Why did Bernhard Riemann, arguably the most original mathematician of his generation, spend the last year of life investigating the mechanism of hearing? Fighting tuberculosis and the hostility of eminent scientists such as Hermann Helmholtz, he appeared to forsake mathematics to prosecute a case close to his heart. Only sketchy pages from his last paper remain, but here we assemble some significant clues and triangulate from them to build a broad picture of what he might have been driving (...) at. Our interpretation is that Riemann was a committed idealist and from this philosophical standpoint saw that the scientific enterprise was lame without the “poetry of hypothesis”. He believed that human thought was fundamentally the dynamics of “mind-masses” and that the human mind interpenetrated, and became part of, the microscopic physical domain of the cochlea. Therefore, a full description of hearing must necessarily include the perceptual dimensions of what he saw as a single manifold. The manifold contains all the psychophysical aspects of hearing, including the logarithmic transformations that arise from Fechner’s law, faithfully preserving all the subtle perceptual qualities of sound. For Riemann, hearing was a unitary physical and mental event, and parallels with modern ideas about consciousness and quantum biology are made. A unifying quantum mechanical model for an atom of consciousness—drawing on Riemann’s mind-masses and the similar “psychons” proposed by Eccles—is put forward. (shrink)

This paper attempts to show how the logical empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as the initiator of a 19th century geometrical tradition, whose main protagonists were Helmholtz and Poincaré, the logical empiricists neglected the fact that Riemann’s revolutionary insight flourished instead in a non-geometrical tradition dominated by the works of Christoffel and Ricci-Curbastro roughly in the same years. I will argue that, in the (...) attempt to interpret general relativity as the last link of the chain Riemann–Helmholtz–Poincaré–Einstein, logical empiricists were led to argue that Einstein’s theory of gravitation mainly raised a problem of mathematical under-determination, i.e. the discovery that there are physical differences that cannot be expressed in the relevant mathematical structure of the theory. However, a historical reconstruction of the alternative Riemann–Christoffel–Ricci–Einstein line of evolution shows on the contrary that the main philosophical issue raised by Einstein’s theory was instead that of mathematical over-determination, i.e. the recognition of the presence of redundant mathematical differences that do not have any correspondence in physical reality. (shrink)

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such (...) later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism. (shrink)

Among the various lecture courses that Edmund Husserl held during his time as a Privatdozent at the University of Halle (1887-1901), there was one on "Ausgewählte Fragen aus der Philosophie der Mathematik" (Selected Questions from the Philosophy of Mathematics), which he gave twice, once in the WS 1889/90 and again in WS 1890/91. As Husserl reports in his letter to Carl Stumpf of February 1890, he lectured mainly on “spatial-logical questions” and gave an extensive critique of the Riemann-Helmholtz (...) theories. Indeed, in K I 28 many lectures on this subject can be found, which are for the greater part published in Husserliana XXI. The lecture contained in K I 28/4-12 at the Husserl-Archives Leuven, however, was left out of the selection, because the lecture contained “an analysis of the concept of number” whose content is “already known” from the Philosophie der Arithmetik. Indeed, since the lecture is from the WS 1889/90, the manuscript allows a glimpse of Husserl’s ideas halfway between his Habilitationsschrift (1887) and the Philosophie der Arithmetik (1891). Among other things, in this lecture we find the first documented use of the terms "Gestalt" and "Gestaltmoment" in Husserl. (shrink)

