To all these institutions we express our warm gratitude. We are also grateful to the members of t... more To all these institutions we express our warm gratitude. We are also grateful to the members of the PILM scientific committee for their invaluable help in preparing the program and reporting on so many lectures, as well as to the staff of the Poincaré Archives for their help in the preparation of the conference and their expert assistance in various ways. We particularly express our gratitude to Dr. Prosper Doh (Poincaré Archives) who has taken on the job of technical editor for this book and who has realized the index and the camera-ready copy. Finally, the editors are indebted to the editorial board of "Logic, Epistemology, and the Unity of Science" for accepting this volume in their series. They would also like to thank Springer Publishers and, in particular, Floor Oosting.
l'accord avec les conditions générales d'utilisation (http://www. numdam.org/conditions). Toute u... more l'accord avec les conditions générales d'utilisation (http://www. numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ E.W. Beth and the Logical Empiricists
"Omstreeks 1900 vonden veranderingen en vernieuwingen in de filosofie plaats, die hun in... more "Omstreeks 1900 vonden veranderingen en vernieuwingen in de filosofie plaats, die hun invloed en doorwerking in de gehele twintigste eeuw hebben gekregen", zo constateert Van Dooren in zijn Denkwegen in de geschiedenis van de nieuwere wijsbegeerte. Het was de tijd van de opleving van vele neo-richtingen zoals neokantianisme, neohegelianisme, neothomisme, maar meer nog van de opkomst van volstrekt nieuwe visies
Wittgenstein — Eine Neubewertung / Wittgenstein — Towards a Re-Evaluation, 1990
In 1915, the Viennese bookseller Braumuller published a book by Richard Wahle, The, tragecomedy o... more In 1915, the Viennese bookseller Braumuller published a book by Richard Wahle, The, tragecomedy of wisdom — the results and history of philosophizing, in which the author, a professor in philosophy at the University of Czernowitz, says that the insight to which philosophy has come is as follows: ‘the best is silence’.1 “Philosophy exists only as questions, not as answers”.2 Though the book has two editions — the second in 1925 — it cannot be maintained that the author became famous. It is true that the Pictorial history of philosophy by Runes contains a portrait and a short biography of Wahle3, but I have not yet seen commemorations of the year of his death, let alone celebrations of his birthday.
... From the larger German-speaking area one also hears names like Frege, Hertz, Schopenhauer, an... more ... From the larger German-speaking area one also hears names like Frege, Hertz, Schopenhauer, and Spengler, but the ideas of Spengler like ... One thinks of Fritz Mauthner (1849-1923) 17and of Anton Marty (1847-1914) who both corresponded with and were influenced by Mach ...
Moses Mendelssohn, once a member of a "Berlin Circle", together with distinguished mathematicians... more Moses Mendelssohn, once a member of a "Berlin Circle", together with distinguished mathematicians such as Euler, was, like him, interested in "mathematical music". 1 But different from Euler, who was an expert in "natural" tonal relationships, Mendelssohn wrote about an artificial way of solving the problem of intonation for organs, harpsichords and clavichords. He connected solutions of the ancient Greek Delian problem (of constructing distances with the length of the cubic root of a given length) with the problem of equal temperament tuning. Thereby he gave an original proof for Newton"s solution. Mendelssohn"s method was not adopted in practice, for two reasons: the reluctance of musicians to tune their instruments with an equal division of the octave at all, and the alleged practical difficulty of working with a monochord on the basis of Mendelssohn"s approximations. 2 As a result, only the title of Mendelssohn"s article was mentioned in the musico-theoretical literature, without a closer inspection of its content. And his mathematical contribution was ignored by mathematicians who have extensively written on the subject. 3 (Conti 1900 and 1907). For a proper appreciation of Mendelssohn"s mathematical talents, an analysis is given of the way he proved Newton"s theorem with Euclidean geometrical means. This requires some geometrical knowledge and familiarity with the algebraic theory of proportions, but I will try to explain Mendelssohn"s proof in a hopefully lucid way. I will end with a short discussion of the question whether equal temperament tuning is compatible with Mendelssohn"s aesthetics of music. The lecture begins with a short introduction, in which the need of special tuning ways is expounded. 4 Cavallo, Of the temperament, 253-254. 5 Valerius, Nederlandtsche Gedenckklank, p. 168. The English text is as follows: "We gather together to ask the Lord"s blessing; He chastens and hastens His will to make known.". 6 Harmonization attributed to Hassler.
