Mathematics and infinity in descartes and newton
© 2015, Springer International Publishing Switzerland. The concept of the infinite has often been regarded as inherently problematic in mathematics and in philosophy. The idea that the universe itself might be infinite has been the subject of intense debate not only on mathematical and philosophical grounds, but for theological and political reasons as well. When Copernicus and his followers challenged the old Aristotelian and Ptolemaic conceptions of the world’s finiteness, if not its boundedness, the idea of an infinite, if not merely unbounded, world seemed more attractive. Indeed, the infinity of space has been called the “fundamental principle of the new ontology” (Koyré in From the Closed World to the Infinite Universe. Johns Hopkins University Press, Baltimore, 1957, p. 126). Influential scholarship in the first half of the twentieth century helped to solidify the idea that it was specifically in the seventeenth century that astronomers and natural philosophers fully embraced the infinity of the universe. As Kuhn writes in his Copernican Revolution (1957, p. 289): “From Bruno ’s death in 1600 to the publication of Descartes ’s Principles of Philosophy in 1644, no Copernican of any prominence appears to have espoused the infinite universe, at least in public. After Descartes, however, no Copernican seems to have opposed the conception.” That same year saw the publication of Alexandre Koyré ’s sweeping volume about the scientific revolution, From the Closed World to the Infinite Universe. The decision to describe and conceive of the world as infinite might be seen as a crucial, if not decisive, aspect of the overthrow of Scholasticism. As Kuhn and Koyré knew, one finds a particularly invigorating expression of this historical-philosophical interpretation in an earlier article by Marjorie Nicholson (Studies in Philology 25:356–374, 1929, p. 370).
- Trends in the History of Science
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