Among the various lecture courses that Edmund Husserl held during his time as a Privatdozent at the University of Halle (1887-1901), there was one on Ausgewählte Fragen aus der Philosophie der Mathematik (Selected Questions from the Philosophy of Mathematics), which he gave twice, once in the WS 1889/90 and again in WS 1890/91. As Husserl reports in his letter to Carl Stumpf of February 1890, he lectured mainly on “spatial-logical questions” and gave an extensive critique of the Riemann-Helmholtz (...) theories. Indeed, in K I 28 many lectures on this subject can be found, which are for the greater part published in Husserliana XXI. The lecture contained in K I 28/4-12 at the Husserl-Archives Leuven, however, was left out of the selection, because the lecture contained “an analysis of the concept of number” whose content is “already known” from the Philosophie der Arithmetik. Indeed, since the lecture is from the WS 1889/90, the manuscript allows a glimpse of Husserl’s ideas halfway between his Habilitationsschrift (1887) and the Philosophie der Arithmetik (1891). From an exam- ple Husserl gives in the lecture: “Der wievielte Januar ist heute?” (The how-many-th of January is it today?), it can be estimated to be from January 1890, placing it in close relation to the letter to Stumpf and the views and doubts expressed therein. The bundle of papers K I 28 is wrapped in a blue cover, bearing only “Vor- lesungen” (Lectures) as a title. The lecture “On the concept of Number” in K I 28/4-12 is contained again in a separate cover, without any title. As in the case of most of his lectures, Husserl folded the paper in half, using the right half as a margin for annotations. Before the lecture there is a single page (K I 28/3) with some annotations on the treatment of imaginary numbers as assumptions in calculation. This text is published here as an Appendix to the lecture, because, while it is not part of the lecture itself, it is closely related to the subjects discussed therein. (shrink)

This paper discusses Husserl’s views on physical theories in the first volume of his Logical Investigations, and compares them with those of his contemporaries Pierre Duhem and Henri Poincaré. Poincaré’s views serve as a bridge to a discussion of Husserl’s almost unknown views on physical geometry from about 1890 on, which in comparison even with Poincaré’s—not to say Frege’s—or almost any other philosopher of his time, represented a rupture with the philosophical tradition and were much more in tune with the (...) physical geometry underlying the Einstein-Hilbert general theory of relativity developed more than two decades later. (shrink)

Richard Tieszen [Tieszen, R. (2005). Philosophy and Phenomenological Research, LXX(1), 153–173.] has argued that the group-theoretical approach to modern geometry can be seen as a realization of Edmund Husserl’s view of eidetic intuition. In support of Tieszen’s claim, the present article discusses Husserl’s approach to geometry in 1886–1902. Husserl’s first detailed discussion of the concept of group and invariants under transformations takes place in his notes on Hilbert’s Memoir Ueber die Grundlagen der Geometrie that Hilbert wrote during the winter 1901–1902. (...) Husserl’s interest in the Memoir is a continuation of his long-standing concern about analytic geometry and in particular Riemann and Helmholtz’s approach to geometry. Husserl favored a non-metrical approach to geometry; thus the topological nature of Hilbert’s Memoir must have been intriguing to him. The task of phenomenology is to describe the givenness of this logos, hence Husserl needed to develop the notion of eidetic intuition. (shrink)

Beaucoup de « géomètres » du XIXe siècle - Bernhard Riemann, Hermann von Helmholtz, Felix Klein, Riccardo De Paolis, Mario Pieri, Henri Poincaré, Federigo Enriques, et autres - ont joué un rôle important dans la discussion sur les fondements des mathématiques. Mais, contrairement aux idées d'Euclide, ils n'ont pas identifié «l'espace physique» avec« l'espace de nos sens». Partant de notre expérience dans l'espace, ils ont cherché à identifier les propriétés les plus importantes de l'espace et les ont posées (...) à la base de la géométrie. C'est sur la connaissance active de l'espace que les axiomes de la géométrie ont été élaborés ; ils ne pouvaient donc pas être a priori comme ils le sont dans la philosophie kantienne. En outre, pendant la dernière décade du siècle, certains mathématiciens italiens - De Paolis, Gino Fano, Pieri, et autres - ont fondé le concept de nombre sur la géométrie, en employant des résultats de la géométrie projective. Ainsi, on fondait l'arithmétique sur la géométrie et non l'inverse, comme David Hilbert a cherché à faire quelques années après, sans succès. (shrink)

