Philip Beeley

Physical arguments and moral inducements: John Wallis on questions of antiquarianism and natural philosophy

In his posthumously published work Chartham News (1669), the antiquary William Somner tentatively sought to link the discovery of fossilized remains near Canterbury to the prehistoric existence of an isthmus connecting Britain and France, before calling on natural philosophers to pursue his explanation further. This call was eventually heeded by the Oxford mathematician John Wallis, but only after more than thirty years had elapsed. The arrival in England of a catalogue of questions concerning the geology of the Channel led to the republication of Chartham News in the Philosophical Transactions, prompting Wallis to develop a physical explanation based on his intimate knowledge of the Kent coastline. Unbeknown to Wallis at the time, that catalogue had been sent by G. W. Leibniz, who had in turn received it from G. D. Schmidt, the former Resident of Brunswick-Lüneburg in Sweden. Walliss explanation, based on the principle of establishing physical causes both for the rupturing of the isthmus and for the origin of fossils, placed him in a camp opposed by Newtonian authors such as John Harris at a time when the priority dispute over the discovery of the calculus led to the severing of his ties with the German mathematician and philosopher Leibniz.

‘To the publike advancement’ John Collins and the promotion of mathematical knowledge in Restoration England

Dedicated to the memory of Jacqueline Stedall

Sarah Dry, The Newton Papers: The Strange and True Odyssey of Isaac Newton’s Manuscripts. Oxford: Oxford University Press, 2014, xi + 238 pages.

The Newton Papers is an important, exceptionally well-written book, serving the needs of a scholarly community that is increasingly concerned to know more about the provenance of manuscripts to be found in the greater and lesser collections around the globe. Sarah Dry illuminates the motivations of collectors such as Keynes and Yahuda, shows the impact of socioeconomic developments on the custodianship of manuscript collections, takes us into the world of the early twentieth-century book and manuscript traders, and above all tells us not a little about the ways in which the reception of Newton’s manuscripts challenged the orthodoxy of existing conceptions of the great man’s scientific legacy. What emerges is that the current predilection for a Newton of many parts to a large extent reflects the various and often complex paths taken by his letters and papers following his demise.

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Up to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibnizs thought.

G.W. Leibniz, Interrelations Between Mathematics and Philosophy

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.

The Interrelations Between Mathematics and Philosophy in Leibniz’s Thought

Like no other philosopher in his time, Leibniz was concerned to develop a metaphysics which could provide an intellectually rigorous account of the success of the mathematical sciences in harnessing and explaining the natural world. Part of the motivation for this concern was his recognition that disciplines such as optics, pneumatics, and mechanics contributed substantially to the improvement of the human condition, this being on his view the ultimate aim of all philosophical endeavour.