About this topic
Summary

Mathematical explanations are explanations in which mathematics plays a fundamental role. The expression ‘mathematical explanation’ (ME) has two distinct, although connected, meanings: in relation to pure mathematics ME denotes proofs that are able not only to demonstrate the truth of a given mathematical statement, but also to explain why the statement is true, whereas in connection with empirical sciences ME refers to explanations of non-mathematical facts (physical, biological, social, psychological) justified by recourse to mathematics. 

Although the concept of ME has been the subject of analysis at least since Aristotle’s distinction between apodeixis tou oti and apodeixis tou dioti (Post. An. I.13), and has been dealt with a few times over the course of the development of Western thought (e.g. Descartes, Newton, and Bolzano), it is only since the 1970s that an intense philosophical debate has sprung up regarding the nature of ME. This debate, linked to the gradual diffusion of Quinean epistemology (Steiner 1978) and the development of the anti-foundationalist philosophy of mathematics (the so-called ‘maverick’ tradition, Cellucci 2008), centers on the following questions: Do mathematical explanations exist? If mathematical explanations exist, can they be reduced to a single model or are they heterogeneous among themselves? What implications does the comprehension of the concept of mathematical explanation have for some of the most important problems of the contemporary philosophy of science (e.g. indispensability arguments, inference to the best explanation, and the theory of scientific explanation)? 

Key works

The key works about mathematical explanation within mathematics are Steiner 1978 (for criticisms of the model proposed by Steiner see Resnik & Kushner 1987, Weber & Verhoeven 2002, and Mancosu & JØrgensen 2006), Kitcher 1983, and Kitcher 1989 (a careful analysis of the limitations of the model proposed by Kitcher can be found in Mancosu & Hafner 2008). Regarding the notion of mathematical explanation in natural sciences, see Batterman 2001, Baker 2005, Pincock 2007, and Baker 2009.

Introductions For  general overviews on the subject, see Mancosu 2011Pincock & Mancosu 2012, and Molinini 2014.
Related categories

123 found
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  1. added 2020-05-05
    The Role of Mathematical Tools in Scientific Phenomenon Explanation–A Guarantee of Reliability or a Pillar of False Credibility?Vladimir Drekalović - 2020 - Filosofija. Sociologija 31 (1).
    Ever since its beginnings, mathematics has occupied a special position among all sciences, natural, as well as social sciences and humanities. It has not only provided a role model in terms of methodology, particularly when it comes to natural sciences, but other sciences have always relied on mathematics extensively both in their development and for solving various open questions. The beginning of the 21st century foregrounded the issue of the so-called explanatory role of mathematics in science. However, the reference literature (...)
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  2. added 2020-04-30
    Modality and Constitution in Distinctively Mathematical Explanations.Mark Povich - forthcoming - European Journal for Philosophy of Science.
    Lange (2013; 2016) argues that some natural phenomena can be explained by appeal to mathematical, rather than natural, facts. In these “distinctively mathematical” explanations (DMEs), the core explanatory facts are either modally stronger than facts about ordinary causal law or understood to be constitutive of the physical task or arrangement at issue. Craver and Povich (2017) argue that Lange’s account of DME fails to exclude certain “reversals”. Lange (forthcoming) has replied that his account can avoid these directionality charges. Specifically, Lange (...)
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  3. added 2020-02-04
    A Dilemma for Mathematical Constructivism.Samuel Kahn - 2020 - Axiomathes:01-10.
    In this paper I argue that constructivism in mathematics faces a dilemma. In particular, I maintain that constructivism is unable to explain (i) the application of mathematics to nature and (ii) the intersubjectivity of mathematics unless (iii) it is conjoined with two theses that reduce it to a form of mathematical Platonism. The paper is divided into five sections. In the first section of the paper, I explain the difference between mathematical constructivism and mathematical Platonism and I outline my argument. (...)
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  4. added 2019-12-21
    O que significa paraconsistente, indecível, aleatório, computável e incompleto?- Uma revisão da ‘Godel’s Way: exploits into an undecidable world’ (Maneira de Godel: façanhas em um mundo indecidível) por Gregory Chaitin, Francisco A Doria, Newton C.A. da costa 160P (2012) (revisão revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 168-182.