This paper attempts to explain the emergence of the logical empiricist philosophy of space and time as a collision of mathematical traditions. The historical development of the ``Riemannian'' and ``Helmholtzian'' traditions in 19th century mathematics is investigated. Whereas Helmholtz's insistence on rigid bodies in geometry was developed group theoretically by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag triggered Christoffel's and Lipschitz's work on quadratic differential forms, paving the way to Ricci's absolute differential calculus. The transition from special to (...) general relativity is briefly sketched as a process of escaping from the Helmholtzian tradition and entering the Riemannian one. Early logical empiricist conventionalism, it is argued, emerges as the failed attempt to interpret Einstein's reflections on rods and clocks in general relativity through the conceptual resources of the Helmholtzian tradition. Einstein's epistemology of geometry should, in spite of his rhetorical appeal to Helmholtz and Poincaré, be understood in the wake the Riemannian tradition and of its aftermath in the work of Levi-Civita, Weyl, Eddington, and others. (shrink)

The reception of Poincaré’s conventionalist doctrine of space by mathematicians is studied for the period 1891–1911. The opposing view of Riemann and Helmholtz, according to which the geometry of space is an empirical question, is shown to have swayed several geometers. This preference is considered in the context of changing views of the nature of space in theoretical physics, and with respect to structural and social changes within mathematics. Included in the latter evolution is the emergence of non-Euclidean (...) geometry as a new sub-discipline. (shrink)

