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16Guest Editors’ IntroductionTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (2): 267-269. 2018.
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19IntroductionJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (1): 89-92. 2020.
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3What Are Mathematical Practices? The Web-of-Practices ApproachIn Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer. pp. 2793-2819. 2024.This chapter can be considered as made up of two parts, a general discussion of the notion of mathematical practice and the limits of its use, comprised by the first three sections, and a particular case study that is presented in order to exemplify the idea of the web of practices, which occupies the remaining three. The presentation of my approach to the notion of mathematical practice is brief and synthetic but more articulated theoretically than in a previous book (Ferreirós 2016). Considera…Read more
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6Introdução ao Habilitationsvortag de Bernhard RiemannKairos 2 101-139. 2011.info:eu-repo/semantics/publishedVersion.
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20Joel D. Hamkins. Lectures on the Philosophy of MathematicsPhilosophia Mathematica 32 (1): 124-127. 2024.
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53Degrees of Objectivity? Mathemata and Social ObjectsTopoi 42 (1): 199-209. 2022.A down-to-earth admission of abstract objects can be based on detailed explanation of where the objectivity of mathematics comes from, and how a ‘thin’ notion of object emerges from objective mathematical discourse or practices. We offer a sketch of arguments concerning both points, as a basis for critical scrutiny of the idea that mathematical and social objects are essentially of the same kind—which is criticized. Some authors have proposed that mathematical entities are indeed institutional o…Read more
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86Conceptual StructuralismJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 54 (1): 125-148. 2023.This paper defends a conceptualistic version of structuralism as the most convincing way of elaborating a philosophical understanding of structuralism in line with the classical tradition. The argument begins with a revision of the tradition of “conceptual mathematics”, incarnated in key figures of the period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led to a structuralist methodology. Then the tension between the ‘presuppositionless’ approach of those authors, and …Read more
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26Dedekind and Wolffian Deductive MethodJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 53 (4): 345-365. 2022.Dedekind’s methodology, in his classic booklet on the foundations of arithmetic, has been the topic of some debate. While some authors make it closely analogue to Hilbert’s early axiomatics, others emphasize its idiosyncratic features, most importantly the fact that no axioms are stated and its careful deductive structure apparently rests on definitions alone. In particular, the so-called Dedekind “axioms” of arithmetic are presented by him as “characteristic conditions” in the _definition_ of t…Read more
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6La herencia oscura del logicismoMetatheoria – Revista de Filosofía E Historia de la Ciencia 10 (2): 19--30. 2020.Logicism finds a prominent place in textbooks as one of the main alternatives in the foundations of mathematics, even though it lost much of its attraction from about 1950. Of course the neologicist trend has revitalized the movement on the basis of Hume’s Principle and Frege’s Theorem, but even so neologicism restricts itself to arithmetic and does not aim to account for all of mathematics. The present contribution does not focus on the classical logicism of Frege and Dedekind, nor on the Russe…Read more
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15Labyrinth of Thought. A history of set theory and its role in modern mathematicsBirkhäuser Verlag. 2001.Review by A. Kanamori, Boston University (author of The Higher Infinite), review in The Bulletin of Symbolic Logic: “Notwithstanding and braving the daunting complexities of this labyrinth, José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of th…Read more
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331The Road to Modern Logic—An InterpretationBulletin of Symbolic Logic 7 (4): 441-484. 2001.This paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order-Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emerge…Read more
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38C.K. Raju. Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE.: Critical Studies/Book Reviews (review)Philosophia Mathematica 17 (3): 378-381. 2009.This book is part of a major project undertaken by the Centre for Studies in Civilizations , being one of a total of ninety-six planned volumes. The author is a statistician and computer scientist by training, who has concentrated on historical matters for the last ten years or so. The book has very ambitious aims, proposing an alternative philosophy of mathematics and a deviant history of the calculus. Throughout, there is an emphasis on the need to combine history and philosophy of mathematics…Read more
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Bernhard Riemann: Riemanniana SelectaCSIC. 2000.A book-length study of Riemann's multi-dimensional work (in Spanish), which considers his contributions to physics, philosophy and mathematics. Plus a bi-lingual edition (German-Spanish) of some of his landmark papers: the lecture on geometry, with Weyl's comments; the paper introducing the Riemann Conjecture, part of his 1857 paper on function theory; all of the philosophical fragments, etc. These different contributions, and their interconnections, are carefully studied in the introductory ess…Read more
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22Riemanniana Selecta: introducciónIn Jose Ferreiros (ed.), Bernhard Riemann: Riemanniana Selecta, Csic. 2000.This is my introduction to a bilingual Spanish-German edition of selected writings by Bernhard Riemann. Published in Madrid: CSIC, 2000.
