The Philosophical Mathematics of Isaac Barrow (1630-1677): Conserving the Ancient Geometry of the Euclidean School

The Philosophical Mathematics of Isaac Barrow (1630-1677): Conserving the Ancient Geometry of the Euclidean School

By: Gregory Gillette (author)Hardback

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Isaac Barrow is largely responsible for that preservation and promulgation of the Euclidean tradition which invigorated the physical science and mathematics of Newton and others, and allowed for an ongoing engagement with classical Greek mathematics. Barrow's philosophy of mathematics remains relevant to many key issues still at the forefront of modern philosophies of mathematics. The tradition of mathematics as a liberal discipline, which is the main topic of this book, reaches back to the educational ideals of Plato and Aristotle, and was brought to an early state of near perfection in the Euclidean school of Greek geometry. Within this framework mathematics is practiced as the means of training and cultivating our formal powers: the intellect and imagination function together to achieve a high degree of familiarity with the geometrical structures, patterns and relations that we find embedded in the world around us. The ultimate goal is liberation of the spirit from exclusive preoccupation with mundane concerns. However, we remain at the same time anchored to a realistic philosophical conception of the world, in which our mathematical notions arise by abstraction from real, objective properties of things outside ourselves. This practice of mathematics as a liberal discipline is exemplified nowhere more completely than in the work of Isaac Barrow. The interplay between these modern philosophies and liberal educational ideals forms a recurrent theme of this book. Separate chapters are devoted to Barrow's development as a translator of Greek mathematics and as a mathematician in his own right; to his contributions to the birth of the infinitesimal calculus; to his conception of geometry as the most fundamental and realistic form of mathematics; to his treatment of physical space and time; and to the philosophical and theological implications of the constructive ideal which lies at the heart of classical geometry.

Product Details

  • ISBN13: 9780773447721
  • Format: Hardback
  • Number Of Pages: 240
  • ID: 9780773447721
  • ISBN10: 0773447725

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