About this topic
Summary Philosophical discussions about mathematics have a long history, which basically coincides with the history of philosophy. The main historiographic divisions are thus the same as for philosophy in general, i.e. there is philosophy of mathematics in Ancient Philosophy, in Medieval Philosophy, in Early Modern Philosophy (16th-18th centuries), and in Late Modern Philosophy (19th-20th centuries). For a general introduction to the topic, including source material, see R. Marcus and M. McEvoy, eds., A Historical Introduction to the Philosophy of Mathematics: A Reader (Bloomsbury, 2016). For excerpts and translations from crucial authors since Kant, compare W. Ewald, ed., From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vols. I-II (Oxford University Press, 1996).  And for the late 19th and the first half of the 20th centuries, see P. Benacerraf and H. Putnam, eds., Philosophy of Mathematics: Selected Readings (2nd ed., Cambridge University Press, 1984).
Key works Logicism, formalism, intuitionism, structuralism, foundations, logic, proof, truth, axioms, infinity.
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483 found
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1 — 50 / 483
  1. Frege's Basic Law V and Cantor's Theorem.Manuel Bremer - manuscript
    The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These ontological (...)
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  2. On some historical aspects of the theory of Riemann zeta function.Giuseppe Iurato -
    This comprehensive historical account concerns that non-void intersection region between Riemann zeta function and entire function theory, with a view towards possible physical applications.
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  3. Wittgenstein's philosophy of mathematics.Victor Rodych - unknown - Stanford Encyclopedia of Philosophy.
  4. Conceptions of infinity and set in Lorenzen’s operationist system.Carolin Antos - forthcoming - In Logic, Epistemology and the Unity of Science. Springer.
    In the late 1940s and early 1950s Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as the precursor to the more well-known dialogical logic and one could assumed that the same philosophical motivations were present in both works. However we want to show that this is not always the case. In particular, we claim, that Lorenzen’s well-known rejection of the actual infinite as stated in Lorenzen (1957) was not a major motivation (...)
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  5. Ms.Natasha Bailie - forthcoming - British Journal for the History of Mathematics.
    The reception of Newton's Principia in 1687 led to the attempt of many European scholars to ‘mathematicise' their field of expertise. An important example of this ‘mathematicisation' lies in the work of Irish-Scottish philosopher Francis Hutcheson, a key figure in the Scottish Enlightenment. This essay aims to discuss the mathematical aspects of Hutcheson's work and its impact on British thought in the following centuries, providing a case in point for the importance of the interactions between mathematics and philosophy throughout time.
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  6. Russell Marcus and Mark McEvoy, eds. An Historical Introduction to the Philosophy of Mathematics: A Reader.James Robert Brown - forthcoming - Philosophia Mathematica:nkw033.
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  7. Hilbert on number, geometry and continuity.M. Hallett - forthcoming - Bulletin of Symbolic Logic.
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  8. Frege and Peano on definitions.Edoardo Rivello - forthcoming - In Proceedings of the "Frege: Freunde und Feinde" conference, held in Wismar, May 12-15, 2013.
    Frege and Peano started in 1896 a debate where they contrasted the respective conceptions on the theory and practice of mathematical definitions. Which was (if any) the influence of the Frege-Peano debate on the conceptions by the two authors on the theme of defining in mathematics and which was the role played by this debate in the broader context of their scientific interaction?
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  9. Ian Hacking, Why Is There Philosophy of Mathematics at All? [REVIEW]Max Harris Siegel - forthcoming - Mind 124.
  10. Du Châtelet’s Philosophy of Mathematics.Aaron Wells - forthcoming - In The Bloomsbury Companion to Du Châtelet. Bloomsbury.
    I begin by outlining Du Châtelet’s ontology of mathematical objects: she is an idealist, and mathematical objects are fictions dependent on acts of abstraction. Next, I consider how this idealism can be reconciled with her endorsement of necessary truths in mathematics, which are grounded in essences that we do not create. Finally, I discuss how mathematics and physics relate within Du Châtelet’s idealism. Because the primary objects of physics are partly grounded in the same kinds of acts as yield mathematical (...)
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  11. “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects.Aaron Wells - forthcoming - In Between Leibniz, Newton, and Kant, Second Edition. Springer.
