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  1. 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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  • Fictionalism in the philosophy of mathematics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.
    Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a (...)
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  • (1 other version)Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • Six Roles for Inclination.Zach Barnett - 2024 - Mind 133 (532):972-1000.
    Initially, you judge that p. You then learn that most experts disagree. All things considered, you believe that the experts are probably right. Still, p continues to seem right to you, in some sense. You don’t yet see what, if anything, is wrong with your original reasoning. In such a case, we’ll say that you are ‘inclined’ toward p. This paper explores various roles that this state of inclination can play, both within epistemology and more broadly. Specifically, it will be (...)
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  • Platonism and Intra-mathematical Explanation.Sam Baron - forthcoming - Philosophical Quarterly.
    I introduce an argument for Platonism based on intra-mathematical explanation: the explanation of one mathematical fact by another. The argument is important for two reasons. First, if the argument succeeds then it provides a basis for Platonism that does not proceed via standard indispensability considerations. Second, if the argument fails it can only do so for one of three reasons: either because there are no intra-mathematical explanations, or because not all explanations are backed by dependence relations, or because some form (...)
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  • Are mathematical explanations causal explanations in disguise?A. Jha, Douglas Campbell, Clemency Montelle & Phillip L. Wilson - 2024 - Philosophy of Science (NA):1-19.
    There is a major debate as to whether there are non-causal mathematical explanations of physical facts that show how the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws. We focus on Marc Lange’s account of distinctively mathematical explanations to argue that purported mathematical explanations are essentially causal explanations in disguise and are no different from ordinary applications of mathematics. This is because these explanations work not by appealing to what the (...)
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  • A Conventionalist Account of Distinctively Mathematical Explanation.Mark Povich - 2023 - Philosophical Problems in Science 74:171–223.
    Distinctively mathematical explanations (DMEs) explain natural phenomena primarily by appeal to mathematical facts. One important question is whether there can be an ontic account of DME. An ontic account of DME would treat the explananda and explanantia of DMEs as ontic structures and the explanatory relation between them as an ontic relation (e.g., Pincock 2015, Povich 2021). Here I present a conventionalist account of DME, defend it against objections, and argue that it should be considered ontic. Notably, if indeed it (...)
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  • (1 other version)Mathematical Pluralism and Indispensability.Silvia Jonas - 2023 - Erkenntnis 1:1-25.
    Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at most (...)
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  • What could mathematics be for it to function in distinctively mathematical scientific explanations?Marc Lange - 2021 - Studies in History and Philosophy of Science Part A 87 (C):44-53.
    Several philosophers have suggested that some scientific explanations work not by virtue of describing aspects of the world’s causal history and relations, but rather by citing mathematical facts. This paper investigates what mathematical facts could be in order for them to figure in such “distinctively mathematical” scientific explanations. For “distinctively mathematical explanations” to be explanations by constraint, mathematical language cannot operate in science as representationalism or platonism describes. It can operate as Aristotelian realism describes. That is because Aristotelian realism enables (...)
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  • Colors, Perceptual Variation, and Science.Michael Watkins & Elay Shech - 2024 - Erkenntnis 89 (3):1157-1181.
    Arguments from perceptual variation challenge the view that colors are objective properties of objects, properties that objects have independent of how they are perceived. This paper attempts, first, to diagnose one central reason why arguments from perceptual variation seem especially challenging for objectivists about color. Second, we offer a response to this challenge, claiming that once we focus on determinate colors rather than the determinables they determine, a response to arguments from perceptual variation becomes apparent. Third, our nominal opponents are (...)
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  • (1 other version)Not so distinctively mathematical explanations: topology and dynamical systems.Aditya Jha, Douglas Campbell, Clemency Montelle & Phillip L. Wilson - 2022 - Synthese 200 (3):1-40.
    So-called ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any n-tuple pendulum system on the ground that such explanations are (...)
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  • Inference to the best explanation as supporting the expansion of mathematicians’ ontological commitments.Marc Lange - 2022 - Synthese 200 (2):1-26.
