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  1. What is Field's Epistemological Objection to Platonism?Ylwa Sjölin Wirling - 2019 - In Robin Stenwall & Tobias Hansson Wahlberg (eds.), Maurinian Truths. 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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  • Mathematical Surrealism as an Alternative to Easy-Road Fictionalism.Kenneth Boyce - forthcoming - Philosophical Studies.
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  • Evidential Holism.Joe Morrison - 2017 - Philosophy Compass (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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  • 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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  • A Role for Mathematics in the Physical Sciences.Chris Pincock - 2007 - Noûs 41 (2):253-275.
    Conflicting accounts of the role of mathematics in our physical theories can be traced to two principles. Mathematics appears to be both (1) theoretically indispensable, as we have no acceptable non-mathematical versions of our theories, and (2) metaphysically dispensable, as mathematical entities, if they existed, would lack a relevant causal role in the physical world. I offer a new account of a role for mathematics in the physical sciences that emphasizes the epistemic benefits of having mathematics around when we do (...)
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  • Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
    Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss (...)
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  • 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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  • 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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  • Is the Enhanced Indispensability Argument a Useful Tool in the Hands of Platonists?Vladimir Drekalović - 2019 - Philosophia 47 (4):1111-1126.
    Platonists in mathematics endeavour to prove the truthfulness of the proposal about the existence of mathematical objects. However, there have not been many explicit proofs of this proposal. One of the explicit ones is doubtlessly Baker’s Enhanced Indispensability Argument, formulated as a sort of modal syllogism. We aim at showing that the purpose of its creation – the defence of Platonist viewpoint – was not accomplished. Namely, the second premise of the Argument was imprecisely formulated, which gave space for various (...)
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  • The End of Mystery.Sam Baron & Mark Colyvan - 2019 - American Philosophical Quarterly 56 (3):247-264.
    Tim travels back in time and tries to kill his grandfather before his father was born. Tim fails. But why? Lewis's response was to cite "coincidences": Tim is the unlucky subject of gun jammings, banana peels, sudden changes of heart, and so on. A number of challenges have been raised against Lewis's response. The latest of these focuses on explanation. This paper diagnoses the source of this new disgruntlement and offers an alternative explanation for Tim's failure, one that Lewis would (...)
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  • Non-Naturalistic Moral Explanation.Samuel Baron, Mark Colyvan, Kristie Miller & Michael Rubin - forthcoming - Synthese.
    This paper focuses on a particular kind of non-naturalism: moral non-naturalism. Our primary aim is to argue that the moral non-naturalist places herself in an invidious position if she simply accepts that the non-natural moral facts that she posits are not explanatory. This has, hitherto, been the route that moral non-naturalists have taken. They have attempted to make their position more palatable by pointing out that there is reason to be suspicious of the explanatory criterion of ontological commitment. That is (...)
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  • 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 Indispensability-Driven Platonists Be Presentists?Sam Baron - 2014 - Theoria 80 (2):153-173.
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  • Estructuralismo, ficcionalismo, y la aplicabilidad de las matemáticas en ciencia.Manuel Barrantes - 2019 - Areté. Revista de Filosofía 31 (1):7-34.
    “Structuralism, Fictionalism, and the Applicability of Mathematics in Science”. This article has two objectives. The first one is to review some of the most important questions in the contemporary philosophy of mathematics: What is the nature of mathematical objects? How do we acquire knowledge about these objects? Should mathematical statements be interpreted differently than ordinary ones? And, finally, how can we explain the applicability of mathematics in science? The debate that guides these reflections is the one between mathematical realism and (...)
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  • Mathematical Application and the No Confirmation Thesis.Kenneth Boyce - forthcoming - Analysis:anz021.
    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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  • Against Mathematical Convenientism.Seungbae Park - 2016 - Axiomathes 26 (2):115-122.