    Du Châtelet holds that mathematical representations play an explanatory role in natural science. Moreover, things proceed in nature as they do in geometry. How should we square these assertions with Du Châtelet’s idealism about mathematical objects, on which they are ‘fictions’ dependent on acts of abstraction? The question is especially pressing because some of her important interlocutors (Wolff, Maupertuis, and Voltaire) denied that mathematics informs us about the properties of real things. After situating Du Châtelet in this debate, this chapter (...)
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  12. Cultures of Mathematical Practice in Alexandria in Egypt: Claudius Ptolemy and His Commentators (Second–Fourth Century CE).Alberto Bardi - 2023 - In Handbook of the History and Philosophy of Mathematical Practice.
    Claudius Ptolemy’s mathematical astronomy originated in Alexandria in Egypt under Roman rule in the second century CE and held for more than a millennium, even beyond the Copernican theories (sixteenth century). To trace the flourishing of such mathematical creativity requires an understanding of Ptolemy’s philosophy of mathematical practice, the ancient commentators of Ptolemaic works, and the historical context of Alexandria in Egypt, a multicultural city which became a cradle of cultures of mathematical practices and blossomed into the Ptolemaic system and (...)
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  13. A Reassessment of Cantorian Abstraction based on the $$\varepsilon $$ ε -operator.Nicola Bonatti - 2022 - Synthese 200 (5):1-26.
    Cantor’s abstractionist account of cardinal numbers has been criticized by Frege as a psychological theory of numbers which leads to contradiction. The aim of the paper is to meet these objections by proposing a reassessment of Cantor’s proposal based upon the set theoretic framework of Bourbaki—called BK—which is a First-order set theory extended with Hilbert’s \-operator. Moreover, it is argued that the BK system and the \-operator provide a faithful reconstruction of Cantor’s insights on cardinal numbers. I will introduce first (...)
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  14. Degeneration and Entropy.Eugene Y. S. Chua - 2022 - Kriterion - Journal of Philosophy 36 (2):123-155.
    [Accepted for publication in Lakatos's Undone Work: The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, special issue of Kriterion: Journal of Philosophy. Edited by S. Nagler, H. Pilin, and D. Sarikaya.] Lakatos’s analysis of progress and degeneration in the Methodology of Scientific Research Programmes is well-known. Less known, however, are his thoughts on degeneration in Proofs and Refutations. I propose and motivate two new criteria for degeneration based on the discussion in Proofs and Refutations (...)
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  15. Mirja Hartimo* Husserl and Mathematics.Jairo José da Silva - 2022 - Philosophia Mathematica 30 (3):396-414.
    1. INTRODUCTIONIt has been some time now since the philosophical community has learned to appreciate Husserl’s contribution to the philosophies of logic, mathematics, and science in general, despite still some prejudices and misinterpretations in certain academic circles incapable of reading Husserl beyond the incompetent and malicious review which Frege wrote in 1894 of his Philosophie der Arithmetik (PA) [1891/2003], hereafter Hua XII.Husserl’s philosophy of mathematics, in particular, has been the subject of many articles and books and has attracted the attention (...)
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  16. The collapse of the Hilbert program: A variation on the gödelian theme.Saul A. Kripke - 2022 - Bulletin of Symbolic Logic 28 (3):413-426.
    The Hilbert program was actually a specific approach for proving consistency, a kind of constructive model theory. Quantifiers were supposed to be replaced by ε-terms. εxA(x) was supposed to denote a witness to ∃xA(x), or something arbitrary if there is none. The Hilbertians claimed that in any proof in a number-theoretic system S, each ε-term can be replaced by a numeral, making each line provable and true. This implies that S must not only be consistent, but also 1-consistent. Here we (...)
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  17. Paul Rusnock and Jan Šebestík. Bernard Bolzano: His Life and His Work.Sandra Lapointe - 2022 - Philosophia Mathematica 30 (1):138-140.
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  18. Carnap's philosophy of mathematics.Benjamin Marschall - 2022 - Philosophy Compass 17 (11):e12884.
    For several decades, Carnap's philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture. It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that supposedly decisive objections against his position target a straw man. This raises two questions. First, how exactly should (...)
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  19. 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 Science, which gave rise to this special issue. Lastly, (...)
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  20. Conceptual Frameworks on the Relationship Between Physics–Mathematics in the Newton Principia Geneva Edition (1822).Raffaele Pisano & Paolo Bussotti - 2022 - Foundations of Science 27 (3).
