Results for 'Philosophy Mathematics'

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  1. Mathematical Modeling in Biology: Philosophy and Pragmatics.Rasmus Grønfeldt Winther - 2012 - Frontiers in Plant Evolution and Development 2012:1-3.
    Philosophy can shed light on mathematical modeling and the juxtaposition of modeling and empirical data. This paper explores three philosophical traditions of the structure of scientific theory—Syntactic, Semantic, and Pragmatic—to show that each illuminates mathematical modeling. The Pragmatic View identifies four critical functions of mathematical modeling: (1) unification of both models and data, (2) model fitting to data, (3) mechanism identification accounting for observation, and (4) prediction of future observations. Such facets are explored using a recent exchange between two (...)
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  2. Mathematics as a Science of Non-Abstract Reality: Aristotelian Realist Philosophies of Mathematics.James Franklin - 2022 - Foundations of Science 27 (2):327-344.
    There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity, relations. The article (...)
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  3. Hobbes on Natural Philosophy as "True Physics" and Mixed Mathematics.Marcus P. Adams - 2016 - Studies in History and Philosophy of Science Part A 56:43-51.
    I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the (...)
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  4. Mathematical Metaphors in Natorp’s Neo-Kantian Epistemology and Philosophy of Science.Thomas Mormann - 2005 - In Falk Seeger, Johannes Lenard & Michael H. G. Hoffmann (eds.), Activity and Sign. Grounding Mathematical Education. Springer.
    A basic thesis of Neokantian epistemology and philosophy of science contends that the knowing subject and the object to be known are only abstractions. What really exists, is the relation between both. For the elucidation of this “knowledge relation ("Erkenntnisrelation") the Neokantians of the Marburg school used a variety of mathematical metaphors. In this con-tribution I reconsider some of these metaphors proposed by Paul Natorp, who was one of the leading members of the Marburg school. It is shown that (...)
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  5. Spinoza and the Philosophy of Science: Mathematics, Motion, and Being.Eric Schliesser - 1986, 2002
    This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the proper method for the study of nature presented in the Theological-Political Treatise (TTP) points away from the one commonly associated with the mechanical philosophy. Moreover, throughout his works Spinoza’s views on the very possibility of knowledge of nature are decidedly sceptical (as specified below). Third, in the seventeenth-century debates over proper methods in (...)
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  6. From Mathematics to Quantum Mechanics - On the Conceptual Unity of Cassirer’s Philosophy of Science.Thomas Mormann - 2015 - In Sebastian Luft & J. Tyler Friedman (eds.), The Philosophy of Ernst Cassirer: A Novel Assessment. De Gruyter. pp. 31-64.
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  7. Aristotelianism in the Philosophy of Mathematics.James Franklin - 2011 - Studia Neoaristotelica 8 (1):3-15.
    Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio (...)
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  8. Models, Mathematics and Deleuze's Philosophy: Some Remarks on Simon Duffy's Deleuze and the History of Mathematics: In Defence of the New.James Williams - 2017 - Deleuze and Guatarri Studies 11 (3):475-481.
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  9. Walter Dubislav’s Philosophy of Science and Mathematics.Nikolay Milkov - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):96-116.
    Walter Dubislav (1895–1937) was a leading member of the Berlin Group for scientific philosophy. This “sister group” of the more famous Vienna Circle emerged around Hans Reichenbach’s seminars at the University of Berlin in 1927 and 1928. Dubislav was to collaborate with Reichenbach, an association that eventuated in their conjointly conducting university colloquia. Dubislav produced original work in philosophy of mathematics, logic, and science, consequently following David Hilbert’s axiomatic method. This brought him to defend formalism in these (...)
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  10. The Philosophy of Mathematics and the Independent 'Other'.Penelope Rush - unknown
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  11. Deleuze and the Mathematical Philosophy of Albert Lautman.Simon B. Duffy - 2009 - In Jon Roffe & Graham Jones (eds.), Deleuze’s Philosophical Lineage. Edinburgh University Press.
    In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon (...)
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  12. Assessing the “Empirical Philosophy of Mathematics”.Markus Pantsar - 2015 - Discipline Filosofiche:111-130.
    Abstract In the new millennium there have been important empirical developments in the philosophy of mathematics. One of these is the so-called “Empirical Philosophy of Mathematics”(EPM) of Buldt, Löwe, Müller and Müller-Hill, which aims to complement the methodology of the philosophy of mathematics with empirical work. Among other things, this includes surveys of mathematicians, which EPM believes to give philosophically important results. In this paper I take a critical look at the sociological part of (...)