    Indispensablists argue that when our belief system conflicts with our experiences, we can negate a mathematical belief but we do not because if we do, we would have to make an excessive revision of our belief system. Thus, we retain a mathematical belief not because we have good evidence for it but because it is convenient to do so. I call this view ‘ mathematical convenientism.’ I argue that mathematical convenientism commits the consequential fallacy and that it demolishes the Quine-Putnam (...)
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  • Explanation and Explanationism in Science and Metaphysics.Juha Saatsi - forthcoming - In Matthew Slater & Zanja Yudell (eds.), Metaphysics and the Philosophy of Science: New Essays. Oxford University Press.
    This chapter examines the status of inference to the best explanation in naturalistic metaphysics. The methodology of inference to the best explanation in metaphysics is studied from the perspective of contemporary views on scientific explanation and explanatory inferences in the history and philosophy of science. This reveals serious shortcomings in prevalent attempts to vindicate metaphysical "explanationism" by reference to similarities between science and naturalistic metaphysics. This critique is brought out by considering a common gambit of methodological unity: (1) Both metaphysics (...)
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  • 'Explanatory Indispensability Arguments in Metaethics and Philosophy of Mathematics'.Debbie Roberts - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford University Press.
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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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  • Grounding and the Argument From Explanatoriness.David Kovacs - 2017 - Philosophical Studies 174 (12):2927-2952.
    In recent years, metaphysics has undergone what some describe as a revolution: it has become standard to understand a vast array of questions as questions about grounding, a metaphysical notion of determination. Why should we believe in grounding, though? Supporters of the revolution often gesture at what I call the Argument from Explanatoriness: the notion of grounding is somehow indispensable to a metaphysical type of explanation. I challenge this argument and along the way develop a “reactionary” view, according to which (...)
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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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  • The Unreasonable Effectiveness of Abstract Metaphysics.Daniel Nolan - 2015 - Oxford Studies in Metaphysics 9:61-88.
    In Metaphysics A, Aristotle offers some objections to Plato’s theory of Forms to the effect that Plato’s Forms would not be explanatory in the right way, and seems to suggest that they might even make the explanatory project worse. One interesting historical puzzle is whether Aristotle can avoid these same objections to his own theory of universals. The concerns Aristotle raises are, I think, cousins of contemporary concerns about the usefulness and explanatoriness of abstract objects, some of which have recently (...)
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  • The Directionality of Distinctively Mathematical Explanations.Carl F. Craver & Mark Povich - 2017 - Studies in History and Philosophy of Science Part A 63:31-38.
    In “What Makes a Scientific Explanation Distinctively Mathematical?” (2013b), Lange uses several compelling examples to argue that certain explanations for natural phenomena appeal primarily to mathematical, rather than natural, facts. In such explanations, the core explanatory facts are modally stronger than facts about causation, regularity, and other natural relations. We show that Lange's account of distinctively mathematical explanation is flawed in that it fails to account for the implicit directionality in each of his examples. This inadequacy is remediable in each (...)
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  • Inference to the Best Explanation and Mathematical Realism.Sorin Ioan Bangu - 2008 - Synthese 160 (1):13-20.
    Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.
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  • Inference, Explanation, and Asymmetry.Kareem Khalifa, Jared Millson & Mark Risjord - 2018 - Synthese.
    Explanation is asymmetric: if A explains B, then B does not explain A. Tradition- ally, the asymmetry of explanation was thought to favor causal accounts of explanation over their rivals, such as those that take explanations to be inferences. In this paper, we develop a new inferential approach to explanation that outperforms causal approaches in accounting for the asymmetry of explanation.
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  • The Search of “Canonical” Explanations for the Cerebral Cortex.Alessio Plebe - 2018 - History and Philosophy of the Life Sciences 40 (3):40.
