explanation of some phenomena are moral or mathematical, and this implies the relevant form of realism. One popular way to resist the premiss of such arguments is to hold that any supposed explanation provided by moral or mathematical properties is in fact provided only by the non-moral or non-mathematical grounds of those properties. Many realists have responded to this objection by urging that the explanations provided by the (...)
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  47. Indispensability and Explanation: An Overview and Introduction.Daniele Molinini, Fabrice Pataut & Andrea Sereni - 2016 - Synthese 193 (2):317-332.
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  48. The Varieties of Indispensability Arguments.Marco Panza & Andrea Sereni - 2016 - Synthese 193 (2):469-516.
    The indispensability argument comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA (...)
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  49. Comments on “Parsimony and Inference to the Best Mathematical Explanation”.Fabrice Pataut - 2016 - Synthese 193 (2):351-363.
    The author of “Parsimony and inference to the best mathematical explanation” argues for platonism by way of an enhanced indispensability argument based on an inference to yet better mathematical optimization explanations in the natural sciences. Since such explanations yield beneficial trade-offs between stronger mathematical existential claims and fewer concrete ontological commitments than those involved in merely good mathematical explanations, one must countenance the mathematical objects that play a theoretical role in them via an application of the relevant mathematical results. The (...)
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  50. 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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