    Em "Godel's Way", três cientistas eminentes discutem questões como a undecidability, incompletude, aleatoriedade, computabilidade e paraconsistência. Eu abordar estas questões do ponto de vista Wittgensteinian que existem duas questões básicas que têm soluções completamente diferentes. Há as questões científicas ou empíricas, que são fatos sobre o mundo que precisam ser investigados observacionalmente e questões filosóficas sobre como a linguagem pode ser usada inteligìvelmente (que incluem certas questões em matemática e lógica), que precisam ser decidido por olhar uma como nós realmente (...)
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  5. added 2019-11-29
    Wolpert, Chaitin y Wittgenstein sobre la imposibilidad, la incompletitud, la paradoja mentirosa, el teísmo, los límites de la computación, un principio de incertidumbre mecánica no cuántica y el universo como computadora, el teorema definitivo en la teoría de la máquina de Turing (revisado en 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 64-70.
    It is commonly thought that Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were mostly resolved by Wittgenstein over 80years ago. -/- “What we are ‘tempted to say’ in such a case is, of course, not philosophy, but it is its raw material. Thus, for example, what a mathematician is (...)
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  6. added 2019-11-29
    ¿Qué significa paraconsistente, indescifrable, aleatorio, computable e incompleto? Una revisión de la Manera de Godel: explota en un mundo indecible (Godel’s Way: exploits into an undecidable world) por Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160P (2012) (revisión revisada 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 44-63.
    En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paraconsistencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...)
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  7. added 2019-11-15
    Counterfactual Scheming.Sam Baron - 2020 - Mind 129 (514):535-562.
    Mathematics appears to play a genuine explanatory role in science. But how do mathematical explanations work? Recently, a counterfactual approach to mathematical explanation has been suggested. I argue that such a view fails to differentiate the explanatory uses of mathematics within science from the non-explanatory uses. I go on to offer a solution to this problem by combining elements of the counterfactual theory of explanation with elements of a unification theory of explanation. The result is a theory according to which (...)
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  8. added 2019-11-15
    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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  9. added 2019-11-15
    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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  10. added 2019-08-27
    اظهارات در مورد عدم امکان ، بی کامل بودن ، پاراستشتها، Undecidability ، اتفاقی ، Computability ، پارادوکس ، و عدم قطعیت در Chaitin ، ویتگنشتاین ، Hofstadter ، Wolpert ، doria ، دا کوستا ، گودل ، سرل ، رودیچ ، برتو ، فلوید ، مویال-شرراک و یانفسکی.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    معمولا تصور می شود که عدم امکان ، بی کامل بودن ، پارامونشتها ، Undecidability ، اتفاقی ، قابلیت های مختلف ، پارادوکس ، عدم قطعیت و محدودیت های دلیل ، مسائل فیزیکی و ریاضی علمی و یا با داشتن کمی یا هیچ چیز در مشترک. من پیشنهاد می کنم که آنها تا حد زیادی مشکلات فلسفی استاندارد (به عنوان مثال ، بازی های زبان) که عمدتا توسط ویتگنشتاین بیش از 80 سال پیش حل و فصل شد. -/- "آنچه ما (...)
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  11. added 2019-08-09
    Teaching and Learning Guide For: Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".
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  12. added 2019-08-06
    Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...)
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  13. added 2019-07-24
    Non-Causal Explanations in Physics.Juha Saatsi - forthcoming - In Eleanor Knox & Alastair Wilson (eds.), Routledge Companion to the Philosophy of Physics. Routledge.
  14. added 2019-07-18
    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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  15. added 2019-06-13
    Universality Caused: The Case of Renormalization Group Explanation.Emily Sullivan - 2019 - European Journal for Philosophy of Science 9 (3):36.
