The role of mathematics in eighteenth-century science and philosophy of science can hardly be ove... more The role of mathematics in eighteenth-century science and philosophy of science can hardly be overestimated, though it was and is frequently misunderstood. From today’s point of view, one might be tempted to say that philosophers and scientists in the seventeenth and even more in the eighteenth century became aware of the importance of mathematics as a means of ‘representing’ physical phenomena or as an ‘instrument’ of deductive explanation and prediction. According to this view, the rise of mathematical physics is a peripheral aspect of the new experimental sciences, and the mathematical part of physics is a methodologically directed, constructive enterprise that is somehow ‘parasitical’ with respect to experimental and observational data. But such modernising outcomes of logical empiricism are missing the central point, i.e., the ‘mathematical nature of nature’ according to mechanical philosophy. I will start with some general considerations about mathematics under the premise of mechanism before coming to the aim of my paper.
The central questions of the following outline 1 are motivated both by the topic of this conferen... more The central questions of the following outline 1 are motivated both by the topic of this conference and by a remarkable revival: 'History of ideas' denominates a tradition of viewing and doing history which was founded by A. E. Lovejoy in the 1930ties and soon gained considerable influence. Due to a stronger social and pragmatic coining of history-at least in the sense of historia rerum gestarumand other, more 'external' reasons it entered a state of crisis in the 1960ties 2. However, it never disappeared and regained strength during the last decade 3-though
Carl Gustav Jakob Jacobi (1804 - 1851) gilt heute nach C. F. Gau und neben P. G. Lejeune Dirichle... more Carl Gustav Jakob Jacobi (1804 - 1851) gilt heute nach C. F. Gau und neben P. G. Lejeune Dirichlet als der wichtigste deutsche Mathematiker der ersten H lfte des 19. Jahrhunderts. Als Vertreter der "reinen" Mathematik machte er sich v. a. durch seine Beitr ge zur Zahlentheorie und Theorie der elliptischen Funktionen einen Namen. Jacobi leistete jedoch auch wesentliche Beitr ge zur Analytischen Mechanik, die er in der Tradition Eulers, Lagranges und Hamiltons v. a. als einen Zweig der h heren Analysis betrachtete.Den umfassendsten und authentischsten Einblick in seine Anschauungen zu dieser Disziplin geben seine "Vorlesungen ber analytische Mechanik," Jacobi las diese Vorlesung im Wintersemester 1847/ 48 in Berlin; es handelt sich um seine letzte Veranstaltung zur Mechanik berhaupt. Jacobis Sch ler Wilhelm Scheibner (1826 - 1907) fertigte eine vollst ndige und sorgf ltige Mitschrift dieser Vorlesung an. Der Text wurde von Helmut Pulte editiert und mit Einleitung u...
Until today, conventionalism is mainly regarded from the point of view of geometry, both in histo... more Until today, conventionalism is mainly regarded from the point of view of geometry, both in historical as in philosophical perspective. This paper, which corresponds in a certain way with earlier studies of J. Giedymin, aims at a broader interpretation. The importance of the so-called 'physics of principles', rooted in the tradition of analytical mechanics, for Poincaré's conventionalism is emphasized. It is argued that important elements of physical conventionalism can already be found in this tradition that underwent a fundamental change in the course of the 19th century.
The concept of analogy plays an important role in KANT'S philosophy not just of scientific th... more The concept of analogy plays an important role in KANT'S philosophy not just of scientific theory but also of moral philosophy. This contribution concentrates on outlining different types of analogies within the context of the philosophy of science. Besides "analogies of experience" so-called "symbolic analogies" will also be addressed, along with their role in the unity of scientific experience. References to more recent debates within science and its philosophy signal its actuality, in part also the unavoidability of KANT'S thoughts on analogies. As a part of his methodology and heuristics, they are of significance to modern science and philosophy of science even after the collapse of the aprioristic foundational program.
When the pl,rysicßt Ernst Mach states that Charles Darwin's 'special great discoveries... more When the pl,rysicßt Ernst Mach states that Charles Darwin's 'special great discoveries' could 'by no means have been made by a physicist' (Mach I99I,I97), this seems at first glance trivial and tautological: physics traditionally has to do with inorganic nature and its laws,while Darwin's focus was precisely on animate nature, on the origin and explanation of its species.l On this basis, Mach's remark appears only too logical. If on the other hand non-physicists pronounce Darwin to be 'the Copernicus of the orgaruc world' (Emil Du Bois-Reymond), the new 'Galileo' (Asa Gray) or allude to him as the 'Newton of the grass blade' who after Kant should never have been (Ernst Haeckel), they are also staring that Darwin made discoveries of revolutionary significance which changed accepted conceptions ofthe world a circumstance that up to that point was only known wichin the fields of physics2 and was presumably expected only of that scienc...
