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The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics (Hardcover, 1st ed. 2019)
Loot Price: R3,066
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The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics (Hardcover, 1st ed. 2019)
Series: The Western Ontario Series in Philosophy of Science, 82
Expected to ship within 12 - 17 working days
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This book explores and articulates the concepts of the continuous
and the infinitesimal from two points of view: the philosophical
and the mathematical. The first section covers the history of these
ideas in philosophy. Chapter one, entitled 'The continuous and the
discrete in Ancient Greece, the Orient and the European Middle
Ages,' reviews the work of Plato, Aristotle, Epicurus, and other
Ancient Greeks; the elements of early Chinese, Indian and Islamic
thought; and early Europeans including Henry of Harclay, Nicholas
of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine
and Nicolas Oreme. The second chapter of the book covers European
thinkers of the sixteenth and seventeenth centuries: Galileo,
Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter
three, 'The age of continuity,' discusses eighteenth century
mathematicians including Euler and Carnot, and philosophers, among
them Hume, Kant and Hegel. Examining the nineteenth and early
twentieth centuries, the fourth chapter describes the reduction of
the continuous to the discrete, citing the contributions of
Bolzano, Cauchy and Reimann. Part one of the book concludes with a
chapter on divergent conceptions of the continuum, with the work of
nineteenth and early twentieth century philosophers and
mathematicians, including Veronese, Poincare, Brouwer, and Weyl.
Part two of this book covers contemporary mathematics, discussing
topology and manifolds, categories, and functors, Grothendieck
topologies, sheaves, and elementary topoi. Among the theories
presented in detail are non-standard analysis, constructive and
intuitionist analysis, and smooth infinitesimal analysis/synthetic
differential geometry. No other book so thoroughly covers the
history and development of the concepts of the continuous and the
infinitesimal.
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