    Recently, many have argued that there are certain kinds of abstract mathematical explanations that are noncausal. In particular, the irrelevancy approach suggests that abstracting away irrelevant causal details can leave us with a noncausal explanation. In this paper, I argue that the common example of Renormalization Group explanations of universality used to motivate the irrelevancy approach deserves more critical attention. I argue that the reasons given by those who hold up RG as noncausal do not stand up to critical scrutiny. (...)
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  16. added 2019-06-12
    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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  17. added 2019-06-05
    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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  18. added 2019-05-28
    The Enhanced Indispensability Argument, the Circularity Problem, and the Interpretability Strategy.Jan Heylen & Lars Arthur Tump - forthcoming - Synthese:1-13.
    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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  19. added 2019-04-26
    Reconstruction in Philosophy of Mathematics.Davide Rizza - 2018 - Dewey Studies 2 (2):31-53.
    Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...)
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  20. added 2019-03-30
    Explanation in Mathematical Conversations: An Empirical Investigation.Alison Pease, Andrew Aberdein & Ursula Martin - 2019 - Philosophical Transactions of the Royal Society A 377.
    Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, the other on a random sample of comments lacking (...)
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  21. added 2019-03-21
    Understanding Does Not Depend on (Causal) Explanation.Philippe Verreault-Julien - 2019 - European Journal for Philosophy of Science 9 (2):18.
    One can find in the literature two sets of views concerning the relationship between understanding and explanation: that one understands only if 1) one has knowledge of causes and 2) that knowledge is provided by an explanation. Taken together, these tenets characterize what I call the narrow knowledge account of understanding. While the first tenet has recently come under severe attack, the second has been more resistant to change. I argue that we have good reasons to reject it on the (...)
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  22. added 2019-03-15
    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 - forthcoming - Synthese:1-23.
    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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  23. added 2019-03-08
    Because Without Cause: Non-Causal Explanations in Science and Mathematics.Mark Povich & Carl F. Craver - 2018 - Philosophical Review 127 (3):422-426.
    Lange’s collection of expanded, mostly previously published essays, packed with numerous, beautiful examples of putatively non-causal explanations from biology, physics, and mathematics, challenges the increasingly ossified causal consensus about scientific explanation, and, in so doing, launches a new field of philosophic investigation. However, those who embraced causal monism about explanation have done so because appeal to causal factors sorts good from bad scientific explanations and because the explanatory force of good explanations seems to derive from revealing the relevant causal (or (...)
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  24. added 2019-02-22
    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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  25. added 2019-02-22
    Minimal Models and the Generalized Ontic Conception of Scientific Explanation.Mark Povich - 2018 - British Journal for the Philosophy of Science 69 (1):117-137.
    Batterman and Rice ([2014]) argue that minimal models possess explanatory power that cannot be captured by what they call ‘common features’ approaches to explanation. Minimal models are explanatory, according to Batterman and Rice, not in virtue of accurately representing relevant features, but in virtue of answering three questions that provide a ‘story about why large classes of features are irrelevant to the explanandum phenomenon’ ([2014], p. 356). In this article, I argue, first, that a method (the renormalization group) they propose (...)
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  26. added 2018-11-15
    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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  27. added 2018-08-31
    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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  28. added 2018-08-31
    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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  29. added 2018-04-30
    Tuples All the Way Down?Simon Thomas Hewitt - 2018 - Thought: A Journal of Philosophy 7 (3):161-169.
  30. added 2018-03-13
    Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations.Alexander Reutlinger & Juha Saatsi (eds.) - 2018 - Oxford University Press.
    Explanations are very important to us in many contexts: in science, mathematics, philosophy, and also in everyday and juridical contexts. But what is an explanation? In the philosophical study of explanation, there is long-standing, influential tradition that links explanation intimately to causation: we often explain by providing accurate information about the causes of the phenomenon to be explained. Such causal accounts have been the received view of the nature of explanation, particularly in philosophy of science, since the 1980s. However, philosophers (...)
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  31. added 2018-03-01
    Problemas para a Explicação Matemática.Eduardo Castro - 2017 - Revista Portuguesa de Filosofia 73 (3-4):1437-1462.
