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  1. 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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  2. Connecting the revolutionary with the conventional: Rethinking the differences between the works of Brouwer, Heyting, and Weyl.Kati Kish Bar-On - forthcoming - Philosophy of Science:1-34.
    Brouwer’s intuitionism was a far-reaching attempt to reform the foundations of mathematics. While the mathematical community was reluctant to accept Brouwer’s work, its response to later-developed brands of intuitionism, such as those presented by Hermann Weyl and Arend Heyting, was different. The paper accounts for this difference by analyzing the intuitionistic versions of Brouwer, Weyl, and Heyting in light of a two-tiered model of the body and image of mathematical knowledge. Such a perspective provides a richer account of each story (...)
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  3. Ian Hacking, Why Is There Philosophy of Mathematics at All? [REVIEW]Max Harris Siegel - forthcoming - Mind 124.
  4. From Philosophical Traditions to Scientific Developments: Reconsidering the Response to Brouwer’s Intuitionism.Kati Kish Bar-On - 2022 - Synthese 200 (6):1–25.
    Brouwer’s intuitionistic program was an intriguing attempt to reform the foundations of mathematics that eventually did not prevail. The current paper offers a new perspective on the scientific community’s lack of reception to Brouwer’s intuitionism by considering it in light of Michael Friedman’s model of parallel transitions in philosophy and science, specifically focusing on Friedman’s story of Einstein’s theory of relativity. Such a juxtaposition raises onto the surface the differences between Brouwer’s and Einstein’s stories and suggests that contrary to Einstein’s (...)
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  5. Schopenhauers Logikdiagramme in den Mathematiklehrbüchern Adolph Diesterwegs.Jens Lemanski - 2022 - Siegener Beiträge Zur Geschichte Und Philosophie der Mathematik 16:97-127.
    Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betreffen, in Frage gestellt oder sogar ausgeräumt. In Kapitel 3 wird dann die Philosophie der Mathematik und der (...)
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  6. An Okapi Hypothesis: Non-Euclidean Geometry and the Professional Expert in American Mathematics.Jemma Lorenat - 2022 - Isis 113 (1):85-107.
    Open Court began publishingThe Monistin 1890 as a journal“devotedto the philosophy of science”that regularly included mathematics. The audiencewas understood to be“cultured people who have not a technical mathematicaltraining”but nevertheless“have a mathematical penchant.”With these constraints,the mathematical content varied from recreations to logical foundations, but every-one had something to say about non-Euclidean geometry, in debates that rangedfrom psychology to semantics. The focus in this essay is on the contested value ofmathematical expertise in legitimating what should be considered as mathematics.While some mathematicians urgedThe (...)
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  7. Philip Beeley; Yelda Nasifoglu; Benjamin Wardhaugh (Editors). Reading Mathematics in Early Modern Europe: Studies in the Production, Collection, and Use of Mathematical Books. (Material Readings in Early Modern Culture.) 348 pp., illus. London: Routledge, 2020. $160 (cloth); ISBN 9780367609252. E-book available. [REVIEW]Lisa Wilde - 2022 - Isis 113 (1):181-182.
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  8. Towards a new philosophical perspective on Hermann Weyl’s turn to intuitionism.Kati Kish Bar-On - 2021 - Science in Context 34 (1):51-68.
    The paper explores Hermann Weyl’s turn to intuitionism through a philosophical prism of normative framework transitions. It focuses on three central themes that occupied Weyl’s thought: the notion of the continuum, logical existence, and the necessity of intuitionism, constructivism, and formalism to adequately address the foundational crisis of mathematics. The analysis of these themes reveals Weyl’s continuous endeavor to deal with such fundamental problems and suggests a view that provides a different perspective concerning Weyl’s wavering foundational positions. Building on a (...)
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  9. Bolzano’s Mathematical Infinite.Anna Bellomo & Guillaume Massas - 2021 - Review of Symbolic Logic:1-55.
    Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums can be equipped (...)
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  10. Mathematical Selves and the Shaping of Mathematical Modernism: Conflicting Epistemic Ideals in the Emergence of Enumerative Geometry.Nicolas Michel - 2021 - Isis 112 (1):68-92.
  11. Essay on Machines in General (1786): Text, Translations and Commentaries. Lazare Carnot’s Mechanics—Volume 1.Raffaele Pisano, Jennifer Coopersmith & Murray Peake - 2021 - Springer.
    This book offers insights relevant to modern history and epistemology of physics, mathematics and, indeed, to all the sciences and engineering disciplines emerging of 19th century. This research volume is the first of a set of three Springer books on Lazare Nicolas Marguérite Carnot’s (1753–1823) remarkable work: Essay on Machines in General (Essai sur les machines en général [1783] 1786). The other two forthcoming volumes are: Principes fondamentaux de l’équilibre et du mouvement (1803) and Géométrie de position (1803). Lazare Carnot (...)