A study of Ernst Mach’s philosophical influence in the Netherlands and of ideas similar to his ca... more A study of Ernst Mach’s philosophical influence in the Netherlands and of ideas similar to his can scarcely avoid an initial conclusion that with comparatively few exceptions significant impact has been centered at a single university, though it has seemed to survive well there. It appears that virtually all the philosophy chairs at other Dutch universities from the late 19th century well into the 20th century were occupied by Neo-Kantians,1 who considered themselves to be supporters of what they called “critical philosophy”, or by psychologists and Hegelians.2
Emphasis in historiography of science is naturally placed on the discoveries and inventions which... more Emphasis in historiography of science is naturally placed on the discoveries and inventions which scientists make and generally less on new methods of doing science, but sometimes the latter can he an important clue to help us understand the former. For example, while we all acknowledge how great the contributions of Maxwell, Boltzmann, Planck, and Einstein were to physics from roughly 1870 to 1920, we often overlook the significance of a methodological phrase which was popular during that same period, namely, what in German was called “Bildtheorie” or in English “picture theory”. But even before we can properly study its significance we have to know what the theory was, but even this presents problems, since the meaning changed. In fact, this paper is an attempt not only to describe the history of that change from Maxwell to Wittgenstein but to study in particular how Boltzmann’s conception of Bildtheorie seems to have been at least partly incorporated into the approach of Ludwig W...
In the Logisch-philosophische Abhandlung Wittgenstein says so little about physics that commentat... more In the Logisch-philosophische Abhandlung Wittgenstein says so little about physics that commentators have had the greatest trouble to comment on it. (See, for example, Black (I964).) It even happened that a misprint in the first edition of this elliptic treatise went unnoticed for sixty years. The explanation seems to be that it did not occur to anyone that Wittgenstein in his philosophy of physics did little more than summarize parts of a few articles Mach wrote in his Popular-wissenschaftliche Vorlesungen. (Ryle (195 I) even said of Wittgenstein: 'He was influenced by Frege and Russell, not by Mach.') In order to show that Wittgenstein was directly influenced by Mach, I will confine myself to the following subjects on which Wittgenstein commented: (i) chronometry, geometry and problems of space and time (6.36I I, 6.36I I I), and (2) physical principles 6.32-6.34). Mach wrote on the first of these subjects in the last essay that appeared in the fourth edition of the aforementioned book, 'Eine Betrachtung fiber Zeit und Raum'. The second he treated in his articles 'Ueber das Princip der Erhaltung der Energie' and 'Werden Vorstellungen, Gedanken vererbt?' (Mach (I91o).) I am not concerned here with the influence of Part VI of Russell's Principles of mathematics on Wittgenstein's Abhandlung, nor with the influence of Hertz's Prinzipien der Mechanik on both works, I only want to point out that the similarity of Wittgenstein's remarks with some of Mach's popular-scientific agruments is so striking that one cannot but conclude that Wittgenstein had read at least some of the articles of Mach's Popular-wissenschaftliche Vorlesungen. First, there are Wittgenstein's comments on Kant's problem of the right and left hand which cannot be made to cover one another: (i) this problem occurs already in the plane, and even in one-dimensional space; (2) the right and left hand are in fact completely congruent; (3) a right-hand giove could be put on a left hand if it could be turned in four-dimensional space (cf. 6.36III). Mach made similar remarks, but he at least did not omit his source: according to Mach, M6bius remarked about I827 'that a linear figure abc, that can be seen as the symmetrical counterpart of a'b'c'mirrored in SS on the same straight line, can never be made to cover the latter on this line; for this purpose one has to take the figure out of the straight line and turn it; in order to do that at least two dimensions are needed, so a plane' (ibid., pp. 502-503). In addition Mach mentioned M6bius' generalisation, not only for triangles in a plane, but also for congruent three-dimensional bodies, that cannot be made to cover each other in any way in space: 'But one could
To all these institutions we express our warm gratitude. We are also grateful to the members of t... more To all these institutions we express our warm gratitude. We are also grateful to the members of the PILM scientific committee for their invaluable help in preparing the program and reporting on so many lectures, as well as to the staff of the Poincaré Archives for their help in the preparation of the conference and their expert assistance in various ways. We particularly express our gratitude to Dr. Prosper Doh (Poincaré Archives) who has taken on the job of technical editor for this book and who has realized the index and the camera-ready copy. Finally, the editors are indebted to the editorial board of "Logic, Epistemology, and the Unity of Science" for accepting this volume in their series. They would also like to thank Springer Publishers and, in particular, Floor Oosting.
