This paper consists of three main sections. In the first section, we consider how early attempts at understanding the relationship between mathematics and philosophy in Leibniz’s thought were often made within the framework of grand reconstructions guided by intellectual trends such as the search for “the ideal of system”. In the second section, we proceed to recount Leibniz’s first encounter with contemporary mathematics during his four years of study in Paris presenting some of the earliest mathematical successes which he made (...) there. In particular, we argue that recently published letters and papers reveal how his youthful mathematical reflexions were deeply intertwined with important philosophical insights that, in turn, acted as guiding ideas for his mathematical research. Finally, in the third section, we situate the central themes of the essays of the present volume within the new understanding of the interrelations between philosophy and mathematics in Leibniz’s thought briefly indicated in the opening section. (shrink)

Mathematical practitioners in seventeenth-century London formed a cohesive knowledge community that intersected closely with instrument-makers, printers and booksellers. Many wrote books for an increasingly numerate metropolitan market on topics covering a wide range of mathematical disciplines, ranging from algebra to arithmetic, from merchants’ accounts to the art of surveying. They were also teachers of mathematics like John Kersey or Euclid Speidell who would use their own rooms or the premises of instrument-makers for instruction. There was a high degree of interdependency (...) even beyond their immediate milieu. Authors would cite not only each other, but also practitioners of other professions, especially those artisans with whom they collaborated closely. Practical mathematical books effectively served as an advertising medium for the increasingly self-conscious members of a new emerging professional class. Contemporaries would talk explicitly of ‘the London mathematicians’ in distinction to their academic counterparts at Oxford or Cambridge. The article takes a closer look at this metropolitan knowledge culture during the second half of the century, considering its locations, its meeting places and the mathematical clubs which helped forge the identity of its practitioners. It discusses their backgrounds, teaching practices and relations to the London book trade, which supplied inexpensive practical mathematical books to a seemingly insatiable public. (shrink)

On numerous occasions Leibniz stressed the importance of providing the new infinitesimal calculus with the solid foundations it required by means of rigorous proofs. His treatise on the arithmetical quadrature of the circle, the ellipse and the hyperbola shows clearly that this was in fact a foremost consideration right from the outset.

When the translator and editor of the German edition of Bayle’s Historical and Critical Dictionary, Johann Christoph Gottsched, sug gested to Johann Georg Wachter that he supply an explanation of his views on Spinoza for inclusion in the eponymous article, he gladly obliged. Wachter, a failed university professor in Duisburg who had since managed to find employment in the council library in Gottsched’s adopted home town of Leipzig, had good reasons for doing this. Not only had his Elucidarius cabalisticus been (...) fiercely attacked in the Respublica litteraria as being the work of a new cabbalist evidently out to defend atheism and other purported evils of Spinoza’s philosophy, but also he appeared in that book to have adopted a philosophical position diametrically opposed to the one he had held just a few years earlier. His Der Spinozismus Im Jüdenthumb, which he had published in 1699 after a year-long stay in Amsterdam and which had been directed against a certain Moses Germanus, had after all sought to defend natural religion against Spinoza’s phi losophy by attacking those elements in it which were seen to represent the greatest threat to an understanding of God and the duties of man based solely on rational knowledge, in particular, its fundamental pantheism. In effect, while Wachter had there used the demonstration of the cabbalistic roots and the detrimental ethical consequences of Spinoza’s philosophy to show that Christianity and Judaism are fundamentally irreconcilable, he now used the first part of that demonstration as the basis for presenting the theory contained in the Ethics as a tenable philosophical theology. (shrink)

When the translator and editor of the German edition of Bayle’s Historical and Critical Dictionary, Johann Christoph Gottsched, sug gested to Johann Georg Wachter that he supply an explanation of his views on Spinoza for inclusion in the eponymous article, he gladly obliged. Wachter, a failed university professor in Duisburg who had since managed to find employment in the council library in Gottsched’s adopted home town of Leipzig, had good reasons for doing this. Not only had his Elucidarius cabalisticus been (...) fiercely attacked in the Respublica litteraria as being the work of a new cabbalist evidently out to defend atheism and other purported evils of Spinoza’s philosophy, but also he appeared in that book to have adopted a philosophical position diametrically opposed to the one he had held just a few years earlier. His Der Spinozismus Im Jüdenthumb, which he had published in 1699 after a year-long stay in Amsterdam and which had been directed against a certain Moses Germanus, had after all sought to defend natural religion against Spinoza’s phi losophy by attacking those elements in it which were seen to represent the greatest threat to an understanding of God and the duties of man based solely on rational knowledge, in particular, its fundamental pantheism. In effect, while Wachter had there used the demonstration of the cabbalistic roots and the detrimental ethical consequences of Spinoza’s philosophy to show that Christianity and Judaism are fundamentally irreconcilable, he now used the first part of that demonstration as the basis for presenting the theory contained in the Ethics as a tenable philosophical theology. (shrink)