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  12. Permanence as a Principle of Practice.Iulian D. Toader - 2021 - Historia Mathematica 54:77-94.
    The paper discusses Peano's defense and application of permanence as a principle of practice, and Hahn's further point that, even if it were a principle of logic, permanence would not eliminate all logical ambiguity. Dedicated to the memory of Mic Detlefsen.
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  13. From practical to pure geometry and back.Mario Bacelar Valente - 2020 - Revista Brasileira de História da Matemática 20 (39):13-33.
    The purpose of this work is to address the relation existing between ancient Greek practical geometry and ancient Greek pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically (...)
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  14. On Archimedes’ statics.Mario Bacelar Valente - 2020 - Theoria. An International Journal for Theory, History and Foundations of Science 35 (2):235-242.
    Archimedes’ statics is considered as an example of ancient Greek applied mathematics; it is even seen as the beginning of mechanics. Wilbur Knorr made the case regarding this work, as other works by him or other mathematicians from ancient Greece, that it lacks references to the physical phenomena it is supposed to address. According to Knorr, this is understandable if we consider the propositions of the treatise in terms of purely mathematical elaborations suggested by quantitative aspects of the phenomena. In (...)
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  15. On the correctness of problem solving in ancient mathematical procedure texts.Mario Bacelar Valente - 2020 - Revista de Humanidades de Valparaíso 16:169-189.
    It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian mathematical procedure texts – (...)
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  16. Michael Brooks. The Quantum Astrologer’s Handbook: A History of the Renaissance Mathematics That Birthed Imaginary Numbers, Probability, and the New Physics of the Universe. 256 pp. Melbourne/London: Scribe Publications, 2017. $26 (cloth); ISBN 9781947534810. Paper and e-book available. [REVIEW]Howard G. Barth - 2020 - Isis 111 (4):874-875.
  17. Anthony Turner. Mathematical Instruments in the Collections of the Bibliothèque Nationale de France. 335 pp., bibl. London: Brepols, 2018. €150 (paper). Hardcover available. [REVIEW]Jim Bennett - 2020 - Isis 111 (3):647-648.
  18. Benjamin Wardhaugh. Gunpowder and Geometry: The Life of Charles Hutton: Pit Boy, Mathematician, and Scientific Rebel. 312 pp., bibl., notes, illus., index. London: William Collins, 2019. £20 (cloth). E-book available. [REVIEW]Victor D. Boantza - 2020 - Isis 111 (3):672-674.
  19. Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D’Alessandro - 2020 - Synthese (9):1-44.
    Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...)
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  20. David Aubin. L’élite sous la mitraille: Les normaliens, les mathématiques et la Grande Guerre 1900–1925. (Figures Normaliennes.) xi + 360 pp., notes, bibl., figs., tables, index. Paris: Éditions Rue d’Ulm, 2018. [REVIEW]Christophe Eckes - 2020 - Isis 111 (2):418-419.
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  21. 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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  22. Giorgio Israel (General Editor). Correspondence of Luigi Cremona (1830–1903): Conserved in the Department of Mathematics, “Sapienza” Università di Roma. 2 volumes. 1,824 pp., bibl., index. Turnhout: Brepols, 2017. €190 (cloth). [REVIEW]Angelo Guerraggio - 2020 - Isis 111 (3):683-684.
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  23. Jacqueline Feke. Ptolemy’s Philosophy: Mathematics as a Way of Life. xi + 234 pp., illus., bibl., index. Princeton, N.J./Oxford: Princeton University Press, 2018. $39.50 (cloth); ISBN 9780691179582. Paper and e-book available. [REVIEW]Matthieu Husson - 2020 - Isis 111 (4):866-867.
  24. Brendan Dooley (Editor). The Continued Exercise of Reason: Public Addresses by George Boole. ix + 237 pp., notes, index. Cambridge, Mass./London: MIT Press, 2018. [REVIEW]Volker Peckhaus - 2020 - Isis 111 (3):682-683.
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  25. From the four-color theorem to a generalizing “four-letter theorem”: A sketch for “human proof” and the philosophical interpretation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (21):1-10.
    The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA plan of any alive being. Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters. That admits to be formulated as a “four-letter theorem”, and thus one can search for (...)
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  26. Who Wants to Be a Mathematician? [REVIEW]Christopher J. Phillips - 2020 - Isis 111 (4):845-848.
