The studies that make up this book were written and brought together to honor the memory of Jan Pinborg. His unexpected death in 1982 at the age of forty-five shocked and saddened students of medieval philosophy everywhere and left them with a keen sense of disappoint ment. In his fifteen-year career Jan Pinborg had done so much for our field with his more than ninety books, editions, articles, and reviews and had done it all so well that we recognized him (...) as a leader and counted on many more years of his scholarship, his help, and his friendship. To be missed so sorely by his international colleagues in an academic field is a mark of Jan's achievement, but only of one aspect of it, for historians of philosophy are not the only scholars who have reacted in this way to Jan's death. In his decade and a half of intense productivity he also acquired the same sort of special status among historians of linguistics, whose volume of essays in his memory is being G. L. Bursill-Hall almost simultane published under the editorship of ously with this one. Sten Ebbesen, Jan's student, colleague, and successor as Director of the Institute of Medieval Greek and Latin Philology at the University of Copenhagen, has earned the gratitude of all of us by memorializing Jan 1 in various biographical sketches, one of which is accompanied by a 2 complete bibliography of his publications. (shrink)

This journal article has been superseded by a revised version, published in the collection _Essays on the Philosophy and Science of Rene Descartes_, ed. by Stephen Voss (Oxford University Press, 1993), 259–287.

El reconocimiento de Dios a partir del conocimiento de las verdades matemáticas explica la presencia, en la totalidad de la obra filosófica de Marin Mersenne (1588-1648), de un discurso científico sobre la divinidad o de su representación a través de las ciencias matemáticas. Fácilmente, es posible encontrar, en los escritos del Mínimo, innumerables imágenes, comparaciones, analogías y expresiones que ilustran la concepción de un Dios matemático; experto no sólo en las ciencias puras, sino también en las matemáticas mixtas o subalternas. (...) Por esta razón, Mersenne se refiere a Dios como el Gran director del concierto cósmico o al Gran arquitecto del mundo, del unísono como la unión de las tres personas divinas, del Sol como fuente de la creación, del centro de la circunferencia… Este artículo tienecomo objetivo principal, en primer lugar, determinar si existe una asociación entre este discurso matemático sobre Dios y la teología natural. En segundo lugar, se pretende discutir si la hipótesis de la univocidad de las matemáticas justifica una identificación entre la teología, las matemáticas y la metafísica. Para ello, cuestionamos unos de los pocos e importantes aportes en la materia, a saber las hipótesis de Jean-Luc Marion y Vincent Carraud, publicadas en 1994. Ambos eruditos sostienen la identificación de las matemáticas con la metafísica y su consecuente univocidad. (shrink)

The Jesuit C.F. Milliet Dechales, author of one of the most famous early modern mathematical encyclopedias, Cursus seu mundus mathematicus, wrote a hundred-folio-page long treatise devoted to the “progress of mathematics,” which was published in the second, enlarged edition of his encyclopedia. His historical treatise covers the gamut of mixed mathematics—including astronomy, mechanics, optics, music, geography and navigation, ars tignaria, and architecture. The early modern historical narratives about the mathematical sciences, from Regiomontanus’s Oratio onwards, have been aptly characterized by their (...) literary form and goals rather than their historical content. Rhetoric, humanistic topoi, and philosophical filiation turned the histories of mathematics into powerful tools for different purposes. My account of Dechales’ tract on the “progress of mathematics” analyzes the ways in which it dovetails with Jesuit approaches to mathematics, provides legitimation to the mathematical sciences as well as to their authors, and contributes to define the role and boundaries of the discipline, in particular vis-à-vis natural philosophy. (shrink)

The pigeonhole principle is a well-known mathematical principle and is quite simple to understand. It goes as follows: If n items are placed into m containers, and if m (...) an identifier (nominal). They suggest quantities first need to be turned into categories. We believe this difference can instead be explained by pragmatic factors not taken into account in their study. We disambiguate the problems given to participants and study the effects of their disambiguation and the influence of different kinds of quantities: countable and mass. We show that using a problem with countable quantities instead of hair, usually understood as non-countable, increase the performance of participants, no longer distinguishable from that of the nominal problem. (shrink)

Contentions about the origin of early modern empiricism have been floating about at least since the 1980s, where its exclusive “Britishness” was initially question, and the name of Gassendi was provocatively put forward as the putative “founder” of the current to the detriment of Francis Bacon. Recent scholarship has shown that early modern empiricism did not derive from philosophical speculation exclusively but had multiple sources and “foundations.” Yet, from a historical viewpoint, the question whether Bacon’s method had any influence on (...) the origin and development of Gassendi’s version of empiricism still carries significance, for its answer may open up different views on how the relation between British and “continental” empiricisms shall be framed. In this paper, I deal with Gassendi’s reception of Bacon. On the basis of a deep examination of Gassendi’s corpus, I contend that there is no trace of a consistent influence of Bacon on Gassendi’s empiricism before 1650s; although I show that an indirect influence can be found through the mediation of Peiresc, I put forward the hypothesis that it was more the empirical attitude characterizing Peiresc’s intellectual figure, rather than his interest in Baconianism, to be relevant, along with Epicurus’ philosophy, for Gassendi’s early empiricism. I then analyze Gassendi’s treatment of Bacon’s logic in Gassendi’s Syntagma philosophicum. I show that despite Gassendi’s sympathy for Bacon’s project, his own logic lays on fundamentally different assumptions. Despite this, I argue for Gassendi’s reception of Bacon’s theory of the idols in Syntagma philosophicum. On this basis, I conclude by restating the untenability of “national” accounts of the rise of empiricism, and the importance of highlighting instead the sharing of ideas between its actors. (shrink)

Change in the human past, studied by historians, includes changes in philosophy's past, which can be explained by causes, motives and reasons. In the case of philosophy, must explanatory antecedents of change always be philosophical? Should philosophers ever treat non-philosophical reasons as belonging to the history of philosophy? Saying ‘never’ is absolutely internalist, while ‘sometimes’ rejects this absolutely internalist rule. To show that ‘sometimes’ is the better answer, I examine two case histories from the early modern period: these cases, framed (...) by a taxonomy of historical narrative, eliminate absolute internalism. (shrink)

RESUMENEl presente artículo examina el análisis efectuado por La Mothe le Vayer acerca del hecho religioso y su problemática en su obra Dialogues faits à l´imitation des anciens. Desde un acusado escepticismo, presenta la religión como una construcción cultural y convencional. La filosofía, en tanto ejercicio de análisis escéptico, ofrecerá una visión de la moral y la religión alejadas por completo de toda sacralizad. Serán, sin embargo, instrumentos muy útiles para el Estado y, si se administran bien, redundarán en la (...) cohesión social y en la pax politica.PALABRAS CLAVEESCEPTICISMO, CONVENCIÓN, RAZÓN DE ESTADOABSTRACTIn this paper we examine the analysis carried out by La Mothe le Vayer of the religious matter and its problems in his work Dialogues faits à l´imitation des anciens. From a marked scepticism, he presents religion as a cultural and conventional entity. Philosophy, as an exercise of sceptical analysis, offers a view of morality and religion totally removed from any sacredness. Both are, however, very useful instruments for the State and, when well administered, beneficial to social cohesion and pax politica.KEY WORDSSCEPTICISM, CONVENTIOM, REASON OF STATE. (shrink)