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42From Gauss to Riemann Through Jacobi: Interactions Between the Epistemologies of Geometry and Mechanics?Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (1): 147-172. 2020.The aim of this paper is to argue that there existed relevant interactions between mechanics and geometry during the first half of the nineteenth century, following a path that goes from Gauss to Riemann through Jacobi. By presenting a rich historical context we hope to throw light on the philosophical change of epistemological categories applied by these authors to the fundamental principles of both disciplines. We intend to show that presentations of the changing status of the principles of me…Read more
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31IntroductionJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (1): 89-92. 2018.Guest Editors’ introduction to the Monographic Section.
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42Beyond natural geometry: on the nature of proto-geometryPhilosophical Psychology 33 (2): 181-205. 2020.ABSTRACTWe discuss the thesis of universality of geometric notions and offer critical reflections on the concept of “natural geometry” employed by Spelke and others. Promoting interdisciplinary wor...
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49Mathematical Knowledge and the Interplay of PracticesPrinceton University Press. 2015.On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding
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17La gran antinomiaRevista de Humanidades de Valparaíso 8 123-128. 2016.We formulate and discuss a “great antinomy” between theoreticist/foundationist conceptions and pragmatist conceptions, in relation to a wide diversity of scientific and/or philosophical approaches. The contrast is illustrated in particular with the concept of time, considering the ‘timelessness crowd’ that has been guided by a theoreticist vision.
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46¿“Natural” y “Euclidiana”? Reflexiones sobre la geometría práctica y sus raíces cognitivasTheoria : An International Journal for Theory, History and Fundations of Science 33 (2): 325-344. 2018.We discuss critically some recent theses about geometric cognition, namely claims of universality made by Dehaene et al., and the idea of a “natural geometry” employed by Spelke et al. We offer arguments for the need to distinguish visuo-spatial cognition from basic geometric knowledge, furthermore we claim that the latter cannot be identified with Euclidean geometry. The main aim of the paper is to advance toward a characterization of basic, practical geometry – which in our view requires a com…Read more
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14This is a contribution to the philosophy of experimental work, engaging with questions posed by Hacking, Franklin, Pickering, Schaffer and Collins. It focuses on the dynamics of experimentation and offers a detailed argument that one finds no "regress" of the kind posited by Collins. In particular, we reanalyze the celebrated series of experimental investigations by Newton on optical phenomena, taking into account Schaffer's partial reconstruction, and we show how it must be supplemented to obta…Read more
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46The place of Richard Dedekind in the history of logicism is a controversial matter. The conception of logic incorporated in his work is certainly old-fashioned, in spite of innovative elements that would play an important role in late 19th and early 20th century discussions. Yet his understanding of logic and logicism remains of interest for the light it throws upon the development of modern logic in general, and logicist views of the foundations of mathematics in particular. The paper clarifies…Read more
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52Roi Wagner. Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice (review)Philosophia Mathematica 26 (1): 131-136. 2018.© The Authors [2018]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] mathematics a reflection of some already-given realm? It would not matter whether we are talking about the empirical world in a Millian way, or the domain of a priori truths in Leibnizian or maybe Kantian style, or some world of analytical truths à la Carnap. Or perhaps — could mathematics be something more, or something less, than such a reflection? Mig…Read more
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18La lógica matemática: una disciplina en busca de encuadreTheoria 25 (3): 279-299. 2010.We offer an analysis of the disciplinary transformations underwent by mathematical or symbolic logic since its emergence in the late 19 th century. Examined are its origins as a hybrid of philosophy and mathematics, the maturity and institutionalisation attained under the label “logic and foundations,” a second wave of institutionalisation in the Postwar period, and the institutional developments since 1975 in connection with computer science and with the study of language and informatics. Altho…Read more
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8Sobre los orígenes de la Matemática abstractaTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 7 (1-3): 473-498. 1992.Dedekind used to refer to Riemann as his main model concerning mathematical methodology, particularly regarding the use of abstract notions as a basis for mathematical theories. So, in passages written in 1876 and 1895 he compared his approach to ideal theory with Riemann’s theory of complex functions. In this paper, I try to make sense of those declarations, showing the role of abstract notions in Riemann’s function theory, its influence on Dedekind, and the importance of the methodological pri…Read more
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31Notes on types, sets, and logicism, 1930-1950Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 12 (1): 91-124. 1997.The present paper is a contribution to the history of logic and its philosophy toward the mid-20th century. It examines the interplay between logic, type theory and set theory during the 1930s and 40s, before the reign of first-order logic, and the closely connected issue of the fate of logicism. After a brief presentation of the emergence of logicism, set theory, and type theory, Quine’s work is our central concern, since he was seemingly the most outstanding logicist around 1940, though he wou…Read more