l'accord avec les conditions générales d'utilisation (http://www. numdam.org/conditions). Toute u... more l'accord avec les conditions générales d'utilisation (http://www. numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ E.W. Beth and the Logical Empiricists
"Omstreeks 1900 vonden veranderingen en vernieuwingen in de filosofie plaats, die hun in... more "Omstreeks 1900 vonden veranderingen en vernieuwingen in de filosofie plaats, die hun invloed en doorwerking in de gehele twintigste eeuw hebben gekregen", zo constateert Van Dooren in zijn Denkwegen in de geschiedenis van de nieuwere wijsbegeerte. Het was de tijd van de opleving van vele neo-richtingen zoals neokantianisme, neohegelianisme, neothomisme, maar meer nog van de opkomst van volstrekt nieuwe visies
Wittgenstein — Eine Neubewertung / Wittgenstein — Towards a Re-Evaluation, 1990
In 1915, the Viennese bookseller Braumuller published a book by Richard Wahle, The, tragecomedy o... more In 1915, the Viennese bookseller Braumuller published a book by Richard Wahle, The, tragecomedy of wisdom — the results and history of philosophizing, in which the author, a professor in philosophy at the University of Czernowitz, says that the insight to which philosophy has come is as follows: ‘the best is silence’.1 “Philosophy exists only as questions, not as answers”.2 Though the book has two editions — the second in 1925 — it cannot be maintained that the author became famous. It is true that the Pictorial history of philosophy by Runes contains a portrait and a short biography of Wahle3, but I have not yet seen commemorations of the year of his death, let alone celebrations of his birthday.
... From the larger German-speaking area one also hears names like Frege, Hertz, Schopenhauer, an... more ... From the larger German-speaking area one also hears names like Frege, Hertz, Schopenhauer, and Spengler, but the ideas of Spengler like ... One thinks of Fritz Mauthner (1849-1923) 17and of Anton Marty (1847-1914) who both corresponded with and were influenced by Mach ...
Moses Mendelssohn, once a member of a "Berlin Circle", together with distinguished mathematicians... more Moses Mendelssohn, once a member of a "Berlin Circle", together with distinguished mathematicians such as Euler, was, like him, interested in "mathematical music". 1 But different from Euler, who was an expert in "natural" tonal relationships, Mendelssohn wrote about an artificial way of solving the problem of intonation for organs, harpsichords and clavichords. He connected solutions of the ancient Greek Delian problem (of constructing distances with the length of the cubic root of a given length) with the problem of equal temperament tuning. Thereby he gave an original proof for Newton"s solution. Mendelssohn"s method was not adopted in practice, for two reasons: the reluctance of musicians to tune their instruments with an equal division of the octave at all, and the alleged practical difficulty of working with a monochord on the basis of Mendelssohn"s approximations. 2 As a result, only the title of Mendelssohn"s article was mentioned in the musico-theoretical literature, without a closer inspection of its content. And his mathematical contribution was ignored by mathematicians who have extensively written on the subject. 3 (Conti 1900 and 1907). For a proper appreciation of Mendelssohn"s mathematical talents, an analysis is given of the way he proved Newton"s theorem with Euclidean geometrical means. This requires some geometrical knowledge and familiarity with the algebraic theory of proportions, but I will try to explain Mendelssohn"s proof in a hopefully lucid way. I will end with a short discussion of the question whether equal temperament tuning is compatible with Mendelssohn"s aesthetics of music. The lecture begins with a short introduction, in which the need of special tuning ways is expounded. 4 Cavallo, Of the temperament, 253-254. 5 Valerius, Nederlandtsche Gedenckklank, p. 168. The English text is as follows: "We gather together to ask the Lord"s blessing; He chastens and hastens His will to make known.". 6 Harmonization attributed to Hassler.
