Defending the Axioms

On the Philosophical Foundations of Set Theory

Author: Penelope Maddy

Publisher: Oxford University Press

ISBN: 0199596182

Category: Mathematics

Page: 150

View: 9072

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Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
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Quine, New Foundations, and the Philosophy of Set Theory

Author: Sean Morris

Publisher: Cambridge University Press

ISBN: 1108604536

Category: Philosophy

Page: N.A

View: 2620

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Quine's set theory, New Foundations, has often been treated as an anomaly in the history and philosophy of set theory. In this book, Sean Morris shows that it is in fact well-motivated, emerging in a natural way from the early development of set theory. Morris introduces and explores the notion of set theory as explication: the view that there is no single correct axiomatization of set theory, but rather that the various axiomatizations all serve to explicate the notion of set and are judged largely according to pragmatic criteria. Morris also brings out the important interplay between New Foundations, Quine's philosophy of set theory, and his philosophy more generally. We see that his early technical work in logic foreshadows his later famed naturalism, with his philosophy of set theory playing a crucial role in his primary philosophical project of clarifying our conceptual scheme and specifically its logical and mathematical components.
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God and Abstract Objects

The Coherence of Theism: Aseity

Author: William Lane Craig

Publisher: Springer

ISBN: 3319553844

Category: Philosophy

Page: 540

View: 9448

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This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments.
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God Over All

Divine Aseity and the Challenge of Platonism

Author: William Lane Craig

Publisher: Oxford University Press

ISBN: 0191090557

Category: Religion

Page: 280

View: 2435

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God Over All: Divine Aseity and the Challenge of Platonism is a defense of God's aseity and unique status as the Creator of all things apart from Himself in the face of the challenge posed by mathematical Platonism. After providing the biblical, theological, and philosophical basis for the traditional doctrine of divine aseity, William Lane Craig explains the challenge presented to that doctrine by the Indispensability Argument for Platonism, which postulates the existence of uncreated abstract objects. Craig provides detailed examination of a wide range of responses to that argument, both realist and anti-realist, with a view toward assessing the most promising options for the theist. A synoptic work in analytic philosophy of religion, this groundbreaking volume engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology.
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Mathematics and the Image of Reason

Author: Mary Tiles

Publisher: Routledge

ISBN: 1134967713

Category: Philosophy

Page: 200

View: 320

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A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.
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Finsler Set Theory

Platonism and Circularity; Translations of Paul Finsler's Papers on Set Theory with Introductory Comments

Author: Paul Finsler

Publisher: Springer Science & Business Media

ISBN: 9783764354008

Category: Mathematics

Page: 278

View: 616

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This English translation of Paul Finsler's papers on set theory reflects the central concerns of his investigations, namely the philosophical, foundational, and combinatorial approaches. Each section contains an introduction to the field by the editors, and a technical background is not necessary.
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A Brief History of Analytic Philosophy

From Russell to Rawls

Author: Stephen P. Schwartz

Publisher: John Wiley & Sons

ISBN: 1118271726

Category: Philosophy

Page: 368

View: 8617

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A Brief History of Analytic Philosophy: From Russell toRawls presents a comprehensive overview of the historicaldevelopment of all major aspects of analytic philosophy, thedominant Anglo-American philosophical tradition in the twentiethcentury. Features coverage of all the major subject areasand figures in analytic philosophy - includingWittgenstein, Bertrand Russell, G.E. Moore, Gottlob Frege, Carnap,Quine, Davidson, Kripke, Putnam, and many others Contains explanatory background material to help make cleartechnical philosophical concepts Includes listings of suggested further readings Written in a clear, direct style that presupposes littleprevious knowledge of philosophy
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