Cristoforo Borri and the epistemological status of mathematics in seventeenth-century Portugal (original) (raw)
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This paper argues that the epistemological promotion of mathematics by the Jesuit Cristoforo Borri, while he was teaching at the Coimbra Jesuit College in the late 1620s, played a decisive role in the updating of cosmological ideas in 17th-century Portugal. The paper focuses on Borri's position on the celebrated quaestio de certitudine mathematicarum and on his understanding of the classification of sciences. It argues that by conferring on mathematics the status of Aristotelian causal science, Borri made it possible to integrate mathematical data into the philosophical debate, particularly with regard to the new cosmology. Sumário Neste estudo defende-se a tese de que a promoção do estatuto epistemológico da matemática concretizada pelo jesuíta Cristoforo Borri, enquanto professor de matemática no Colégio das Artes (Coimbra) no final da década de vinte do século XVII, teve um papel decisivo na actualização das ideias cosmológicas no Portugal de Seiscentos. Este artigo tem como objecto a posição de Borri na célebre quaestio de certitudine mathematicarum, bem como concepção deste matemático jesuíta no que respeita à classificação das ciências. Neste estudo argumenta-se que Borri, ao conferir à matemática o estatuto de ciência causal aristotélica, permitiu a inserção no debate filosófico e, particularmente no domínio cosmológico, de dados provenientes da reflexão matemática.
Natural Philosophy and Mathematics in Portuguese Universities, 1550–1650
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The Teaching of the Mathematical Disciplines in Sixteenth-Century Spain*
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This essay examines some aspects of the teaching of mathematics and its applications in three of the principal sixteenth century Spanish universities (Salamanca, Valencia and Alcala´) and in other institutions sponsored by the monarchy, such as the ''Casa de la Con-tratacio´n'' (House of Trade) of Seville and the so-called Academy of Mathematics of Madrid. All three of the above universities had chairs of mathematics. In the Casa de la Contratacio´n and other nautical schools the teaching of mathematics was oriented toward providing the foundations of navigation (nautical astronomy, instruments and maps, etc.). The Academy of Mathematics was oriented mainly towards subjects related to cosmography and navigation. Although the different areas of the teaching of mathematics imposed conditions on the discourses and practices of the mathematical disciplines, they did not impede the circulation of persons, knowledge, and practices among these areas.
Francisco Sánchez and the Quaestio de certitudine mathematicarum: A sceptical approach
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In this paper I analyse Francisco Sánchez's role in the Quaestio de certitudine mathematicarum debate. Despite some studies on the philosophical and medical scepticism of Sánchez and, his extant letter with Christopher Clavius, a participant in the debate, we have few analyses about Sánchez's position regarding the certainty of mathematics. Sánchez discussed some problems that Clavius analysed in his Prolegomena to propose an empirical basis for mathematics through a questioning of its certainty. I will trace the conceptual connections between Sánchez's 1589 letter to Clavius and the Quaestio debate, to introduce Sánchez's sceptical approach to analysing the certainty of mathematics.
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We consider the possibility of using bibliographic as well as reference data for research in the history of mathematics during the formation of the mathematical scientific community in Europe at the second half of the XIX-the first half of the XX centuries. Considering an example of the mathematical scientific community in Portugal, which was still being formed at that time, we explore participation and citing of Portuguese researchers in different bibliographic European projects. We note that bibliographic data can be interpreted in the broader context of the history of Europe as a whole: the link between this local process in the history of mathematical thought and the European historical process can be easily seen in the changing number of publications produced by the mathematical scientific community in Portugal over different time periods. We conclude that the evolution dynamics of international bibliography of the mathematical scientific communities in different countries can be used as a research methodology to understand the social history of mathematics. Towards the History of the Emergence of the World Mathematical Scientific Community Much of the existing literature in the history of mathematics is devoted to the process of formation and development of the national mathematical scientific communities as well as to the emergence of the international mathematical scientific community based on these national communities in the second half of the XIX-first quarter of the XX centuries. This literature dates back to the second half of the XX century and new insights are constantly emerging. In recent decades, several researchers have paid their attention to the research on development of the global mathematical scientific community (Goldstein et al. 1996; Grattan-Guinness et al. 2000; Parshall et al. 2002).
Copernicanism in the classroom: Jesuit natural philosophy and mathematics after 1633
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This article examines presentations of the Copernican system in courses of natural philosophy and mathematics at the Jesuit Collegio Romano during the seventeenth century. Using printed and manuscript teaching materials, it documents how the introduction of Copernicanism, especially following Galileo's condemnation, prompted subtle modifications to the types of questions and evidence presented to students and led professors to appropriate topics from mathematics into their philosophical curriculum and vice versa. These patterns offer insight into the local context and circumstances in which Jesuit professors both interpreted the Catholic Church's condemnation and were impelled to innovate their curriculum in response to new intellectual currents.