A study of Ernst Mach’s philosophical influence in the Netherlands and of ideas similar to his ca... more A study of Ernst Mach’s philosophical influence in the Netherlands and of ideas similar to his can scarcely avoid an initial conclusion that with comparatively few exceptions significant impact has been centered at a single university, though it has seemed to survive well there. It appears that virtually all the philosophy chairs at other Dutch universities from the late 19th century well into the 20th century were occupied by Neo-Kantians,1 who considered themselves to be supporters of what they called “critical philosophy”, or by psychologists and Hegelians.2
Emphasis in historiography of science is naturally placed on the discoveries and inventions which... more Emphasis in historiography of science is naturally placed on the discoveries and inventions which scientists make and generally less on new methods of doing science, but sometimes the latter can he an important clue to help us understand the former. For example, while we all acknowledge how great the contributions of Maxwell, Boltzmann, Planck, and Einstein were to physics from roughly 1870 to 1920, we often overlook the significance of a methodological phrase which was popular during that same period, namely, what in German was called “Bildtheorie” or in English “picture theory”. But even before we can properly study its significance we have to know what the theory was, but even this presents problems, since the meaning changed. In fact, this paper is an attempt not only to describe the history of that change from Maxwell to Wittgenstein but to study in particular how Boltzmann’s conception of Bildtheorie seems to have been at least partly incorporated into the approach of Ludwig W...
In the Logisch-philosophische Abhandlung Wittgenstein says so little about physics that commentat... more In the Logisch-philosophische Abhandlung Wittgenstein says so little about physics that commentators have had the greatest trouble to comment on it. (See, for example, Black (I964).) It even happened that a misprint in the first edition of this elliptic treatise went unnoticed for sixty years. The explanation seems to be that it did not occur to anyone that Wittgenstein in his philosophy of physics did little more than summarize parts of a few articles Mach wrote in his Popular-wissenschaftliche Vorlesungen. (Ryle (195 I) even said of Wittgenstein: 'He was influenced by Frege and Russell, not by Mach.') In order to show that Wittgenstein was directly influenced by Mach, I will confine myself to the following subjects on which Wittgenstein commented: (i) chronometry, geometry and problems of space and time (6.36I I, 6.36I I I), and (2) physical principles 6.32-6.34). Mach wrote on the first of these subjects in the last essay that appeared in the fourth edition of the aforementioned book, 'Eine Betrachtung fiber Zeit und Raum'. The second he treated in his articles 'Ueber das Princip der Erhaltung der Energie' and 'Werden Vorstellungen, Gedanken vererbt?' (Mach (I91o).) I am not concerned here with the influence of Part VI of Russell's Principles of mathematics on Wittgenstein's Abhandlung, nor with the influence of Hertz's Prinzipien der Mechanik on both works, I only want to point out that the similarity of Wittgenstein's remarks with some of Mach's popular-scientific agruments is so striking that one cannot but conclude that Wittgenstein had read at least some of the articles of Mach's Popular-wissenschaftliche Vorlesungen. First, there are Wittgenstein's comments on Kant's problem of the right and left hand which cannot be made to cover one another: (i) this problem occurs already in the plane, and even in one-dimensional space; (2) the right and left hand are in fact completely congruent; (3) a right-hand giove could be put on a left hand if it could be turned in four-dimensional space (cf. 6.36III). Mach made similar remarks, but he at least did not omit his source: according to Mach, M6bius remarked about I827 'that a linear figure abc, that can be seen as the symmetrical counterpart of a'b'c'mirrored in SS on the same straight line, can never be made to cover the latter on this line; for this purpose one has to take the figure out of the straight line and turn it; in order to do that at least two dimensions are needed, so a plane' (ibid., pp. 502-503). In addition Mach mentioned M6bius' generalisation, not only for triangles in a plane, but also for congruent three-dimensional bodies, that cannot be made to cover each other in any way in space: 'But one could
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