This book investigates Hermann Weyls work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl deduces, with group-theoretical technicalities, that there is only one kind of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem.
Contributing authors mark out the double trajectory that goes through Weyls texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrödinger, Eddington).
This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.
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Part I Weyl's Intellectual Neighborhoods and the Theory of Subjectivity |
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1 Internationalization of Scientific Activity in Spain in the Interwar Period |
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3 | (22) |
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2 Hermann Weyl chez Gaston Bachelard |
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25 | (10) |
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3 Le residu philosophique du probleme de l'espace chez Weyl et Husserl |
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35 | (64) |
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4 Neighbourhoods and Intersubjectivity |
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99 | (26) |
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Part II Weyl's Theory of the Continuum: Intuitionism and Dimensionnality of Space |
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5 Weyl and Intuitionistic Infinitesimals |
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125 | (36) |
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6 Entre phenomenologie et intuitionnisme: la definition du continu |
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161 | (28) |
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7 From the Problem of Space to the Epistemology of Science: Hermann Weyl's Reflection on the Dimensionality of the World |
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189 | (24) |
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Part III From Aprioristic to Physical Foundations of the Metric |
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8 The Changing Faces of the Problem of Space in the Work of Hermann Weyl |
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213 | (18) |
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9 H. Weyl's Deep Insights into the Mathematical and Physical Worlds: His Important Contribution to the Philosophy of Space, Time and Matter |
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231 | (34) |
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265 | (30) |
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11 The Plasticine Ball Argument |
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295 | (52) |
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12 Intuition and Conceptual Construction in Weyl's Analysis of the Problem of Space |
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347 | (24) |
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Part IV Weyl's Methodological Issues: Intuition, Symbolic Thought and Manifolds of Possibilities |
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13 Espace et varite de possibility chez Hermann Weyl |
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371 | (18) |
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14 Husserl and Weyl on the Constitution of Space |
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389 | (14) |
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15 The Scientific Implications of Epistemology: Weyl and Husserl |
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Julien Bernard is currently assistant professor at Aix-Marseille University. His laboratory is the Centre Gilles Gaston Granger, UMR 7304. Before this, he was postdoctorate researcher at Zukunftskolleg (University of Constance), and also worked for the ANR Gödel on Kurt Gödels unpublished papers. His research interest is primarily in philosophy of physics, mathematics and logic, focussing on the relationships between the great traditional philosophical systems (Leibnizian metaphysics, neo-Kantianism, Husserlian phenomenology) and the scientific revolutions of the beginning of the twentieth century.
He has published two monographs Lidéalisme dans linfinitésimal and LAnalyse mathématique du problčme de lespace (French-German commented edition of Weyls text) and several specialized articles on Hermann Weyl, on the problem of space, on Gödels Leibnizian interpretation of quantum mechanics, and on the foundations of mathematics. He serves as reviewerfor the journals Lato Sensu, Journal of Symbolic Logic, and for the GDR 3719 Philosophie des mathématiques. He has also been awarded by the Prix Paul Ricoeur 2013 of University Paris-Nanterre, and was winner of several important funding programs for his Art-Philosophy-Science project Biomorphism (notably: the Interdisciplinarite 2016 AMIDEX funding program at Aix-Marseille and the funding program of the Foundation Daniel and Nina Carasso, Paris).
Carlos Lobo is currently member of the Collčge international de philosophie and of the Center of Philosophy of Sciences (University of Lisbon). For over 30 years, while preparing students to the Ecole Normal Supérieure competitive exam, he pursued his research in phenomenology and epistemology. After a first monograph on the methodology of transcendental phenomenology (Le phénoménologue et ses exemples, in 2000), he published several contributions on phenomenological issues such as intersubjectivity, temporality, individuation, and axiology, showing their epistemological import for the understanding and critical clarification of formal logic, probability theory, and physics. Those contributions are particularly illustrated by a series of contributions such as Self-variation and self-modification in The Phenomenology of Embodied Subjectivity, Springer, 2013, 263283, Husserls Reform of Logic. An introduction in New Yearbook for Phenomenology and Phenomenological Philosophy, 2017; Some Reasons to reopen the question of foundations of probability theory following the Rota way in The Philosophers and Mathematicians, ed. H. Tahiri, Springer, 2018; Le maniérisme épistémologique de Gilles Chātelet. Relativité et exploration de la priori esthétique chez Chātelet, Weyl et Husserl, Revue de Synthčse, Brill, n° 137, 2018. As a translator (from German, English, and Spanish), Lobo has published Husserls Les leēons sur léthique et la théoriede la valeur, PUF, 1999, and more recently Weyls Philosophie des mathématiques et des sciences de la nature, Métis Presses, Geneva, 2017.
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