    The aim of this paper is twofold: (1) to show the principal aspects of the way in which Newton conceived his mathematical concepts and methods and applied them to rational mechanics in his Principia; (2) to explain how the editors of the Geneva Edition interpreted, clarified, and made accessible to a broader public Newton’s perfect but often elliptic proofs. Following this line of inquiry, we will explain the successes of Newton’s mechanics, but also the problematic aspects of his perfect geometrical (...)
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  21. Paul Weingartner and Hans-Peter Leeb, eds, Kreisel’s Interests: On the Foundations of Logic and Mathematics.Dag Prawitz - 2022 - Philosophia Mathematica 30 (1):121-126.
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  22. How can a line segment with extension be composed of extensionless points?Brian Reese, Michael Vazquez & Scott Weinstein - 2022 - Synthese 200 (2):1-28.
    We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. Armed with this (...)
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  23. Kuhn, Lakatos, and the Historical Turn in the Philosophy of Mathematics.Vladislav A. Shaposhnikov - 2022 - Epistemology and Philosophy of Science 59 (4):144-162.
    The paper deals with Kuhn’s and Lakatos’s ideas related to the so-called “historical turn” and its application to the philosophy of mathematics. In the first part the meaning of the term “postpositivism” is specified. If we lack such a specification we can hardly discuss the philosophy of science that comes “after postpositivism”. With this end in view, the metaphor of “generations” in the philosophy of science is used. It is proposed that we restrict the use of the term “post-positivism” to (...)
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  24. Two Lost Operations of Arithmetic: Duplation and Mediation.Lloyd Strickland - 2022 - Mathematics Today 65:212-213.
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  25. A Neglected Chapter in the History of Philosophy of Mathematical Thought Experiments: Insights from Jean Piaget’s Reception of Edmond Goblot.Marco Buzzoni - 2021 - Hopos: The Journal of the International Society for the History of Philosophy of Science 11 (1):282-304.
    Since the beginning of the twentieth century, prominent authors including Jean Piaget have drawn attention to Edmond Goblot’s account of mathematical thought experiments. But his contribution to today’s debate has been neglected so far. The main goal of this article is to reconstruct and discuss Goblot’s account of logical operations (the term he used for thought experiments in mathematics) and its interpretation by Piaget against the theoretical background of two open questions in today’s debate: (1) the relationship between empirical and (...)
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  26. A Neglected Chapter in the History of Philosophy of Mathematical Thought Experiments: Insights from Jean Piaget’s Reception of Edmond Goblot.Marco Buzzoni - 2021 - Hopos: The Journal of the International Society for the History of Philosophy of Science 11 (1):282-304.
    Since the beginning of the twentieth century, prominent authors including Jean Piaget have drawn attention to Edmond Goblot’s account of mathematical thought experiments. But his contribution to today’s debate has been neglected so far. The main goal of this article is to reconstruct and discuss Goblot’s account of logical operations (the term he used for thought experiments in mathematics) and its interpretation by Piaget against the theoretical background of two open questions in today’s debate: (1) the relationship between empirical and (...)
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  27. Dedekind et la crèation du continu arithmétique.Emmylou Haffner & Dirk Schlimm - 2021 - In Emmylou Haffner & David Rabouin (eds.), L'Épistemologie du dedans. Mélanges en l'honneur de Hourya Benis-Sinaceur. Paris, France: pp. 341–378.
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  28. Dedekind on continuity.Emmylou Haffner & Dirk Schlimm - 2021 - In Stewart Shapiro & Geoffrey Hellman (eds.), The History of Continua. Philosophical and mathematical perspectives. New York, NY, USA: pp. 255–282.
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  29. Wittgenstein, Peirce, and Paradoxes of Mathematical Proof.Sergiy Koshkin - 2021 - Analytic Philosophy 62 (3):252-274.
    Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic logic (...)
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  30. Mathematics and metaphysics: The history of the Polish philosophy of mathematics from the Romantic era.Paweł Jan Polak - 2021 - Philosophical Problems in Science 71:45-74.
    The Polish philosophy of mathematics in the 19th century is not a well-researched topic. For this period, only five philosophers are usually mentioned, namely Jan Śniadecki, Józef Maria Hoene-Wroński, Henryk Struve, Samuel Dickstein, and Edward Stamm. This limited and incomplete perspective does not allow us to develop a well-balanced picture of the Polish philosophy of mathematics and gauge its influence on 19th- and 20th-century Polish philosophy in general. To somewhat complete our picture of the history of the Polish philosophy of (...)