In the range of his intellectual interests and the profundity of his mathematical thought Hermann Weyl towered above his contemporaries, many of whom viewed him with awe. This volume, the most ambitious study to date of Weyl's singular contributions to mathematics, physics, and philosophy, looks at the man and his work from a variety of perspectives, though its gaze remains fairly steadily fixed on Weyl the geometer and space‐time theorist. Structurally, the book falls into two parts, described in the general (...) introduction by the editor: Part 1 contains four essays on particular aspects of Weyl's work, highlighting ideas he developed in various editions of his classic Raum‐Zeit‐Materie. Part 2 presents a lengthy study by Robert Coleman and Herbert Korté covering nearly the whole gamut of Weyl's mathematical research, an impressive feat. Both in the introduction as well as in footnotes to the articles Erhard Scholz's editorial voice chimes in discreetly, helping tie all five studies together.Coleman and Korté begin chronologically with Weyl's early work in analysis and the modern theory of Riemann surfaces before turning to differential geometry, unified field theory, and the space problem, a topic they use as a springboard for a discussion of their own recent work on the foundations of space‐time. They then take up Weyl's shift to group representation theory and its applications to quantum mechanics, ending with his much earlier research on the structure of the continuum. All of these topics are well handled, but the authors' own agendas coupled with their penchant for overlooking chronology in order to package Weyl's work into neat little bundles leave one feeling rather stranded and far removed from the sources of Weyl's inspiration. Moreover, the narrative style makes this part of the volume read like a technical appendix, albeit a most informative one. Readers who tackle Scholz's far more contextualized essay will be amply rewarded by comparing his views with the opinions set forth by Coleman and Korté in Part 2.Scholz gives a masterful account of Weyl's intellectual journeys from 1917 to 1925 in a study that serves as a fulcrum for the entire volume. Drawing on a number of recently published studies, including his own, on the interplay between mathematics and physics inspired by Einstein's theory of general relativity, Scholz describes how Weyl responded to this challenge by developing a truly infinitesimal space‐time geometry that generalized classical Riemannian geometry. Although unconvinced by Einstein's critique of his unified field theory, Weyl shifted his focus from this realm to the classical space problem, analyzed earlier with more primitive techniques by Hermann Helmholtz and Sophus Lie. In this connection, it should be mentioned that Thomas Hawkins has given a probing analysis of Weyl's related work on the representation of Lie groups in his tour‐de‐force work, Emergence of the Theory of Lie Groups . Scholz argues that Weyl's struggle to tame his modernized version of the space problem stemmed from a deep‐seated belief in his geometrical ideas, which in turn were nourished by philosophical musings. By demonstrating the closely related conceptual links that motivated Weyl's research in infinitesimal geometry, space‐time physics, and the foundations of mathematics, Scholz nicely illuminates the underlying fabric of epistemological concerns that occupied Weyl's attention during this fertile period.The three remaining essays in Part 1 focus on other aspects of Weyl's work in mathematical physics and cosmology. Skuli Sigurdsson's “Journeys in Spacetime” offers a broad interpretation of Weyl's career, one that emphasizes Weyl's sensitivity to cultural tensions as reflected in his philosophical roots, which combined phenomenology with facets of German idealism. Shaken by the annihilation of cultural values in Nazi Germany, Weyl became deeply aware of the gulf that separated his earlier life in Göttingen and Zurich from the one he took up at Princeton's Institute for Advanced Study in 1933. He tried to adapt, but felt out of place in an Anglo‐American scientific culture openly hostile toward metaphysics and speculative philosophy. Sigurdsson stresses these tensions, contrasting the introspective, creative individual against the backdrop of the collective in the age of the machine, but without spelling out which collective were most important for him. Wolfgang Pauli thought he knew and, like Einstein before him, he had no compunction about bluntly telling Weyl he was a mathematician, not a physicist.Pauli's opinions notwithstanding, Weyl did far more than just dabble around the mathematical edges of the new physics. If Coleman and Korté perhaps press their case for his visionary accomplishments too far, Norbert Straumann's essay “Ursprünge der Eichtheorien” suggests why Weyl's reputation among physicists has risen steadily ever since the advent of Yang‐Mills theory in the 1950s. In the course of describing Weyl's adaptation of his gauge transformation formalism to Dirac's electron theory, Straumann sheds considerable light on Pauli's role as self‐appointed watchman guarding the disciplinary boundary that separated theoretical physics from physical mathematics . He further suggests that disciplinary jealousy was a major reason why Pauli dismissed Weyl's two‐component formalism for spinors out of hand.In the realm of cosmology, on the other hand, Weyl's work has long since passed into the dustbins of history, as Hubert Goenner remarks in recounting a fascinating chapter in the infancy of space‐time physics. While doing so, Goenner shows how initially Weyl almost slavishly adopted what Einstein called Mach's principle, which asserts that the metric structure of space‐time is solely determined by the distribution of matter in the universe. This notion was quickly challenged by Willem De Sitter, who showed that Einstein's matter‐free field equations admitted a global solution with non‐zero constant curvature. Both Einstein and Weyl tried to argue that invisible masses must be present just over the “spatial horizon” of De Sitter's world in order to account for its curvature. Goenner meticulously analyzes the physical and mathematical issues at stake in this debate, stressing how Weyl gradually moved away from a strong physical interpretation to one in which mathematics models rather than physics models simply reveal natural phenomena. He argues further that Weyl's cosmological principle arose as the final expression of his search for a deeper physical meaning.Given the quality of these essays, it is regrettable that this book contains so little about Weyl's professional career, a weakness the editor could have redressed at least partially in his general introduction. This omission is all the more unfortunate given the dearth of readily accessible information about Weyl's life available elsewhere. For however mundane his outward existence may have been, the reader cannot be expected to appreciate the interplay between the world Weyl knew and his creative responses to it without fairly detailed knowledge of his biography. Shorn from these contexts, it becomes difficult to form a flesh‐and‐blood image of Weyl beyond the cliché‐ridden stereotype that sees him as a “heroic thinker in the grand German tradition.” While none of the authors falls into this trap, the collective impression they leave suggests a most enigmatic figure. Either Weyl the man tends to get lost in the shadows of his collected scientific output or he appears as a mystic loner, an outcast who abhorred the machine age in which he lived. Closer attention to the people in his life would no doubt produce a very different picture of the man and his interests. This major lacuna notwithstanding, the present volume will surely remain an indispensable resource for any future investigations of Weyl's staggering intellectual achievements. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Philosophy of PhysicsMartin CurdRoberto Torretti. The Philosophy of Physics. Cambridge: Cambridge University Press, 1999. Pp. xvi + 512. Cloth, $64.95. Paper, $23.95.This is the first volume in a new Cambridge series, "The Evolution of Modern Philosophy." It is a historical work, tracing the interaction between physics and philosophy from the scientific revolution of the seventeenth century through general relativity and quantum mechanics in the twentieth century. The (...) emphasis is on the philosophy in physics (rather than philosophizing about physics) and, with the exceptions noted below, the focus is on scientists (scientist-philosophers in many cases) rather than philosophers outside of science. Most of the book is about the conceptual and mathematical development of the core branches of physics (mainly mechanics, but also geometry, thermodynamics, and field theory). There are seven chapters plus three supplements giving the mathematical essentials of vector analysis, lattice theory, and topology.The hero of chapter one is Galileo who, more than anyone else prior to Newton, set physics on its modern path towards mathematization and away from Aristotle. Also discussed in chapter one are Descartes, Huyghens, and Leibniz. Chapter two is devoted to Newton (both the foundations of Newtonian mechanics and the derivation of the law of universal gravitation) and follows the development of analytical mechanics up to Lagrange and Hamilton. Chapter three, appropriately entitled "Kant," is the only chapter devoted to a philosopher. After a brief discussion of Leibniz, Berkeley, and Kant's pre-critical writings, it covers the important scientific topics in the Critique of Pure Reason (space, time, the three Analogies) but avoids the Metaphysical Foundations of Natural Science (referring the reader to Michael Friedman's Kant and the Exact Sciences). Chapter four looks at scientific developments in three areas that proved to be important for twentieth-century physics: non-Euclidean geometry from Lobachevsky to Riemann, electromagnetic field theory (Maxwell), and thermal physics (classical thermodynamics, the kinetic theory, and statistical mechanics) from Carnot to Boltzmann. The chapter concludes, somewhat untidily, with a section on four philosophers of science (Whewell, Peirce, Mach, and Duhem), selected, we are told, because of their influence on philosophy of science in the second half of the twentieth century. (For the "two great philosopher-scientists" Helmholtz and Poincaré, the reader is referred to Torretti's earlier books, Philosophy of Geometry from Riemann to Poincaré, and Relativity and Geometry.) Chapter five covers both the special and general theory of relativity. After a masterful exposition of the special theory and its Minkowski spacetime representation, the usual topics of philosophical interest are discussed; these include the conventionality of simultaneity thesis, the twin paradox, the relativistic concept of mass, and determinism. The rather brief treatment of the general theory is, unavoidably, mathematically demanding and carries the subject through to recent inflationary cosmological models. Chapter six (also mathematically demanding at times) examines the development and structure of quantum mechanics, aptly praised as "one of the most elegant creations of the human spirit" (340). Torretti wisely ignores the complexities of quantum field theory since the philosophical problems discussed—measurement, the EPR paradox, the interpretation of the y-function—remain when quantum mechanics is made Lorentz invariant; but he urges philosophers of science to follow the lead of Michael Redhead and [End Page 602] Paul Teller in exploring its metaphysical ramifications. Of special note are the author's trenchant criticisms of attempts to solve the quantum mysteries by Bohr (complementarity), Bohm (hidden variables), Putnam (quantum logic), and Everett (the many worlds interpretation). The book concludes with the author's reflections on issues in the philosophy of science. Torretti defends the structuralist explication of physical theories (more familiarly known as the semantic conception or the model-theoretic view) that informs much of his book, arguing that it succeeds where the "received view" of logical empiricism failed while avoiding Kuhnian incommensurability—"a pseudoproblem that made philosophy of science the laughing stock of practicing physicists" (404). The chapter ends with an attack on inductive logic: "one of the blindest alleys in twentieth-century philosophy" (437).The writing is admirably clear and the author has done a commendable job of explaining the arguments of historical scientists while presenting their theories in a clear... (shrink)