    This paper argues that in mathematical practice, conjectures are sometimes confirmed by “Inference to the Best Explanation” as applied to some mathematical evidence. IBE operates in mathematics in the same way as IBE in science. When applied to empirical evidence, IBE sometimes helps to justify the expansion of scientists’ ontological commitments. Analogously, when applied to mathematical evidence, IBE sometimes helps to justify mathematicians' in expanding the range of their ontological commitments. IBE supplements other forms of non-deductive reasoning in mathematics, avoiding (...)
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  • Inference to the Best Explanation - An Overview.Frank Cabrera - 2023 - In Lorenzo Magnani (ed.), Handbook of Abductive Cognition. Springer. pp. 1-34.
    In this article, I will provide a critical overview of the form of non-deductive reasoning commonly known as “Inference to the Best Explanation” (IBE). Roughly speaking, according to IBE, we ought to infer the hypothesis that provides the best explanation of our evidence. In section 2, I survey some contemporary formulations of IBE and highlight some of its putative applications. In section 3, I distinguish IBE from C.S. Peirce’s notion of abduction. After underlining some of the essential elements of IBE, (...)
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  • Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist.Fabio Sterpetti - 2021 - Foundations of Science 27 (3):1073-1105.
    This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the (...)
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  • (1 other version)Mathematical Explanation: A Pythagorean Proposal.Sam Baron - 2024 - British Journal for the Philosophy of Science 75 (3):663-685.
    Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists (...)
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  • An Extra-Mathematical Program Explanation of Color Experience.Nicholas Danne - 2020 - International Studies in the Philosophy of Science 33 (3):153-173.
    In the debate over whether mathematical facts, properties, or entities explain physical events (in what philosophers call “extra-mathematical” explanations), Aidan Lyon’s (2012) affirmative answer stands out for its employment of the program explanation (PE) methodology of Frank Jackson and Philip Pettit (1990). Juha Saatsi (2012; 2016) objects, however, that Lyon’s examples from the indispensabilist literature are (i) unsuitable for PE, (ii) nominalizable into non-mathematical terms, and (iii) mysterious about the explanatory relation alleged to obtain between the PE’s mathematical explanantia and (...)
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  • 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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  • Objectivity in Mathematics, Without Mathematical Objects†.Markus Pantsar - 2021 - Philosophia Mathematica 29 (3):318-352.
    I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...)
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  • The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.Mark Povich - 2021 - British Journal for the Philosophy of Science 72 (2):511-543.
    An account of distinctively mathematical explanation (DME) should satisfy three desiderata: it should account for the modal import of some DMEs; it should distinguish uses of mathematics in explanation that are distinctively mathematical from those that are not (Baron [2016]); and it should also account for the directionality of DMEs (Craver and Povich [2017]). Baron’s (forthcoming) deductive-mathematical account, because it is modelled on the deductive-nomological account, is unlikely to satisfy these desiderata. I provide a counterfactual account of DME, the Narrow (...)
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  • Mathematical Indispensability and Arguments from Design.Silvia Jonas - 2021 - Philosophia 49 (5):2085-2102.
    The recognition of striking regularities in the physical world plays a major role in the justification of hypotheses and the development of new theories both in the natural sciences and in philosophy. However, while scientists consider only strictly natural hypotheses as explanations for such regularities, philosophers also explore meta-natural hypotheses. One example is mathematical realism, which proposes the existence of abstract mathematical entities as an explanation for the applicability of mathematics in the sciences. Another example is theism, which offers the (...)
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  • Unification and mathematical explanation in science.Sam Baron - 2021 - Synthese 199 (3-4):7339-7363.
    Mathematics clearly plays an important role in scientific explanation. Debate continues, however, over the kind of role that mathematics plays. I argue that if pure mathematical explananda and physical explananda are unified under a common explanation within science, then we have good reason to believe that mathematics is explanatory in its own right. The argument motivates the search for a new kind of scientific case study, a case in which pure mathematical facts and physical facts are explanatorily unified. I argue (...)