    This paper addresses a fundamental line of research in neuroscience: the identification of a putative neural processing core of the cerebral cortex, often claimed to be “canonical”. This “canonical” core would be shared by the entire cortex, and would explain why it is so powerful and diversified in tasks and functions, yet so uniform in architecture. The purpose of this paper is to analyze the search for canonical explanations over the past 40 years, discussing the theoretical frameworks informing this research. (...)
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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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  • 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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  • Viewing-as Explanations and Ontic Dependence.William D’Alessandro - forthcoming - Philosophical Studies:1-24.
    According to a widespread view in metaphysics and philosophy of science (the “Dependence Thesis”), all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call “viewing-as explanations”, are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren’t supported by ontic dependence relations. Hence the thesis isn’t true in general. The first part of the paper (...)
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  • Explanatory Proofs and Beautiful Proofs.Marc Lange - unknown
    This paper concerns the relation between a proof’s beauty and its explanatory power – that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical practice has long recognized that certain proofs but not others have explanatory power, and this paper (...)
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  • 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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  • Critiques of Minimal Realism.Seungbae Park - 2017 - Problemos 92:102-114.
    Saatsi’s minimal realism holds that science makes theoretical progress. It is designed to get around the pessimistic induction, to fall between scientific realism and instrumentalism, and to explain the success of scientific theories. I raise the following two objections to it. First, it is not clear whether minimal realism lies between realism and instrumentalism, given that minimal realism does not entail instrumentalism. Second, it is not clear whether minimal realism can explain the success of scientific theories, given that it is (...)
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  • Exclusion in Morality.Lei Zhong - 2016 - Grazer Philosophische Studien 93 (2):275-290.
    Recently some philosophers (e.g. Shafer-Landau 2003; Wedgwood 2007) suggest an exclusion problem for moral non-naturalism, which is similar to the exclusion problem in the philosophy of mind. In this paper, I aim to advance the discussion of exclusion in morality by investigating two influential solutions to the exclusion problem: the autonomy solution and the overdetermination solution. I attempt to show that the moral non-naturalist can solve the exclusion problem in a way that is different from the approach to solving mental-physical (...)
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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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  • 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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  • Mathematical Explanation and Indispensability.Vineberg Susan - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):233-247.
    This paper discusses Baker’s Enhanced Indispensability Argument for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use still does not (...)
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  • Indispensability and Explanation.Sorin Bangu - 2013 - British Journal for the Philosophy of Science 64 (2):255-277.
    The question as to whether there are mathematical explanations of physical phenomena has recently received a great deal of attention in the literature. The answer is potentially relevant for the ontology of mathematics; if affirmative, it would support a new version of the indispensability argument for mathematical realism. In this article, I first review critically a few examples of such explanations and advance a general analysis of the desiderata to be satisfied by them. Second, in an attempt to strengthen the (...)
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  • Why Are Normal Distributions Normal?Aidan Lyon - 2014 - British Journal for the Philosophy of Science 65 (3):621-649.
    It is usually supposed that the central limit theorem explains why various quantities we find in nature are approximately normally distributed—people's heights, examination grades, snowflake sizes, and so on. This sort of explanation is found in many textbooks across the sciences, particularly in biology, economics, and sociology. Contrary to this received wisdom, I argue that in many cases we are not justified in claiming that the central limit theorem explains why a particular quantity is normally distributed, and that in some (...)
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  • Complements, Not Competitors: Causal and Mathematical Explanations.Holly Andersen - 2017 - British Journal for the Philosophy of Science:axw023.
    A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka-Volterra equations. There (...)
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  • Are There Genuine Physical Explanations of Mathematical Phenomena?Brdford Skow - 2015 - British Journal for the Philosophy of Science 66 (1):69-93.
    There are lots of arguments for, or justifications of, mathematical theorems that make use of principles from physics. Do any of these constitute explanations? On the one hand, physical principles do not seem like they should be explanatorily relevant; on the other, some particular examples of physical justifications do look explanatory. In this article, I defend the idea that physical justifications can and do explain mathematical facts. 1 Physical Arguments for Mathematical Truths2 Preview3 Mathematical Facts4 Purity5 Doubts about Purity: I6 (...)