20세기 초 등장한 상대성 이론은 혁신적인 물리학 이론으로서, 물리학의 발전뿐만 아 니라 철학적 사유의 발전을 그 배경으로 삼고 있다. 실제로 뉴턴이 17세기 말 고전역학을 제시한 이후 시간과 공간의 본성에 관한 철학적 문제가 본격적으로 제기되었다. 흄은 시 간과 공간에 대해 인간의 지각에 기초한 경험주의적인 해석을, 칸트는 시간과 공간이 외 부 세계에 존재하는 실체가 아니라 인간의 감각 경험을 가능하게 하는 일종의 인식 형식 이라는 해석을 제시했다. 19세기 전반기에 발견되어 체계적으로 개발된 비유클리드 기하 학은 시간과 공간의 본성에 대한 인간의 이해에 중요한 변화를 가져왔다. (...) 리만과 헬름홀 츠는 기하학의 기초가 되는 가정들이 칸트가 말하는 선험적 종합 명제가 아닌 일종의 경 험적 가설들이며, 물리 세계에 적용되는 기하학의 핵심에는 길이 단위를 측정하는 도구 가 공간 속을 이동하면서 보이는 행태에 대한 가설이 놓여 있다고 보았다. 푸앵카레는 리 만과 헬름홀츠가 제시한 논의의 연장선상에서, 물리학에서 사용되는 기하학과 물리학의 가장 기초적인 법칙들은 필연적 법칙도 아니고 경험적 사실도 아닌 일종의 규약이라는 관점을 제시했다. 마흐는 뉴턴이 제시한 절대적 시간 및 공간 개념을 경험주의적 관점에 서 강하게 비판하고 관계론적 관점에 기반하여 뉴턴에 대항하는 사고 실험을 제시함으로 써, 향후 경험적 사실들에 기초한 관계론적 물리학이 발전할 수 있는 방향을 제시했다. 아인슈타인의 상대성 이론은 전자기학의 발달 및 전자기적 관점과 역학적 관점 사이의 모순이라는 물리학적 맥락뿐만 아니라, 이상과 같은 시간과 공간에 관한 철학적 논의의 맥락 속에서 등장할 수 있었던 물리학 이론이었다. 따라서 상대성 이론의 철학적 의의를 이해하기 위해서는 이상과 같은 이 이론의 철학적 배경을 정확하게 점검할 필요가 있다. (shrink)

