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2 books match the query 'Paris, Václav'
New Infinitary Mathematics
Petr Vopenka
Karolinum Press, 2023
A rethinking of Cantor and infinitary mathematics by the creator of Vopěnka's principle.
The dominant current of twentieth-century mathematics relies on Georg Cantor’s classical theory of infinite sets, which in turn relies on the assumption of the existence of the set of all natural numbers, the only justification for which—a theological justification—is usually concealed and pushed into the background.
This book surveys the theological background, emergence, and development of classical set theory, warning us about the dangers implicit in the construction of set theory, and presents an argument about the absurdity of the assumption of the existence of the set of all natural numbers. It instead proposes and develops a new infinitary mathematics driven by a cautious effort to transcend the horizon bounding the ancient geometric world and mathematics prior to set theory, while allowing mathematics to correspond more closely to the real world surrounding us. Finally, it discusses real numbers and demonstrates how, within a new infinitary mathematics, calculus can be rehabilitated in its original form employing infinitesimals.
The dominant current of twentieth-century mathematics relies on Georg Cantor’s classical theory of infinite sets, which in turn relies on the assumption of the existence of the set of all natural numbers, the only justification for which—a theological justification—is usually concealed and pushed into the background.
This book surveys the theological background, emergence, and development of classical set theory, warning us about the dangers implicit in the construction of set theory, and presents an argument about the absurdity of the assumption of the existence of the set of all natural numbers. It instead proposes and develops a new infinitary mathematics driven by a cautious effort to transcend the horizon bounding the ancient geometric world and mathematics prior to set theory, while allowing mathematics to correspond more closely to the real world surrounding us. Finally, it discusses real numbers and demonstrates how, within a new infinitary mathematics, calculus can be rehabilitated in its original form employing infinitesimals.
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The Philosophy of Living Nature
Zdenek Kratochvíl
Karolinum Press, 2016
The Philosophy of Living Nature focuses on the approach of the Western philosophical tradition to physis, or nature. Zdenek Kratochvíl reveals, on a philosophical level, the roots of today’s environmental crisis, presenting an etymological investigation of the concept of “nature” itself and arguing for the necessity of focusing on the world and its plurality as the background for phenomena and the context of things, as a unity of horizons, as a paradigm for understanding nature. However, as Kratochvíl makes clear, questions about the natural world have stakes far beyond the realm of philosophy: chapters in this wide-ranging and richly nuanced book deal with the identity of living organisms and the relation of life and being. Together, they provide an analysis of Darwinian and neo-Darwinian evolution and question in what sense we may know living beings.
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