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.
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163 found
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  1. Mathematical Explanations of Physical Phenomena.Sorin Bangu - forthcoming - Tandf: Australasian Journal of Philosophy:1-14.
    Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to re-focus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.
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  2. Are Infinite Explanations Self-Explanatory?Alexandre Billon - forthcoming - Erkenntnis:1-20.
    Consider an infinite series whose items are each explained by their immediate successor. Does such an infinite explanation explain the whole series or does it leave something to be explained? Hume arguably claimed that it does fully explain the whole series. Leibniz, however, designed a very telling objection against this claim, an objection involving an infinite series of book copies. In this paper, I argue that the Humean claim can, in certain cases, be saved from the Leibnizian “infinite book copies” (...)
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  3. Topological Explanations: An Opinionated Appraisal.Daniel Kostić - forthcoming - In I. Lawler, E. Shech & K. Khalifa (eds.), Scientific Understanding and Representation: Modeling in the Physical Sciences.
    This chapter provides a systematic overview of topological explanations in the philosophy of science literature. It does so by presenting an account of topological explanation that I (Kostić and Khalifa 2021; Kostić 2020a; 2020b; 2018) have developed in other publications and then comparing this account to other accounts of topological explanation. Finally, this appraisal is opinionated because it highlights some problems in alternative accounts of topological explanations, and also it outlines responses to some of the main criticisms raised by the (...)
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  4. Decoupling Topological Explanations From Mechanisms.Daniel Kostic & Kareem Khalifa - forthcoming - Philosophy of Science:1-39.
    We provide three innovations to recent debates about whether topological or “network” explanations are a species of mechanistic explanation. First, we more precisely characterize the requirement that all topological explanations are mechanistic explanations and show scientific practice to belie such a requirement. Second, we provide an account that unifies mechanistic and non-mechanistic topological explanations, thereby enriching both the mechanist and autonomist programs by highlighting when and where topological explanations are mechanistic. Third, we defend this view against some powerful mechanist objections. (...)
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  5. A Scheme Foiled: A Critique of Baron's Account of Extra-Mathematical Explanation.Mark Povich - forthcoming - Mind.
    Extra-mathematical explanations explain natural phenomena primarily by appeal to mathematical facts. Philosophers disagree about whether there are extra-mathematical explanations, the correct account of them if they exist, and their implications (e.g., for the philosophy of scientific explanation and for the metaphysics of mathematics) (Baker 2005, 2009; Bangu 2008; Colyvan 1998; Craver and Povich 2017; Lange 2013, 2016, 2018; Mancosu 2008; Povich 2019, 2020; Steiner 1978). In this discussion note, I present three desiderata for any account of extra-mathematical explanation and argue (...)
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  6. 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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  7. Înțelegerea lumii cu ajutorul matematicii.Gabriel Târziu - 2022 - Iași, Romania: Editura Universităţii „Alexandru Ioan Cuza”.
    Această carte face parte dintr-un curent recent din filosofia analitică de preocupare cu rolul matematicii în știință și se vrea a fi o contribuție la discuția filosofică recentă despre valoarea explicativă a matematicii în știință și despre contribuția acesteia la înțelegerea naturii. Obiectivul principal al cărții este prezentarea unei teorii filosofice cu privire la felul în care matematica poate contribui la înțelegerea fenomenelor naturii fără a juca un rol explicativ în raport cu acestea.
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  8. 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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  9. A Dilemma for Mathematical Constructivism.Samuel Kahn - 2021 - Axiomathes 31 (1):63-72.
    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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  10. A New Role for Mathematics in Empirical Sciences.Atoosa Kasirzadeh - 2021 - Philosophy of Science 88 (4):686-706.
    Mathematics is often taken to play one of two roles in the empirical sciences: either it represents empirical phenomena or it explains these phenomena by imposing constraints on them. This article identifies a third and distinct role that has not been fully appreciated in the literature on applicability of mathematics and may be pervasive in scientific practice. I call this the “bridging” role of mathematics, according to which mathematics acts as a connecting scheme in our explanatory reasoning about why and (...)
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  11. The Directionality of Topological Explanations.Daniel Kostić & Kareem Khalifa - 2021 - Synthese (5-6):14143-14165.
