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22Dedekind 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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22Riemanniana Selecta: introducciónIn Jose Ferreiros (ed.), Bernhard Riemann: Riemanniana Selecta, . 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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19Joel D. Hamkins. Lectures on the Philosophy of MathematicsPhilosophia Mathematica 32 (1): 124-127. 2024.
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18IntroductionJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (1): 89-92. 2020.
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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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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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14Labyrinth 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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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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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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3Introdução ao Habilitationsvortag de Bernhard RiemannKairos 2 101-139. 2011.info:eu-repo/semantics/publishedVersion.
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2What 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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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