    Mathematical proofs aim to establish the truth of mathematical propositions by means of logical rules. Some recent literature in philosophy of mathematics alleges that some mathematical proofs also reveal why the proved mathematical propositions are true. These mathematical proofs are called explanatory mathematical proofs. In this paper, I present and discuss some salient problems around mathematical explanation: the existence problem, the normative problem, the explanandum problems of truth value and psychological value, the logical structure problem, the regress problem and the (...)
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  32. added 2018-02-25
    Symmetries and Explanatory Dependencies in Physics.Steven French & Juha Saatsi - 2018 - In Alexander Reutlinger & Juha Saatsi (eds.), Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations. Oxford: Oxford University Press. pp. 185-205.
    Many important explanations in physics are based on ideas and assumptions about symmetries, but little has been said about the nature of such explanations. This chapter aims to fill this lacuna, arguing that various symmetry explanations can be naturally captured in the spirit of the counterfactual-dependence account of Woodward, liberalized from its causal trappings. From the perspective of this account symmetries explain by providing modal information about an explanatory dependence, by showing how the explanandum would have been different, had the (...)
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  33. added 2018-02-23
    On Explanations From 'Geometry of Motion'.Juha Saatsi - 2018 - British Journal for the Philosophy of Science 69 (1):253–273.
    This paper examines explanations that turn on non-local geometrical facts about the space of possible configurations a system can occupy. I argue that it makes sense to contrast such explanations from ‘geometry of motion’ with causal explanations. I also explore how my analysis of these explanations cuts across the distinction between kinematics and dynamics.
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  34. added 2018-02-17
    Mathematical Explanations of the Rainbow.Christopher Pincock - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (1):13-22.
    Explanations of three different aspects of the rainbow are considered. The highly mathematical character of these explanations poses some interpretative questions concerning what the success of these explanations tells us about rainbows. I develop a proposal according to which mathematical explanations can highlight what is relevant about a given phenomenon while also indicating what is irrelevant to that phenomenon. This proposal is related to the extensive work by Batterman on asymptotic explanation with special reference to Batterman’s own discussion of the (...)
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  35. added 2017-12-31
    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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  36. added 2017-10-21
    Explanation of Molecular Processes Without Tracking Mechanism Operation.Ingo Brigandt - 2018 - Philosophy of Science 85 (5):984–997.
    Philosophical discussions of systems biology have enriched the notion of mechanistic explanation by pointing to the role of mathematical modeling. However, such accounts still focus on explanation in terms of tracking a mechanism's operation across time (by means of mental or computational simulation). My contention is that there are explanations of molecular systems where the explanatory understanding does not consist in tracking a mechanism's operation and productive continuity. I make this case by a discussion of bifurcation analysis in dynamical systems, (...)
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  37. added 2017-10-16
    Taking Reductionism to the Limit: How to Rebut the Antireductionist Argument From Infinite Limits.Juha Saatsi & Alexander Reutlinger - 2017 - Philosophy of Science (3):455-482.
    This paper analyses the anti-reductionist argument from renormalisation group explanations of universality, and shows how it can be rebutted if one assumes that the explanation in question is captured by the counterfactual dependence account of explanation.
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  38. added 2017-10-06
    Inertia, the Communication of Motion, and Kant's Third Law of Mechanics.Howard Duncan - 1984 - Philosophy of Science 51 (1):93-119.
    In Kant's Metaphysical Foundations of Natural Science are found a dynamist reduction of matter and an account of the communication of motion by impact. One would expect to find an analysis of the causal mechanism involved in the communication of motion between bodies given in terms of the fundamental dynamical nature of bodies. However, Kant's analysis, as given in the discussion of his third law of mechanics (an action-reaction law) is purely kinematical, invoking no causal mechanisms at all, let alone (...)
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  39. added 2017-09-18
    Non-Causal Understanding with Economic Models: The Case of General Equilibrium.Philippe Verreault-Julien - 2017 - Journal of Economic Methodology 24 (3):297-317.
