ArgumentThe purpose of this paper is to provide an analysis of Giordano Bruno’s conception of mathematics. Specifically, it intends to highlight two aspects of this conception that have been neglected in previous studies. First, Bruno’s conception of mathematics changed over time and in parallel with another concept that was central to his thought: the concept of infinity. Specifically, Bruno undertook a reform of mathematics in order to accommodate the concept of the infinitely small or “minimum,” which was introduced at a (...) later stage. Second, contrary to what Héléne Védrine claimed, Bruno believed that mathematical objects were mind-dependent. To chart the parallel development of the conceptions of mathematics and infinity, a seven-year time span is considered, from the publication of Bruno’s first Italian dialogue (La cena de le ceneri,1584) to the publication of one of his last Latin works (De minimo, 1591). (shrink)

This essay deals with Girolamo Fracastoro’s ensouled cosmology. His Homocentrica sive de stellis (1538), an astronomy of concentric spheres, was discussed by the Padua School of Aristotelians. Since the polemics over the immortality of the human soul, which had famously opposed Pomponazzi to Nifo, psychological discussions—including those about heavenly spheres’ souls—raised heated controversies. Fracastoro discussed the foundations of his homocentric planetary theory in a dialogue titled Fracastorius, sive de anima (1555). In a 1531 exchange with Gasparo Contarini, Fracastoro discussed celestial (...) physics, including problems linked to mathematical analysis of physical causation. Contarini expressed his doubts over Fracastoro’s lack of consideration of Aristotelian viewpoints on heavenly souls and intelligences. Fracastoro offered an account of cosmic animation in his later dialogue “On the Soul,” taking a different path than his Paduan teachers. He picked up the Platonic idea of the “world soul,” freely connecting it with Aristotelian views about the ensouled cosmos of concentric spheres, resulting in an eclectic composition of Platonic, Aristotelian, and Averroistic elements. Fracastoro grounded his renewed mathematical astronomy on an understanding of the cosmos as a living whole. His animated homocentric cosmos represented a development of Aristotelian premises and a step beyond this legacy. (shrink)

After a brief review of the relationship between science and value, this paper introduces the value of ‘traditionality’ as a value in the pure and applied sciences. Along with other recognized values, this value can also contribute to formulating hypotheses and determining theories. There are three reasons for legitimizing the internal role of this value in science: first, this value can contribute to scientific progress by presenting more diverse hypotheses; second, the value of external consistency in science entails this value; (...) and third, this value helps to eliminate some of the adverse social and cultural effects of Western science in non-Western societies. ‘Traditionality’ is an extrinsic epistemic value, according to the first two reasons, and at the same time, is an ethical value, according to the last reason. Also, the ethics of belief is adopted to further confirm the ethical role of this value. Finally, this paper discusses three potential criticisms that can be levelled against this idea and responds to each of them. (shrink)

ArgumentThe main thesis of this paper is that Copernicus's avoidance of all admission that scripture was contravened inDe revolutionibusand his composition of its new Preface in 1542, as well as the non-publication of Rheticus'sTreatise on Holy Scripture and the Motion of the Earth, were influenced by the early information they received on the failure of the 1541 Regensburg Protestant-Catholic colloquy, among the major consequences of which were significant increases in the problems concerning publishing works which contravened scripture. This is supported (...) by examining Rheticus's first letter to Paul Eber in conjunction with the documents on the Regensburg colloquy and on censorship in Nuremberg, as well as with the existing literature on Copernicus and his context. In view of the main thesis, Copernicus's apparent dedication of the work to the Pope merits additional explanation, and the second thesis is that components of explanations for several aspects of those parts of the Preface that relate to the Papacy and to theologians can be provided via comparisons with previous diplomacy between Warmia and the Papacy which occurred or was being referred to during Copernicus's time. This is supported by examining these parts of the Preface in the light of a selection of the relevant documents. (shrink)

ArgumentDuring the two decades before the turning point in Copernicus's personal and scientific development in 1510, he had experience of political activity which has been largely ignored by the existing Copernicus literature but part of which is reconstructed in outline in this paper. Given the close linkage between politics and astrology, Copernicus's likely reaction to astrology is re-examined here. This reconstruction also suggests that the turning point in 1510, when Copernicus left his post as secretary to his uncle Lucas Watzenrode (...) the prince-bishop of Warmia, was not only linked to Copernicus's first version of his heliocentric theory in theCommentariolus, but also to major political setbacks being experienced by Watzenrode during these years, and with the publication of Copernicus's translation of theLettersof Theophylactus Simocatta. Some of these considerations contribute to maintaining the view that Copernicus and his work were in several respects exceptional. (shrink)