Chapter ID: CBB974951037

Mathematics and Infinity in Descartes and Newton (2015)

unapi

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 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.

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Authors & Contributors
Janiak, Andrew
Giannetto, Enrico
Casini, Paolo
Labellarte, Alberto
Schliesser, Eric
Demeter, Tamás
Concepts
Natural philosophy
Philosophy of science
Physics
Science and religion
Newtonianism
Philosophy
Time Periods
17th century
18th century
Renaissance
20th century
16th century
Places
Europe
England
Netherlands
Great Britain
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