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  • What Makes a Scientific Explanation Distinctively Mathematical?Marc Lange - 2013 - British Journal for the Philosophy of Science 64 (3):485-511.
    Certain scientific explanations of physical facts have recently been characterized as distinctively mathematical –that is, as mathematical in a different way from ordinary explanations that employ mathematics. This article identifies what it is that makes some scientific explanations distinctively mathematical and how such explanations work. These explanations are non-causal, but this does not mean that they fail to cite the explanandum’s causes, that they abstract away from detailed causal histories, or that they cite no natural laws. Rather, in these explanations, (...)
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  • The Enhanced Indispensability Argument: Representational Versus Explanatory Role of Mathematics in Science.Juha Saatsi - 2011 - British Journal for the Philosophy of Science 62 (1):143-154.
    The Enhanced Indispensability Argument (Baker [ 2009 ]) exemplifies the new wave of the indispensability argument for mathematical Platonism. The new wave capitalizes on mathematics' role in scientific explanations. I will criticize some analyses of mathematics' explanatory function. In turn, I will emphasize the representational role of mathematics, and argue that the debate would significantly benefit from acknowledging this alternative viewpoint to mathematics' contribution to scientific explanations and knowledge.
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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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  • Deductive Nomological Model and Mathematics: Making Dissatisfaction More Satisfactory.Daniele Molinini - 2014 - Theoria : An International Journal for Theory, History and Fundations of Science 29 (2):223-241.
    The discussion on mathematical explanation has inherited the same sense of dissatisfaction that philosophers of science expressed, in the context of scientific explanation, towards the deductive-nomological model. This model is regarded as unable to cover cases of bona fide mathematical explanations and, furthermore, it is largely ignored in the relevant literature. Surprisingly, the reasons for this ostracism are not sufficiently manifest. In this paper I explore a possible extension of the model to the case of mathematical explanations and I claim (...)
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  • Animal Cognition, Species Invariantism, and Mathematical Realism.Helen De Cruz - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 39-61.
    What can we infer from numerical cognition about mathematical realism? In this paper, I will consider one aspect of numerical cognition that has received little attention in the literature: the remarkable similarities of numerical cognitive capacities across many animal species. This Invariantism in Numerical Cognition (INC) indicates that mathematics and morality are disanalogous in an important respect: proto-moral beliefs differ substantially between animal species, whereas proto-mathematical beliefs (at least in the animals studied) seem to show more similarities. This makes moral (...)
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  • Mathematical Narratives.James Robert Brown - 2014 - European Journal of Analytic Philosophy 10 (2):59-73.
    Philosophers and mathematicians have different ideas about the difference between pure and applied mathematics. This should not surprise us, since they have different aims and interests. For mathematicians, pure mathematics is the interesting stuff, even if it has lots of physics involved. This has the consequence that picturesque examples play a role in motivating and justifying mathematical results. Philosophers might find this upsetting, but we find a parallel to mathematician’s attitudes in ethics, which, I argue, is a much better model (...)
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  • The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.Mark Povich - 2019 - British Journal for the Philosophy of Science:axz008.
    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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  • 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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  • 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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  • Beauty Is Not All There Is to Aesthetics in Mathematics.R. S. D. Thomas - forthcoming - Philosophia Mathematica:nkw019.
    Aesthetics in philosophy of mathematics is too narrowly construed. Beauty is not the only feature in mathematics that is arguably aesthetic. While not the highest aesthetic value, being interesting is a sine qua non for publishability. Of the many ways to be interesting, being explanatory has recently been discussed. The motivational power of what is interesting is important for both directing research and stimulating education. The scientific satisfaction of curiosity and the artistic desire for beautiful results are complementary but both (...)
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