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  • Du Châtelet on the Need for Mathematics in Physics.Aaron Wells - 2021 - Philosophy of Science 88 (5):1137-1148.
    There is a tension in Emilie Du Châtelet’s thought on mathematics. The objects of mathematics are ideal or fictional entities; nevertheless, mathematics is presented as indispensable for an account of the physical world. After outlining Du Châtelet’s position, and showing how she departs from Christian Wolff’s pessimism about Newtonian mathematical physics, I show that the tension in her position is only apparent. Du Châtelet has a worked-out defense of the explanatory and epistemic need for mathematical objects, consistent with their metaphysical (...)
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  • Mathematics and the world: explanation and representation.John-Hamish Heron - 2017 - Dissertation, King’s College London
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  • Mathematical Representation and Explanation: structuralism, the similarity account, and the hotchpotch picture.Ziren Yang - 2020 - Dissertation, University of Leeds
    This thesis starts with three challenges to the structuralist accounts of applied mathematics. Structuralism views applied mathematics as a matter of building mapping functions between mathematical and target-ended structures. The first challenge concerns how it is possible for a non-mathematical target to be represented mathematically when the mapping functions per se are mathematical objects. The second challenge arises out of inconsistent early calculus, which suggests that mathematical representation does not require rigorous mathematical structures. The third challenge comes from renormalisation group (...)
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  • 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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  • Teleology and Realism in Leibniz's Philosophy of Science.Nabeel Hamid - 2019 - In Vincenzo De Risi (ed.), Leibniz and the Structure of Sciences: Modern Perspectives on the History of Logic, Mathematics, Epistemology. Springer. pp. 271-298.
    This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, (...)
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  • Humeans are out of this world.Erica Shumener - 2021 - Synthese 198 (6):5897-5916.
    I defend the following argument in this paper. Premise 1: Laws of nature are intrinsic to the universe. Premise 2: Humeanism maintains that laws of nature are extrinsic to the universe. Conclusion: Humeanism is false. This argument is inspired by John Hawthorne’s (2004) argument in “Why Humeans are out of their Minds”. My argument differs from his; Hawthorne focuses on Humean views of causation and how they interact with judgments about consciousness. He thinks Humeans are forced to treat certain mental (...)
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  • 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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  • What is Field's Epistemological Objection to Platonism?Ylwa Sjölin Wirling - 2019 - In Robin Stenwall & Tobias Hansson Wahlberg (eds.), Maurinian Truths : Essays in Honour of Anna-Sofia Maurin on her 50th Birthday. Lund, Sverige: Department of Philosophy, Lund University. pp. 123-133.
    This paper concerns an epistemological objection against mathematical platonism, due to Hartry Field.The argument poses an explanatory challenge – the challenge to explain the reliability of our mathematical beliefs – which the platonist, it’s argued, cannot meet. Is the objection compelling? Philosophers disagree, but they also disagree on (and are sometimes very unclear about) how the objection should be understood. Here I distinguish some options, and highlight some gaps that need to be filled in on the potentially most compelling version (...)
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  • Maurinian Truths : Essays in Honour of Anna-Sofia Maurin on her 50th Birthday.Robin Stenwall & Tobias Hansson Wahlberg (eds.) - 2019 - Lund, Sverige: Department of Philosophy, Lund University.
    This book is in honour of Professor Anna-Sofia Maurin on her 50th birthday. It consists of eighteen essays on metaphysical issues written by Swedish and international scholars.
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  • Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
    Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...)
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  • Non-naturalistic moral explanation.Samuel Baron, Mark Colyvan, Kristie Miller & Michael Rubin - 2019 - Synthese 198 (5):4273-4294.
    It has seemed, to many, that there is an important connection between the ways in which some theoretical posits explain our observations, and our reasons for being ontologically committed to those posits. One way to spell out this connection is in terms of what has become known as the explanatory criterion of ontological commitment. This is, roughly, the view that we ought to posit only those entities that are indispensable to our best explanations. Our primary aim is to argue that (...)