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  13. Nietzsche’s Philosophy of Mathematics.Eric Steinhart - 1999 - International Studies in Philosophy 31 (3):19-27.
    Nietzsche has a surprisingly significant and strikingly positive assessment of mathematics. I discuss Nietzsche's theory of the origin of mathematical practice in the division of the continuum of force, his theory of numbers, his conception of the finite and the infinite, and the relations between Nietzschean mathematics and formalism and intuitionism. I talk about the relations between math, illusion, life, and the will to truth. I distinguish life and world affirming mathematical practice from its ascetic perversion. For Nietzsche, (...)
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  14.  68
    Redrawing Kant's Philosophy of Mathematics.Joshua M. Hall - 2013 - South African Journal of Philosophy 32 (3):235-247.
    This essay offers a strategic reinterpretation of Kant’s philosophy of mathematics in Critique of Pure Reason via a broad, empirically based reconception of Kant’s conception of drawing. It begins with a general overview of Kant’s philosophy of mathematics, observing how he differentiates mathematics in the Critique from both the dynamical and the philosophical. Second, it examines how a recent wave of critical analyses of Kant’s constructivism takes up these issues, largely inspired by Hintikka’s unorthodox conception (...)
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  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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  16. 1983 Review in Mathematical Reviews 83e:03005 Of: Cocchiarella, Nino “The Development of the Theory of Logical Types and the Notion of a Logical Subject in Russell's Early Philosophy: Bertrand Russell's Early Philosophy, Part I”. Synthese 45 (1980), No. 1, 71-115.John Corcoran - 1983 - MATHEMATICAL REVIEWS 83:03005.
    CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .
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  17. Mario Bunge’s Philosophy of Mathematics: An Appraisal.Jean-Pierre Marquis - 2012 - Science & Education 21 (10):1567-1594.
    In this paper, I present and discuss critically the main elements of Mario Bunge’s philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge’s systemic emergent materialism.To Mario, with gratitude.
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  18.  95
    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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  19. Leibniz on Mathematics, Methodology, and the Good: A Reconsideration of the Place of Mathematics in Leibniz's Philosophy.Christia Mercer - 2006 - Early Science and Medicine 11 (4):424-454.
    Scholars have long been interested in the relation between Leibniz, the metaphysician-theologian, and Leibniz, the logician-mathematician. In this collection, we consider the important roles that rhetoric and the "art of thinking" have played in the development of mathematical ideas. By placing Leibniz in this rhetorical tradition, the present essay shows the extent to which he was a rhetorical thinker, and thereby answers the question about the relation between his work as a logician-mathematician and his other work. It becomes clear that (...)
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  20.  41
    Lakatos' Undone Work: The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science_ - Introduction to the Special Issue on _Lakatos’ Undone Work.Sophie Nagler, Hannah Pillin & Deniz Sarikaya - 2022 - Kriterion - Journal of Philosophy 36:1-10.
    We give an overview of Lakatos’ life, his philosophy of mathematics and science, as well as of this issue. Firstly, we briefly delineate Lakatos’ key contributions to philosophy: his anti-formalist philosophy of mathematics, and his methodology of scientific research programmes in the philosophy of science. Secondly, we outline the themes and structure of the masterclass Lakatos’ Undone Work – The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of (...)
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  21. Plato’s Philosophy of Cognition by Mathematical Modelling.Roman S. Kljujkov & Sergey F. Kljujkov - 2014 - Dialogue and Universalism 24 (3):110-115.
    By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a long (...)
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  22.  91
    Practising Philosophy of Mathematics with Children.Elisa Bezençon - 2020 - Philosophy of Mathematics Education Journal 36.
    This article examines the possibility of philosophizing about mathematics with children. It aims at outlining the nature of the practice of philosophy of mathematics with children in a mainly theoretical and exploratory way. First, an attempt at a definition is proposed. Second, I suggest some reasons that might motivate such a practice. My thesis is that one can identify an intrinsic as well as two extrinsic goals of philosophizing about mathematics with children. The intrinsic goal is (...)
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  23.  39
    Øystein Linnebo, Philosophy of mathematics, Princeton University Press, 2017, pp. 216, € 29.00, ISBN 978-0691161402. [REVIEW]Filippo Mancini - 2019 - Universa. Recensioni di Filosofia 8.