Hermann von Helmholtz (1821a "1894) galt als der bedeutendste Physiker und Physiologe seiner Zeit. Er reflektiert in seinen Texten kritisch die Grenzen und den Horizont mAglicher Erkenntnis mit theoretisch-philosophischer Aufmerksamkeit. Aus der FA1/4lle seiner Publikationen stellten der Philosoph Moritz von Schlick und der Physiker und Mathematiker Paul Hertz 1921 aus AnlaA der 100-Jahrfeier seines Geburtstages den Band "Schriften zur Erkenntnistheorie" zusammen: a [ Aoeber den Ursprung und die Bedeutung der geometrischen Axiome (o.J.) a [ Aoeber die Tatsachen, die der (...) Geometrie zugrunde liegen (1868) a [ ZAhlen und Messen, erkenntnistheoretisch betrachtet (1887) a [ Die Tatsachen in der Wahrnehmung (1878). In ihrem Vorwort schreiben Hertz und Schlick: "Der oberste Gesichtspunkt, der uns bei der Auswahl und ErlAuterung der Schriften geleitet hat, war die RA1/4cksicht auf die Sache, auf die zur Sprache kommenden Probleme. Seine Schriften werden hier von neuem dargeboten um der Wahrheit willen, die in ihnen enthalten ist oder sich aus ihnen gewinnen lAAt." Nun erscheint dieses von Schlick und Hertz zusammengestellte Buch in einer bibliophilen Ausgabe...". this is a valuable edition of important papers on the foundations of mathematics published at a reasonable price.a (Zentralblatt fA1/4r Mathematik)..".Zweifellos handelt es sich hier um scharfsinnige Arbeiten, die zum erstenmal in ihrer Zeit die erkenntnistheoretische Relevanz der nichteuklidischen Geometrien thematisierten." (Neue ZA1/4rcher Zeitung). (shrink)