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  • 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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  • 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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  • Explaining the behaviour of random ecological networks: the stability of the microbiome as a case of integrative pluralism.Roger Deulofeu, Javier Suárez & Alberto Pérez-Cervera - 2019 - Synthese 198 (3):2003-2025.
    Explaining the behaviour of ecosystems is one of the key challenges for the biological sciences. Since 2000, new-mechanicism has been the main model to account for the nature of scientific explanation in biology. The universality of the new-mechanist view in biology has been however put into question due to the existence of explanations that account for some biological phenomena in terms of their mathematical properties (mathematical explanations). Supporters of mathematical explanation have argued that the explanation of the behaviour of ecosystems (...)
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  • 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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  • Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research.Catalin Barboianu - 2015 - UNLV Gaming Research and Review Journal 19 (1):17-30.
    Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of (...)
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  • 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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  • 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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  • 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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  • 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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  • Realism and the limits of explanatory reasoning.Juha Saatsi - 2017 - In The Routledge Handbook of Scientific Realism. New York: Routledge. pp. 200-211.
    This chapter examines issues surrounding inference to the best explanation, its justification, and its role in different arguments for scientific realism, as well as more general issues concerning explanations’ ontological commitments. Defending the reliability of inference to the best explanation has been a central plank in various realist arguments, and realists have drawn various ontological conclusions from the premise that a given scientific explanation best explains some phenomenon. This chapter stresses the importance of thinking carefully about the nature of explanation (...)
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  • VI—Nominalistic Adequacy.Jeffrey Ketland - 2011 - Proceedings of the Aristotelian Society 111 (2pt2):201-217.
    Instrumentalist nominalism responds to the indispensability arguments by rejecting the demand that successful mathematicized scientific theories be nominalized, and instead claiming merely that such theories are nominalistically adequate: the concreta behave ‘as if’ the theory is true. This article examines some definitions of the concept of nominalistic adequacy and concludes with some considerations against instrumentalist nominalism.
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  • Two Criticisms against Mathematical Realism.Seungbae Park - 2017 - Diametros 52:96-106.
    Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a tricle is true or false. A tricle is an (...)
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  • Fictionalism and mathematical explanations.Pamela Ann Jose Boongaling - 2019 - Filosofia Unisinos 20 (3).
    In this paper, I place Mary Leng’s version of mathematical instrumentalism within the context of the debate in mathematical realism/anti-realism as well as within the context of the platonism/nominalism debate. I maintain that although her position is able to show how the conjunction of Quinean naturalism and confirmational holism does not necessarily lead to the conclusion that mathematical objects must necessarily exist for they are indispensable in our best scientific theories; her usage of both theses still leads to platonism. Such (...)
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  • 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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  • Explanation beyond causation? New directions in the philosophy of scientific explanation.Alexander Reutlinger - 2017 - Philosophy Compass 12 (2):e12395.
    In this paper, I aim to provide access to the current debate on non-causal explanations in philosophy of science. I will first present examples of non-causal explanations in the sciences. Then, I will outline three alternative approaches to non-causal explanations – that is, causal reductionism, pluralism, and monism – and, corresponding to these three approaches, different strategies for distinguishing between causal and non-causal explanation. Finally, I will raise questions for future research on non-causal explanations.
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  • Numerical cognition and mathematical realism.Helen De Cruz - 2016 - Philosophers' Imprint 16.
    Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that they prima (...)
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  • Realismo/Anti-Realismo.Eduardo Castro - 2014 - Compêndio Em Linha de Problemas de Filosofia Analítica.
    State of the art paper on the topic realism/anti-realism. The first part of the paper elucidates the notions of existence and independence of the metaphysical characterization of the realism/anti-realism dispute. The second part of the paper presents a critical taxonomy of the most important positions and doctrines in the contemporary literature on the domains of science and mathematics: scientific realism, scientific anti-realism, constructive empiricism, structural realism, mathematical Platonism, mathematical indispensability, mathematical empiricism, intuitionism, mathematical fictionalism and second philosophy.
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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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