    David Lindsay Roberts. Republic of Numbers: Unexpected Stories of Mathematical Americans through History. ix + 244 pp., bibl., index. Baltimore: Johns Hopkins University Press, 2019. $29.95 (cloth); ISBN 9781421433080. E-book available. Julian Havil. Curves for the Mathematically Curious: An Anthology of the Unpredictable, Historical, Beautiful, and Romantic. xx + 259 pp., apps., refs., index. Princeton, N.J./Oxford: Princeton University Press, 2019. $29.95 (cloth); ISBN 9780691180052. E-book available. David S. Richeson. Tales of Impossibility: The Two-Thousand-Year Quest to Solve the Mathematical Problems of (...)
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  27. Peter Roquette. The Riemann Hypothesis in Characteristic p in Historical Perspective. (History of Mathematics Subseries: Lecture Notes in Mathematics, 2222.) x + 233 pp., bibl., index. Cham, Switzerland: Springer, 2018. €47.95 (paper). ISBN 9783319990675. [REVIEW]Arkady Plotnitsky - 2020 - Isis 111 (2):411-412.
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  28. 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.
  29. Geometrical objects and figures in practical, pure, and applied geometry.Mario Bacelar Valente - 2020 - Disputatio. Philosophical Research Bulletin 9 (15):33-51.
    The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.
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  30. 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.
  31. 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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  32. 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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  33. Geometry of motion: some elements of its historical development.Mario Bacelar Valente - 2019 - ArtefaCToS. Revista de Estudios de la Ciencia y la Tecnología 8 (2):4-26.
    in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion that was first (...)
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  34. Exploring Predicativity.Laura Crosilla - 2018 - In Klaus Mainzer, Peter Schuster & Helmut Schwichtenberg (eds.), Proof and Computation. World Scientific. pp. 83-108.
    Prominent constructive theories of sets as Martin-Löf type theory and Aczel and Myhill constructive set theory, feature a distinctive form of constructivity: predicativity. This may be phrased as a constructibility requirement for sets, which ought to be finitely specifiable in terms of some uncontroversial initial “objects” and simple operations over them. Predicativity emerged at the beginning of the 20th century as a fundamental component of an influential analysis of the paradoxes by Poincaré and Russell. According to this analysis the paradoxes (...)
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  35. Lautman on problems as the conditions of existence of solutions.Simon B. Duffy - 2018 - Angelaki 23 (2):79-93.
    Albert Lautman (b. 1908–1944) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that: ‘in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe’ (Lautman 2011, 87). He goes on to characterize this (...)
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  36. Karine Chemla, Renaud Chorlay, and David Rabouin, eds. The Oxford Handbook of Generality in Mathematics and the Sciences. Oxford: Oxford University Press, 2016. Pp. xi+528. $150.00 ; $120.00. [REVIEW]Christophe Eckes - 2018 - Hopos: The Journal of the International Society for the History of Philosophy of Science 8 (1):214-217.
  37. Mathematics, core of the past and hope of the future.James Franklin - 2018 - In Catherine A. Runcie & David Brooks (eds.), Reclaiming Education: Renewing Schools and Universities in Contemporary Western Society. Sydney, Australia: Edwin H. Lowe Publishing. pp. 149-162.
    Mathematics has always been a core part of western education, from the medieval quadrivium to the large amount of arithmetic and algebra still compulsory in high schools. It is an essential part. Its commitment to exactitude and to rigid demonstration balances humanist subjects devoted to appreciation and rhetoric as well as giving the lie to postmodernist insinuations that all “truths” are subject to political negotiation. In recent decades, the character of mathematics has changed – or rather broadened: it has become (...)
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  38. Religion and ideological confrontations in early Soviet mathematics: The case of P.A. Nekrasov.Dimitris Kilakos - 2018 - Almagest 9 (2):13-38.
    The influence of religious beliefs to several leading mathematicians in early Soviet years, especially among members of the Moscow Mathematical Society, had drawn the attention of militant Soviet marxists, as well as Soviet authorities. The issue has also drawn significant attention from scholars in the post-Soviet period. According to the currently prevailing interpretation, reported purges against Moscow mathematicians due to their religious inclination are the focal point of the relevant history. However, I maintain that historical data arguably offer reasons to (...)
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  39. A Road Map of Dedekind’s Theorem 66.Ansten Klev - 2018 - Hopos: The Journal of the International Society for the History of Philosophy of Science 8 (2):241-277.
    Richard Dedekind’s theorem 66 states that there exists an infinite set. Its proof invokes such apparently nonmathematical notions as the thought-world and the self. This article discusses the content and context of Dedekind’s proof. It is suggested that Dedekind took the notion of the thought-world from Hermann Lotze. The influence of Kant and Bernard Bolzano on the proof is also discussed, and the reception of the proof in the mathematical and philosophical literature is covered in detail.