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  31. Babbage's guidelines for the design of mathematical notations.Dirk Schlimm & Jonah Dutz - 2021 - Studies in History and Philosophy of Science Part A 1 (88):92–101.
    The design of good notation is a cause that was dear to Charles Babbage's heart throughout his career. He was convinced of the "immense power of signs" (1864, 364), both to rigorously express complex ideas and to facilitate the discovery of new ones. As a young man, he promoted the Leibnizian notation for the calculus in England, and later he developed a Mechanical Notation for designing his computational engines. In addition, he reflected on the principles that underlie the design of (...)
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  32. The Curious Neglect of Geometry in Modern Philosophies of Mathematics.Siavash Shahshahani - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and Their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 379-389.
    From ancient times to 19th century geometryGeometry symbolized the essence of mathematical thinking and method, but modern philosophy of mathematics seems to have marginalized the philosophical status of geometryGeometry. The roots of this transformation will be sought in the ascendance of logical foundations in place of intuitive primacy as the cornerstone of mathematical certainty in the late 19th century. Nevertheless, geometry and geometrical thinking, in multiple manifestations, have continued to occupy a central place in the practice of mathematics proper. We (...)
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  33. Why Did Weyl Think That Emmy Noether Made Algebra the Eldorado of Axiomatics?Iulian D. Toader - 2021 - Hopos: The Journal of the International Society for the History of Philosophy of Science 11 (1):122-142.
    This paper argues that Noether's axiomatic method in algebra cannot be assimilated to Weyl's late view on axiomatics, for his acquiescence to a phenomenological epistemology of correctness led Weyl to resist Noether's principle of detachment.
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  34. Du Châtelet on the Need for Mathematics in Physics.Aaron Wells - 2021 - Philosophy of Science 88 (5):1137-1148.
    There is a tension in Emilie Du Châtelet’s thought on mathematics. The objects of mathematics are ideal or fictional entities; nevertheless, mathematics is presented as indispensable for an account of the physical world. After outlining Du Châtelet’s position, and showing how she departs from Christian Wolff’s pessimism about Newtonian mathematical physics, I show that the tension in her position is only apparent. Du Châtelet has a worked-out defense of the explanatory and epistemic need for mathematical objects, consistent with their metaphysical (...)
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  35. Mathematics, isomorphism, and the identity of objects.Graham White - 2021 - Journal of Knowledge Structures and Systems 2 (2):56-58.
    We compare the medieval projects of commentaries and disputations with the modern projects of formal ontology and of mathematics.
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  36. From Phenomenology to the Philosophy of the Concept: Jean Cavaillès as a Reader of Edmund Husserl.Jean-Paul Cauvin - 2020 - Hopos: The Journal of the International Society for the History of Philosophy of Science 10 (1):24-47.
    The article reconstructs Jean Cavaillès’s polemical engagement with Edmund Husserl’s phenomenological philosophy of mathematics. I argue that Cavaillès’s encounter with Husserl clarifies the scope and ambition of Cavaillès’s philosophy of the concept by identifying three interrelated epistemological problems in Husserl’s phenomenological method: (1) Cavaillès claims that Husserl denies a proper content to mathematics by reducing mathematics to logic. (2) This reduction obliges Husserl, in turn, to mischaracterize the significance of the history of mathematics for the philosophy of mathematics. (3) Finally, (...)
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  37. Hermann Cohen’s Principle of the Infinitesimal Method: A Defense.Scott Edgar - 2020 - Hopos: The Journal of the International Society for the History of Philosophy of Science 10 (2):440-470.
    In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits and infinitesimals (...)
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  38. Arnošt Kolman’s Critique of Mathematical Fetishism.Jakub Mácha & Jan Zouhar - 2020 - In Radek Schuster (ed.), The Vienna Circle in Czechoslovakia. Cham, Switzerland: Springer. pp. 135-150.
    Arnošt Kolman (1892–1979) was a Czech mathematician, philosopher and Communist official. In this paper, we would like to look at Kolman’s arguments against logical positivism which revolve around the notion of the fetishization of mathematics. Kolman derives his notion of fetishism from Marx’s conception of commodity fetishism. Kolman is aiming to show the fact that an entity (system, structure, logical construction) acquires besides its real existence another formal existence. Fetishism means the fantastic detachment of the physical characteristics of real things (...)
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  39. Mathématiques et architecture: le tracé de l’entasis par Nicolas-François Blondel.Dominique Raynaud - 2020 - Archive for History of Exact Sciences 74 (5):445-468.