    How can we use models to understand real phenomena if models misrepresent the very phenomena we seek to understand? Some accounts suggest that models may afford understanding by providing causal knowledge about phenomena via how-possibly explanations. However, general equilibrium models, for example, pose a challenge to this solution since their contribution appears to be purely mathematical results. Despite this, practitioners widely acknowledge that it improves our understanding of the world. I argue that the Arrow–Debreu model provides a mathematical how-possibly explanation (...)
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  40. added 2017-07-19
    Was Regression to the Mean Really the Solution to Darwin’s Problem with Heredity?: Essay Review of Stigler, Stephen M. 2016. The Seven Pillars of Statistical Wisdom. Cambridge, Massachusetts: Harvard University Press. [REVIEW]Adam Krashniak & Ehud Lamm - 2017 - Biology and Philosophy (5):1-10.
    Statistical reasoning is an integral part of modern scientific practice. In The Seven Pillars of Statistical Wisdom Stephen Stigler presents seven core ideas, or pillars, of statistical thinking and the historical developments of each of these pillars, many of which were concurrent with developments in biology. Here we focus on Stigler’s fifth pillar, regression, and his discussion of how regression to the mean came to be thought of as a solution to a challenge for the theory of natural selection. Stigler (...)
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  41. added 2017-05-21
    Arithmetic, Set Theory, Reduction and Explanation.William D’Alessandro - 2018 - Synthese 195 (11):5059-5089.
    Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...)
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  42. added 2017-01-20
    The Varieties of Mathematical Explanation.Hafner Johannes & Paolo Mancosu - 2005 - In Paolo Mancosu (ed.), Visualization, Explanation and Reasoning Styles in Mathematics. Dordrecht: Springer. pp. 215-250.
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  43. added 2016-12-08
    Mathematics and Scientific Representation.Christopher Pincock - 2012 - Oxford University Press USA.
    Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a (...)
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  44. added 2016-10-25
    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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  45. added 2016-09-21
    Abstract Versus Causal Explanations?Reutlinger Alexander & Andersen Holly - 2016 - International Studies in the Philosophy of Science 30 (2):129-146.
    In the recent literature on causal and non-causal scientific explanations, there is an intuitive assumption according to which an explanation is non-causal by virtue of being abstract. In this context, to be ‘abstract’ means that the explanans in question leaves out many or almost all causal microphysical details of the target system. After motivating this assumption, we argue that the abstractness assumption, in placing the abstract and the causal character of an explanation in tension, is misguided in ways that are (...)
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  46. added 2016-09-05
    Explanatory Abstractions.Lina Jansson & Juha Saatsi - 2019 - British Journal for the Philosophy of Science 70 (3):817–844.
    A number of philosophers have recently suggested that some abstract, plausibly non-causal and/or mathematical, explanations explain in a way that is radically dif- ferent from the way causal explanation explain. Namely, while causal explanations explain by providing information about causal dependence, allegedly some abstract explanations explain in a way tied to the independence of the explanandum from the microdetails, or causal laws, for example. We oppose this recent trend to regard abstractions as explanatory in some sui generis way, and argue (...)
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  47. added 2016-07-20
    Does the Counterfactual Theory of Explanation Apply to Non-Causal Explanations in Metaphysics?Alexander Reutlinger - 2016 - European Journal for Philosophy of Science:1-18.
    In the recent philosophy of explanation, a growing attention to and discussion of non-causal explanations has emerged, as there seem to be compelling examples of non-causal explanations in the sciences, in pure mathematics, and in metaphysics. I defend the claim that the counterfactual theory of explanation (CTE) captures the explanatory character of both non-causal scientific and metaphysical explanations. According to the CTE, scientific and metaphysical explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum and the explanans. I (...)
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  48. added 2015-11-21
    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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  49. added 2015-11-18
    Review of Daniele Molinini, Che cos'è una spiegazione matematica. [REVIEW]Gianluca Longa - 2016 - Lo Sguardo. Rivista di Filosofia 20:325-327.
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  50. added 2015-10-29
    Unification and Explanation: A Case Study From Real Algebraic Geometry.Paolo Mancosu & Johannes Hafner - 2008 - In The Philosophy of Mathematical Practice. Oxford University Press. pp. 151--178.
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