    Proponents of ontic conceptions of explanation require all explanations to be backed by causal, constitutive, or similar relations. Among their justifications is that only ontic conceptions can do justice to the ‘directionality’ of explanation, i.e., the requirement that if X explains Y , then not-Y does not explain not-X . Using topological explanations as an illustration, we argue that non-ontic conceptions of explanation have ample resources for securing the directionality of explanations. The different ways in which neuroscientists rely on multiplexes (...)
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  12. Mathematicians’ Assessments of the Explanatory Value of Proofs.Juan Pablo Mejía Ramos, Tanya Evans, Colin Rittberg & Matthew Inglis - 2021 - Axiomathes 31 (5):575-599.
    The literature on mathematical explanation contains numerous examples of explanatory, and not so explanatory proofs. In this paper we report results of an empirical study aimed at investigating mathematicians’ notion of explanatoriness, and its relationship to accounts of mathematical explanation. Using a Comparative Judgement approach, we asked 38 mathematicians to assess the explanatory value of several proofs of the same proposition. We found an extremely high level of agreement among mathematicians, and some inconsistencies between their assessments and claims in the (...)
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  13. Idealizations and Analogies: Explaining Critical Phenomena.Quentin Rodriguez - 2021 - Studies in History and Philosophy of Science Part A 89:235-247.
    The “universality” of critical phenomena is much discussed in philosophy of scientific explanation, idealizations and philosophy of physics. Lange and Reutlinger recently opposed Batterman concerning the role of some deliberate distortions in unifying a large class of phenomena, regardless of microscopic constitution. They argue for an essential explanatory role for “commonalities” rather than that of idealizations. Building on Batterman's insight, this article aims to show that assessing the differences between the universality of critical phenomena and two paradigmatic cases of “commonality (...)
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  14. Non-Causal Explanations in Physics.Juha Saatsi - 2021 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. Routledge.
  15. Mathematical Anti-Realism and Explanatory Structure.Bruno Whittle - 2021 - Synthese 199 (3-4):6203-6217.
    Plausibly, mathematical claims are true, but the fundamental furniture of the world does not include mathematical objects. This can be made sense of by providing mathematical claims with paraphrases, which make clear how the truth of such claims does not require the fundamental existence of mathematical objects. This paper explores the consequences of this type of position for explanatory structure. There is an apparently straightforward relationship between this sort of structure, and the logical sort: i.e. logically complex claims are explained (...)
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  16. 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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  17. 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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  18. General Theory of Topological Explanations and Explanatory Asymmetry.Daniel Kostic - 2020 - Philosophical Transactions of the Royal Society B: Biological Sciences 375 (1796):1-8.
    In this paper, I present a general theory of topological explanations, and illustrate its fruitfulness by showing how it accounts for explanatory asymmetry. My argument is developed in three steps. In the first step, I show what it is for some topological property A to explain some physical or dynamical property B. Based on that, I derive three key criteria of successful topological explanations: a criterion concerning the facticity of topological explanations, i.e. what makes it true of a particular system; (...)
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  19. Plurality of Explanatory Strategies in Biology: Mechanisms and Networks.Alvaro Moreno & Javier Suárez - 2020 - In Methodological Prospects for Scientific Research. pp. 141-165.
    Recent research in philosophy of science has shown that scientists rely on a plurality of strategies to develop successful explanations of different types of phenomena. In the case of biology, most of these strategies go far beyond the traditional and reductionistic models of scientific explanation that have proven so successful in the fundamental sciences. Concretely, in the last two decades, philosophers of science have discovered the existence of at least two different types of scientific explanation at work in the biological (...)
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  20. Modality and constitution in distinctively mathematical explanations.Mark Povich - 2020 - European Journal for Philosophy of Science 10 (3):1-10.
    Lange argues that some natural phenomena can be explained by appeal to mathematical, rather than natural, facts. In these “distinctively mathematical” explanations, 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 argue that Lange’s account of DME fails to exclude certain “reversals”. Lange has replied that his account can avoid these directionality charges. Specifically, Lange argues that in legitimate DMEs, (...)
