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Infinitesimal Differences - Controversies between Leibniz and his Contemporaries (Hardcover, illustrated edition)
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Infinitesimal Differences - Controversies between Leibniz and his Contemporaries (Hardcover, illustrated edition)
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The essays offer a unified and comprehensive view of 17th century
mathematical and metaphysical disputes over status of
infinitesimals, particularly the question whether they were real or
mere fictions. Leibniz's development of the calculus and his
understanding of its metaphysical foundation are taken as both a
point of departure and a frame of reference for the 17th century
discussions of infinitesimals, that involved Hobbes, Wallis,
Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus
was undoubtedly successful in mathematical practice, it remained
controversial because its procedures seemed to lack an adequate
metaphysical or methodological justification. The topic is also of
philosophical interest, because Leibniz freely employed the
language of infinitesimal quantities in the foundations of his
dynamics and theory of forces. Thus, philosophical disputes over
the Leibnizian science of bodies naturally involve questions about
the nature of infinitesimals. The volume also includes newly
discovered Leibnizian marginalia in the mathematical writings of
Hobbes.
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