Discours prononcé par Helmholtz en 1862 pour la prise de fonction de prorecteur à l’université de Heidelberg. Le texte original de référence est : Hermann von Helmholtz, « Über das Verhältnis der Naturwissenschaften zur Gesammtheit der Wissenschaft » (1862), in _Philosophische und populärwissenschaftliche Schriften_, 3 vol., Michael Heidelberger, Helmut Pulte und Gregor Schiemann (éds.), Hamburg : Felix Meiner Verlag, 2017, vol. 1, p. 181–207. Nous indiquons entre crochets dans la marge la pagination allemande de cette édition (NdT).

Hermann von Helmholtz was a leading figure of nineteenth-century European intellectual life, remarkable even among the many scientists of the period for the range and depth of his interests. A pioneer of physiology and physics, he was also deeply concerned with the implications of science for philosophy and culture. From the 1850s to the 1890s, Helmholtz delivered more than two dozen popular lectures, seeking to educate the public and to enlighten the leaders of European society and governments about (...) the potential benefits of science and technology to a developing modern society. David Cahan has selected fifteen of these lectures, which reflect the wide range of topics of crucial importance to Helmholtz and his audiences. Among the subjects discussed are the origins of the planetary system, the relation of natural science to science in general, the aims and progress of the physical sciences, the problems of perception, and academic freedom in German universities. This collection also includes Helmholtz's fascinating lectures on the relation of optics to painting and the physiological causes of harmony in music, which provide insight into the relations between science and aesthetics. Science and Culture makes available again Helmholtz's eloquent arguments on the usefulness, benefits, and, intellectual pleasures of understanding the natural world. With Cahan's Introduction to set these essays in their broader context, this collection makes an important contribution to the philosophical and intellectual history of Europe at a time when science played an increasingly significant role in social, economic, and cultural life. (shrink)

The object in this article is to discuss the philosophical bearing of recent inquiries concerning geometrical axioms and the possibility of working out analytically other systems of geometry with other axioms than Euclid's. Digital edition compiled by Gabriele Dörflinger, Heidelberg University Library.

Gain not only murdered his brother and lied to God, but he also misled many preachers. And while he murdered and lied in a story, he has misled preachers in fact.

The object in this article is to discuss the philosophical bearing of recent inquiries concerning geometrical axioms and the possibility of working out analytically other systems of geometry with other axioms than Euclid's. Digital edition compiled by Gabriele Dörflinger, Heidelberg University Library.

We propose a French translation of the preface written by H. nov Helmholtz to the second part of volume one of the translation of the Treatise on Natural Philosophy due to Sir William Thompson and Tait. The numbers in square brackets refer to the page numbers of the original text.RésuméNous proposons une traduction française de la préface de H. von Helmholtz à la seconde partie du premier volume de la traduction du Treatise on Natural Philosophy de Sir William (...) Thompson et Tait. Les nombres entre crochets rappellent la pagination du texte original. (shrink)

We propose a French translation of the preface written by H. nov Helmholtz to the German translation of Fragments of Science by Tyndall. The German translation was by Anna von Helmholtz and Du-Bois Reymond and reviewed by H. von Helmholtz. The numbers in square brackets refer to the page numbers of the original text.RésuméNous proposons une traduction française de la préface de H. von Helmholtz à la traduction allemande des Fragments of Science de Tyndall, traduction allemande (...) réalisée par Anna von Helmholtz et Du-Bois Reymond et revue par H. von Helmholtz. Les nombres entre crochets rappellent la pagination du texte original. (shrink)