    La matematica viene generalmente considerata uno degli ambiti più affidabili dell’intera impresa scientifica. Il suo successo e la sua solidità sono testimoniati, ad esempio, dall’uso imprescindibile che ne fanno le scienze empiriche e dall’accordo pressoché unanime con cui la comunità dei matematici delibera sulla validità di un nuovo risultato. Tuttavia, dal punto di vista filosofico la matematica rappresenta un puzzle tanto intrigante quanto intricato. Philosophy of Mathematics di Ø. Linnebo si propone di presentare e discutere le concezioni filosofiche (...)
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  24. Natorp's Mathematical Philosophy of Science.Thomas Mormann - forthcoming - In Francesca Biagioli & Marco Giovanelli (eds.), Neo-Kantian Perspectives on the Exact Sciences. London, UK: Routledge.
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  25. Mathematical Platonism and the Nature of Infinity.Gilbert B. Côté - 2013 - Open Journal of Philosophy 3 (3):372-375.
    An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.
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  26. Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics.Jean-Pierre Marquis - 2013 - Synthese 190 (12):2141-2164.
    In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, (...)
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  27. Review of Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics[REVIEW]Chris Smeenk - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (1):194-199.
    Book Review for Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, La Salle, IL: Open Court, 2002. Edited by David Malament. This volume includes thirteen original essays by Howard Stein, spanning a range of topics that Stein has written about with characteristic passion and insight. This review focuses on the essays devoted to history and philosophy of physics.
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  28. Justification and Explanation in Mathematics and Morality.Justin Clarke-Doane - 2015 - Oxford Studies in Metaethics 10.
    In his influential book, The Nature of Morality, Gilbert Harman writes: “In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles.” What is the epistemological relevance of this contrast, if genuine? This chapter argues that ethicists and philosophers of mathematics have misunderstood it. They have confused what the chapter calls the justificatory challenge for realism about an area, (...)
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  29. 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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  30. Dummett and Wittgenstein's Philosophy of Mathematics.Carlo Penco - 1994 - In Brian McGuiness & Gianluigi Oliveri (eds.), The Philosophy of Michael Dummett. Kluwer Academic Publishers. pp. 113--136.
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  31. The connection between mathematics and philosophy on the discrete–structural plane of thinking: the discrete–structural model of the world.Eldar Amirov - 2017 - Гілея: Науковий Вісник 126 (11):266-270.
    The discrete–structural structure of the world is described. In comparison with the idea of Heraclitus about an indissoluble world, preference is given to the discrete world of Democritus. It is noted that if the discrete atoms of Democritus were simple and indivisible, the atoms of the modern world indicated in the article would possess, rather, a structural structure. The article proves the problem of how the mutual connection of mathematics and philosophy influences cognition, which creates a discrete–structural worldview. (...)
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  32. Mathematical Biology and the Existence of Biological Laws.Mauro Dorato - 2012 - In D. Dieks, S. Hartmann, T. Uebel & M. Weber (eds.), Probabilities, Laws and Structure. Springer.
    An influential position in the philosophy of biology claims that there are no biological laws, since any apparently biological generalization is either too accidental, fact-like or contingent to be named a law, or is simply reducible to physical laws that regulate electrical and chemical interactions taking place between merely physical systems. In the following I will stress a neglected aspect of the debate that emerges directly from the growing importance of mathematical models of biological phenomena. My main aim is (...)
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  33.  92
    Review of O. Linnebo Philosophy of Mathematics[REVIEW]Fraser MacBride - 2018 - Notre Dame Philosophical Reviews.
    In this review, as well as discussing the pedagogical of this text book, I also discuss Linnebo's approach to the Caesar problem and the use of metaphysical notions to explicate mathematics.
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  34. What Are Mathematical Diagrams?Silvia De Toffoli - 2022 - Synthese 200 (2):1-29.
    Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for (...)
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  35. Editorial. Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.Plamen L. Simeonov, Arran Gare, Seven M. Rosen & Denis Noble - 2015 - Progress in Biophysics and Molecular Biology 119 (3):208-218.
    The is the Editorial of the 2015 JPBMB Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.
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  36. Mathematics and Argumentation.Andrew Aberdein - 2009 - Foundations of Science 14 (1-2):1-8.
    Some authors have begun to appeal directly to studies of argumentation in their analyses of mathematical practice. These include researchers from an impressively diverse range of disciplines: not only philosophy of mathematics and argumentation theory, but also psychology, education, and computer science. This introduction provides some background to their work.
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  37. Mathematics and Conceptual Analysis.Antony Eagle - 2008 - Synthese 161 (1):67–88.
    Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra Plan’. This philosophical role for intuitions suggests an analogous epistemology for some fundamental parts of mathematics, which casts a number (...)
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  38. Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (3):247–255.