The role of mathematics in eighteenth-century science and philosophy of science can hardly be ove... more The role of mathematics in eighteenth-century science and philosophy of science can hardly be overestimated, though it was and is frequently misunderstood. From today’s point of view, one might be tempted to say that philosophers and scientists in the seventeenth and even more in the eighteenth century became aware of the importance of mathematics as a means of ‘representing’ physical phenomena or as an ‘instrument’ of deductive explanation and prediction. According to this view, the rise of mathematical physics is a peripheral aspect of the new experimental sciences, and the mathematical part of physics is a methodologically directed, constructive enterprise that is somehow ‘parasitical’ with respect to experimental and observational data. But such modernising outcomes of logical empiricism are missing the central point, i.e., the ‘mathematical nature of nature’ according to mechanical philosophy. I will start with some general considerations about mathematics under the premise of mechanism before coming to the aim of my paper.
The central questions of the following outline 1 are motivated both by the topic of this conferen... more The central questions of the following outline 1 are motivated both by the topic of this conference and by a remarkable revival: 'History of ideas' denominates a tradition of viewing and doing history which was founded by A. E. Lovejoy in the 1930ties and soon gained considerable influence. Due to a stronger social and pragmatic coining of history-at least in the sense of historia rerum gestarumand other, more 'external' reasons it entered a state of crisis in the 1960ties 2. However, it never disappeared and regained strength during the last decade 3-though
Carl Gustav Jakob Jacobi (1804 - 1851) gilt heute nach C. F. Gau und neben P. G. Lejeune Dirichle... more Carl Gustav Jakob Jacobi (1804 - 1851) gilt heute nach C. F. Gau und neben P. G. Lejeune Dirichlet als der wichtigste deutsche Mathematiker der ersten H lfte des 19. Jahrhunderts. Als Vertreter der "reinen" Mathematik machte er sich v. a. durch seine Beitr ge zur Zahlentheorie und Theorie der elliptischen Funktionen einen Namen. Jacobi leistete jedoch auch wesentliche Beitr ge zur Analytischen Mechanik, die er in der Tradition Eulers, Lagranges und Hamiltons v. a. als einen Zweig der h heren Analysis betrachtete.Den umfassendsten und authentischsten Einblick in seine Anschauungen zu dieser Disziplin geben seine "Vorlesungen ber analytische Mechanik," Jacobi las diese Vorlesung im Wintersemester 1847/ 48 in Berlin; es handelt sich um seine letzte Veranstaltung zur Mechanik berhaupt. Jacobis Sch ler Wilhelm Scheibner (1826 - 1907) fertigte eine vollst ndige und sorgf ltige Mitschrift dieser Vorlesung an. Der Text wurde von Helmut Pulte editiert und mit Einleitung u...
Until today, conventionalism is mainly regarded from the point of view of geometry, both in histo... more Until today, conventionalism is mainly regarded from the point of view of geometry, both in historical as in philosophical perspective. This paper, which corresponds in a certain way with earlier studies of J. Giedymin, aims at a broader interpretation. The importance of the so-called 'physics of principles', rooted in the tradition of analytical mechanics, for Poincaré's conventionalism is emphasized. It is argued that important elements of physical conventionalism can already be found in this tradition that underwent a fundamental change in the course of the 19th century.
The concept of analogy plays an important role in KANT'S philosophy not just of scientific th... more The concept of analogy plays an important role in KANT'S philosophy not just of scientific theory but also of moral philosophy. This contribution concentrates on outlining different types of analogies within the context of the philosophy of science. Besides "analogies of experience" so-called "symbolic analogies" will also be addressed, along with their role in the unity of scientific experience. References to more recent debates within science and its philosophy signal its actuality, in part also the unavoidability of KANT'S thoughts on analogies. As a part of his methodology and heuristics, they are of significance to modern science and philosophy of science even after the collapse of the aprioristic foundational program.
When the pl,rysicßt Ernst Mach states that Charles Darwin's 'special great discoveries... more When the pl,rysicßt Ernst Mach states that Charles Darwin's 'special great discoveries' could 'by no means have been made by a physicist' (Mach I99I,I97), this seems at first glance trivial and tautological: physics traditionally has to do with inorganic nature and its laws,while Darwin's focus was precisely on animate nature, on the origin and explanation of its species.l On this basis, Mach's remark appears only too logical. If on the other hand non-physicists pronounce Darwin to be 'the Copernicus of the orgaruc world' (Emil Du Bois-Reymond), the new 'Galileo' (Asa Gray) or allude to him as the 'Newton of the grass blade' who after Kant should never have been (Ernst Haeckel), they are also staring that Darwin made discoveries of revolutionary significance which changed accepted conceptions ofthe world a circumstance that up to that point was only known wichin the fields of physics2 and was presumably expected only of that scienc...
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