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  21. Was bedeuten Parakonsistente, Unentscheidbar, Zufällig, Berechenbar und Unvollständige? Eine Rezension von „Godels Weg: Exploits in eine unentscheidbare Welt“ (Godels Way: Exploits into a unecidable world) von Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160p (2012).Michael Richard Starks - 2020 - In Willkommen in der Hölle auf Erden: Babys, Klimawandel, Bitcoin, Kartelle, China, Demokratie, Vielfalt, Dysgenie, Gleichheit, Hacker, Menschenrechte, Islam, Liberalismus, Wohlstand, Internet, Chaos, Hunger, Krankheit, Gewalt, Künstliche Intelligenz, Krieg. Las Vegas, NV , USA: Reality Press. pp. 1171-185.
    In "Godel es Way" diskutieren drei namhafte Wissenschaftler Themen wie Unentschlossenheit, Unvollständigkeit, Zufälligkeit, Berechenbarkeit und Parakonsistenz. Ich gehe diese Fragen aus Wittgensteiner Sicht an, dass es zwei grundlegende Fragen gibt, die völlig unterschiedliche Lösungen haben. Es gibt die wissenschaftlichen oder empirischen Fragen, die Fakten über die Welt sind, die beobachtungs- und philosophische Fragen untersuchen müssen, wie Sprache verständlich verwendet werden kann (die bestimmte Fragen in Mathematik und Logik beinhalten), die entschieden werden müssen, indem man sich anschaut,wie wir Wörter in bestimmten (...)
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  22. 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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  23. 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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  24. 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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  25. 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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  26. 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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  27. Shades of Grey: Granularity, Pragmatics, and Non-Causal Explanation.Hugh Desmond - 2019 - Perspectives on Science 27 (1):68-87.
    Implicit contextual factors mean that the boundary between causal and noncausal explanation is not as neat as one might hope: as the phenomenon to be explained is given descriptions with varying degrees of granularity, the nature of the favored explanation alternates between causal and non-causal. While it is not surprising that different descriptions of the same phenomenon should favor different explanations, it is puzzling why re-describing the phenomenon should make any difference for the causal nature of the favored explanation. I (...)
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  28. 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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  29. 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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  30. 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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  31. Unifying the Debates: Mathematical and Non-Causal Explanations.Daniel Kostić - 2019 - Perspectives on Science 27 (1):1-6.
  32. Using Corpus Linguistics to Investigate Mathematical Explanation.Juan Pablo Mejía Ramos, Lara Alcock, Kristen Lew, Paolo Rago, Chris Sangwin & Matthew Inglis - 2019 - In Eugen Fischer & Mark Curtis (eds.), Methodological Advances in Experimental Philosophy. London: Bloomsbury Academic. pp. 239–263.
    In this chapter we use methods of corpus linguistics to investigate the ways in which mathematicians describe their work as explanatory in their research papers. We analyse use of the words explain/explanation (and various related words and expressions) in a large corpus of texts containing research papers in mathematics and in physical sciences, comparing this with their use in corpora of general, day-to-day English. We find that although mathematicians do use this family of words, such use is considerably less prevalent (...)
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  33. 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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  34. The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.Mark Povich - 2019 - 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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  35. ¿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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  36. 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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  37. 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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  38. 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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  39. 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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  40. 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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  41. Because Without Cause: Non-Causal Explanations in Science and Mathematics, by Marc Lange. [REVIEW]Holly Andersen - 2018 - Mind 127 (506):593-602.
    Because Without Cause: Non-Causal Explanations in Science and Mathematics, by Lange Marc. Oxford: Oxford University Press, 2017. Pp. xxii + 489.
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  42. 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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  43. 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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  44. Mechanisms Meet Structural Explanation.Laura Felline - 2018 - Synthese 195 (1):99-114.
    This paper investigates the relationship between structural explanation and the New Mechanistic account of explanation. The aim of this paper is twofold: firstly, to argue that some phenomena in the domain of fundamental physics, although mechanically brute, are structurally explained; and secondly, by elaborating on the contrast between SE and mechanistic explanation to better clarify some features of SE. Finally, this paper will argue that, notwithstanding their apparently antithetical character, SE and ME can be reconciled within a unified account of (...)
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  45. 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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  46. Tuples All the Way Down?Simon Thomas Hewitt - 2018 - Thought: A Journal of Philosophy 7 (3):161-169.
  47. 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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  48. Because Without Cause: Non-Causal Explanations in Science and Mathematics. [REVIEW]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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  49. 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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  50. 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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