    Callard (2007) argues that it is metaphysically possible that a mathematical object, although abstract, causally affects the brain. I raise the following objections. First, a successful defence of mathematical realism requires not merely the metaphysical possibility but rather the actuality that a mathematical object affects the brain. Second, mathematical realists need to confront a set of three pertinent issues: why a mathematical object does not affect other concrete objects and other mathematical objects, what counts as a mathematical object, and how (...)
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  39. Mathematics and the Theory of Multiplicities: Badiou and Deleuze Revisited.Daniel W. Smith - 2003 - Southern Journal of Philosophy 41 (3):411-449.
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  40. From Mathematical Fictionalism to Truth‐Theoretic Fictionalism.Bradley Armour-Garb & James A. Woodbridge - 2014 - Philosophy and Phenomenological Research 88 (1):93-118.
    We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism.
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  41. Some Remarks on Wittgenstein’s Philosophy of Mathematics.Richard Startup - 2020 - Open Journal of Philosophy 10 (1):45-65.
    Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation (...)
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  42. 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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  43. Volume Introduction – Method, Science and Mathematics: Neo-Kantianism and Analytic Philosophy.Scott Edgar - 2018 - Journal for the History of Analytical Philosophy 6 (3):1-10.
    Introduction to the Special Volume, “Method, Science and Mathematics: Neo-Kantianism and Analytic Philosophy,” edited by Scott Edgar and Lydia Patton. At its core, analytic philosophy concerns urgent questions about philosophy’s relation to the formal and empirical sciences, questions about philosophy’s relation to psychology and the social sciences, and ultimately questions about philosophy’s place in a broader cultural landscape. This picture of analytic philosophy shapes this collection’s focus on the history of the philosophy (...)
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  44.  52
    's Gravesande on the Application of Mathematics in Physics and Philosophy.Jip Van Besouw - 2017 - Noctua 4 (1-2):17-55.
    Willem Jacob ’s Gravesande is widely remembered as a leading advocate of Isaac Newton’s work. In the first half of the eighteenth century, ’s Gravesande was arguably Europe’s most important proponent of what would become known as Newtonian physics. ’s Gravesande himself minimally described this discipline, which he called «physica», as studying empirical regularities mathematically while avoiding hypotheses. Commentators have as yet not progressed much beyond this view of ’s Gravesande’s physics. Therefore, much of its precise nature, its methodology, and (...)
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  45.  70
    Anti-Realism and Anti-Revisionism in Wittgenstein’s Philosophy of Mathematics.Anderson Nakano - 2020 - Grazer Philosophische Studien 97 (3):451-474.
    Since the publication of the Remarks on the Foundations of Mathematics, Wittgenstein’s interpreters have endeavored to reconcile his general constructivist/anti-realist attitude towards mathematics with his confessed anti-revisionary philosophy. In this article, the author revisits the issue and presents a solution. The basic idea consists in exploring the fact that the so-called “non-constructive results” could be interpreted so that they do not appear non-constructive at all. The author substantiates this solution by showing how the translation of mathematical results, (...)
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  46. 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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  47. Can Mathematics Explain the Evolution of Human Language?Guenther Witzany - 2011 - Communicative and Integrative Biology 4 (5):516-520.
    Investigation into the sequence structure of the genetic code by means of an informatic approach is a real success story. The features of human language are also the object of investigation within the realm of formal language theories. They focus on the common rules of a universal grammar that lies behind all languages and determine generation of syntactic structures. This universal grammar is a depiction of material reality, i.e., the hidden logical order of things and its relations determined by natural (...)
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  48.  73
    Semi-Platonist Aristotelianism: Review of James Franklin, An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure[REVIEW]Catherine Legg - 2015 - Australasian Journal of Philosophy 93 (4):837-837.
    This rich book differs from much contemporary philosophy of mathematics in the author’s witty, down to earth style, and his extensive experience as a working mathematician. It accords with the field in focusing on whether mathematical entities are real. Franklin holds that recent discussion of this has oscillated between various forms of Platonism, and various forms of nominalism. He denies nominalism by holding that universals exist and denies Platonism by holding that they are concrete, not abstract - looking (...)
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  49.  36
    Notes on Philosophy, Probability and Mathematics. FP Ramsey. [REVIEW]E. J. Lowe - 1997 - British Journal for the Philosophy of Science 48 (2):300-301.
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  50. Mathematical Knowledge, the Analytic Method, and Naturalism.Fabio Sterpetti - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge. Approaches from Philosophy, Psychology and Cognitive Science. New York, Stati Uniti: pp. 268-293.
    This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors (...)
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