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  40. Geometrie.Jens Lemanski - 2018 - In Daniel Schubbe & Matthias Koßler (eds.), Schopenhauer-Handbuch. Stuttgart, Deutschland: pp. 330–335.
    In mathematics textbooks and special mathematical treatises, themes and theses of Arthur Schopenhauer's elementary geometry appear again and again. Since Schopenhauer's geometry or philosophy of geometry was considered exemplary in the 19th and early 20th centuries in its relation to figures and thus to the intuition, the two-hundred-year reception history sketched in this paper also follows the evaluation of intuition-related geometries, which depends on the mathematical paradigms.
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  41. Logic, Philosophy of Mathematics, and Their History: Essays in Honor of W. W. Tait.Erich H. Reck (ed.) - 2018 - College Publications.
    In a career that spans 60 years so far, W.W. Tait has made many highly influential contributions to logic, the philosophy of mathematics, and their history. The present collection of new essays - contributed by former students, colleagues, and friends - is a Festschrift, i.e., a celebration of his life and work. The essays address a variety of themes prominent in his work or related to it. The collection starts with an introduction in which Tait's contributions are sketched and put (...)
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  42. Paul Erickson. The World the Game Theorists Made. Chicago: University of Chicago Press, 2015. Pp. 384. $35.00.Philip Mirowski - 2017 - Hopos: The Journal of the International Society for the History of Philosophy of Science 7 (1):160-163.
  43. Poincaré on the Foundations of Arithmetic and Geometry. Part 1: Against “Dependence-Hierarchy” Interpretations.Katherine Dunlop - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):274-308.
    The main goal of part 1 is to challenge the widely held view that Poincaré orders the sciences in a hierarchy of dependence, such that all others presuppose arithmetic. Commentators have suggested that the intuition that grounds the use of induction in arithmetic also underlies the conception of a continuum, that the consistency of geometrical axioms must be proved through arithmetical induction, and that arithmetical induction licenses the supposition that certain operations form a group. I criticize each of these readings. (...)
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  44. Review of Gabriele Lolli, Numeri. La creazione continua della matematica. [REVIEW]Longa Gianluca - 2016 - Lo Sguardo. Rivista di Filosofia 21 (II):377-380.
  45. On the role of virtual work in Levi-Civita’s parallel transport.Giuseppe Iurato & Giuseppe Ruta - 2016 - Archive for History of Exact Sciences 70 (5):1-13 (provisional).
    The current literature on history of science reports that Levi-Civita’s parallel transport was motivated by his attempt to provide the covariant derivative of the absolute differential calculus with a geometrical interpretation (For instance, see Scholz in ''The intersection of history and mathematics'', Birkhäuser, Basel, pp 203-230, 1994, Sect. 4). Levi-Civita’s memoir on the subject was explicitly aimed at simplifying the geometrical computation of the curvature of a Riemannian manifold. In the present paper, we wish to point out the possible role (...)
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  46. Snezana Lawrence and Mark McCartney, eds. Mathematicians and Their Gods: Interactions between Mathematics and Religious Beliefs. Oxford: Oxford University Press, 2015. Pp. vi+298, index. $44.95. [REVIEW]Madeline Muntersbjorn - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):333-336.
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  47. Acerbi Il silenzio delle sirene. La matematica greca antica. Rome: Carocci, 2010. Pp. 445. €40. 9788843055791.Federico M. Petrucci - 2016 - Journal of Hellenic Studies 136:294-295.
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  48. The Algebra between History and Education. [REVIEW]Raffaele Pisano - 2016 - Metascience (2):1-5.
    ‘‘What Is Algebra?-Why This Book?’’ This is the amazing prelude to Taming the Unknown by Victor J. Katz, emeritus professor of mathematics at the University of the District of Columbia and Karen Hunger Parshall, professor of history of mathematics at the University of Virginia. This is an excellent book; its accurate historical and pedagogical purpose offers an accessible read for historians and mathematicians. [continue...].
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  49. A Newtonian tale details on notes and proofs in Geneva edition of Newton's Principia.Raffaele Pisano & Paolo Bussotti - 2016 - BSHM-Journal of the British Society for the History of Mathematics:1-19.
    Based on our research regarding the relationship between physics and mathematics in HPS, and recently on Geneva Edition of Newton's Philosophiae Naturalis Principia Mathematica (1739–42) by Thomas Le Seur (1703–70) and François Jacquier (1711–88), in this paper we present some aspects of such Edition: a combination of editorial features and scientific aims. The proof of Proposition XLIII is presented and commented as a case study.
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  50. Equi-Probability Prior to 1650.Rudolf Schüssler - 2016 - Early Science and Medicine 21 (1):54-74.
1 — 50 / 751