When the translator and editor of the German edition of Bayle’s Historical and Critical Dictionary, Johann Christoph Gottsched, sug gested to Johann Georg Wachter that he supply an explanation of his views on Spinoza for inclusion in the eponymous article, he gladly obliged. Wachter, a failed university professor in Duisburg who had since managed to find employment in the council library in Gottsched’s adopted home town of Leipzig, had good reasons for doing this. Not only had his Elucidarius cabalisticus been (...) fiercely attacked in the Respublica litteraria as being the work of a new cabbalist evidently out to defend atheism and other purported evils of Spinoza’s philosophy, but also he appeared in that book to have adopted a philosophical position diametrically opposed to the one he had held just a few years earlier. His Der Spinozismus Im Jüdenthumb, which he had published in 1699 after a year-long stay in Amsterdam and which had been directed against a certain Moses Germanus, had after all sought to defend natural religion against Spinoza’s phi losophy by attacking those elements in it which were seen to represent the greatest threat to an understanding of God and the duties of man based solely on rational knowledge, in particular, its fundamental pantheism. In effect, while Wachter had there used the demonstration of the cabbalistic roots and the detrimental ethical consequences of Spinoza’s philosophy to show that Christianity and Judaism are fundamentally irreconcilable, he now used the first part of that demonstration as the basis for presenting the theory contained in the Ethics as a tenable philosophical theology. (shrink)

In my introduction to Kontinuität und Mechanismus, I expressed surprise at the lack of work which was being done at the time on the young Leibniz in spite of the fact that conditions for investigating the period up to 1676 are almost ideal—certainly in Leibnizian terms. Most of the letters and papers from this period of immediate philosophical significance have now been published in the Akademie-Ausgabe so that there is here an incomparably better starting point for detailed studies than in (...) the case of his later work. (shrink)

In my introduction to Kontinuität und Mechanismus, I expressed surprise at the lack of work which was being done at the time on the young Leibniz in spite of the fact that conditions for investigating the period up to 1676 are almost ideal—certainly in Leibnizian terms. Most of the letters and papers from this period of immediate philosophical significance have now been published in the Akademie-Ausgabe so that there is here an incomparably better starting point for detailed studies than in (...) the case of his later work. (shrink)

In my introduction to Kontinuität und Mechanismus, I expressed surprise at the lack of work which was being done at the time on the young Leibniz in spite of the fact that conditions for investigating the period up to 1676 are almost ideal—certainly in Leibnizian terms. Most of the letters and papers from this period of immediate philosophical significance have now been published in the Akademie-Ausgabe so that there is here an incomparably better starting point for detailed studies than in (...) the case of his later work. (shrink)

Depending on one’s point of view, Leibniz’s early philosophy can either be regarded as preparing the conceptual foundation for the development of the later theory of monads or as an intellectual period in it own right, fascinating in itself, since Leibniz here probably more than later allows the free run of his genius. Irrespective of approach, it has, however, to be said that up to recently this period in Leibniz’s thought has not received the attention it deserves.

Depending on one’s point of view, Leibniz’s early philosophy can either be regarded as preparing the conceptual foundation for the development of the later theory of monads or as an intellectual period in it own right, fascinating in itself, since Leibniz here probably more than later allows the free run of his genius. Irrespective of approach, it has, however, to be said that up to recently this period in Leibniz’s thought has not received the attention it deserves.

Depending on one’s point of view, Leibniz’s early philosophy can either be regarded as preparing the conceptual foundation for the development of the later theory of monads or as an intellectual period in it own right, fascinating in itself, since Leibniz here probably more than later allows the free run of his genius. Irrespective of approach, it has, however, to be said that up to recently this period in Leibniz’s thought has not received the attention it deserves.