    In Résolution des quatre principaux problèmes d’architecture (1673) then in Cours d’architecture (1683), the architect–mathematician Nicolas-François Blondel addresses one of the most famous architectural problems of all times, that of the reduction in columns (entasis). The interest of the text lies in the variety of subjects that are linked to this issue. (1) The text is a response to the challenge launched by Curabelle in 1664 under the name Étrenne à tous les architectes; (2) Blondel mathematicizes the problem in the (...)
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  40. The Pre-History of Mathematical Structuralism.Erich H. Reck & Georg Schiemer (eds.) - 2020 - Oxford: Oxford University Press.
    This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.
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  41. Pasch's empiricism as methodological structuralism.Dirk Schlimm - 2020 - In Erich Reck & Georg Schiemer (eds.), The Pre-History of Mathematical Structuralism. New York: Oxford University Press. pp. 80-105.
  42. Aritmética e conhecimento simbólico: notas sobre o Tractatus Logico-Philosophicus e o ensino de filosofia da matemática.Gisele Dalva Secco - 2020 - Perspectiva Filosófica 47 (2):120-149.
    Departing from and closing with reflections on issues regarding teaching practices of philosophy of mathematics, I propose a comparison between the main features of the Leibnizian notion of symbolic knowledge and some passages from the Tractatus on arithmetic. I argue that this reading allows (i) to shed a new light on the specificities of the Tractarian definition of number, compared to those of Frege and Russell; (ii) to highlight the understanding of the nature of mathematical knowledge as symbolic or formal (...)
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  43. The origin of Europe and the Esprit de Geometrie.Francesco Tampoia - 2020 - Cosmos and History 16.
    ABSTRACT: In searching for the origin of Europe and the cultural region/continent that we call “Europe”, at first glance we have to consider at least a double view: on the one hand the geographical understanding which indicates a region or a continent; on the other a certain form of identity and culture described and defined as European. Rodolphe Gasché taking hint from Husserl’s passage ‘Europe is not to be construed simply as a geographical and political entity’ states that a rigorous (...)
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  44. The Axiom of Choice and the Road Paved by Sierpiński.Valérie Lynn Therrien - 2020 - Hopos: The Journal of the International Society for the History of Philosophy of Science 10 (2):504-523.
  45. William Boos. Metamathematics and the Philosophical Tradition. Edited by Florence S. Boos. 481 pp., bibl., indexes. Berlin/Boston: De Gruyter, 2018. $124.99 (cloth). [REVIEW]Lukas M. Verburgt - 2020 - Isis 111 (2):380-381.
  46. Euclid’s Kinds and (Their) Attributes.Benjamin Wilck - 2020 - History of Philosophy & Logical Analysis 23 (2):362-397.
    Relying upon a very close reading of all of the definitions given in Euclid’s Elements, I argue that this mathematical treatise contains a philosophical treatment of mathematical objects. Specifically, I show that Euclid draws elaborate metaphysical distinctions between substances and non-substantial attributes of substances, different kinds of substance, and different kinds of non-substance. While the general metaphysical theory adopted in the Elements resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at (...)
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  47. Research in History and Philosophy of Mathematics: The CSHPM 2018 Volume.Maria Zack & Dirk Schlimm (eds.) - 2020 - New York, USA: Springer Verlag.
    This volume contains ten papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics from the seventeenth century to the modern era. -/- The volume begins with an exposition of the life and work of Professor Bolesław Sobociński. It then moves on to cover a collection of topics about twentieth-century philosophy (...)
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  48. The Idea of Continuity as Mathematical-Philosophical Invariant.Eldar Amirov - 2019 - Metafizika 2 (8):p. 87-100.
    The concept of ‘ideas’ plays central role in philosophy. The genesis of the idea of continuity and its essential role in intellectual history have been analyzed in this research. The main question of this research is how the idea of continuity came to the human cognitive system. In this context, we analyzed the epistemological function of this idea. In intellectual history, the idea of continuity was first introduced by Leibniz. After him, this idea, as a paradigm, formed the base of (...)
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  49. Mathesis Universalis, Computability and Proof.Stefania Centrone, Sara Negri, Deniz Sarikaya & Peter M. Schuster (eds.) - 2019 - Cham, Switzerland: Springer Verlag.
    In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is (...)
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  50. Mathematical Creation in Frege's Grundgesetze.Philip A. Ebert & Marcus Rossberg - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 325-342.
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