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Foundations Without Foundationalism

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Release : 1991-09-19
Genre : Mathematics
Kind : eBook
Book Rating : 918/5 ( reviews)

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Book Synopsis Foundations Without Foundationalism by : Stewart Shapiro

Download or read book Foundations Without Foundationalism written by Stewart Shapiro. This book was released on 1991-09-19. Available in PDF, EPUB and Kindle. Book excerpt: Stewart Shapiro presents a distinctive original view of the foundations of mathematics, arguing that second-order logic has a central role to play in laying these foundations.

Foundations without Foundationalism

Download Foundations without Foundationalism PDF Online Free

Author :
Release : 1991-09-19
Genre : Mathematics
Kind : eBook
Book Rating : 018/5 ( reviews)

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Book Synopsis Foundations without Foundationalism by : Stewart Shapiro

Download or read book Foundations without Foundationalism written by Stewart Shapiro. This book was released on 1991-09-19. Available in PDF, EPUB and Kindle. Book excerpt: The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in this subject.

Without Foundations

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Author :
Release : 2018-03-15
Genre : Political Science
Kind : eBook
Book Rating : 014/5 ( reviews)

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Book Synopsis Without Foundations by : Donald J. Herzog

Download or read book Without Foundations written by Donald J. Herzog. This book was released on 2018-03-15. Available in PDF, EPUB and Kindle. Book excerpt: Can political theorists justify their ideas? Do sound political theories need foundations? What constitutes a well-justified argument in political discourse? Don Herzog attempts to answer these questions by investigating the ways in which major theorists in the Anglo-American political tradition have justified their views. Making use of a wide range of primary texts, Herzog examines the work of such important theorists as Thomas Hobbes, John Locke, the utilitarians (Jeremy Bentham, J. S. Mill. Henry Sidgwick, J. C. Harsanyi, R. M. Hare, and R. B. Brandt), David Hume, and Adam Smith. Herzog argues that Hobbes, Locke, and the utilitarians fail to justify their theories because they try to ground the volatile world of politics in immutable aspects of human nature, language, theology, or rationality. Herzog concludes that the works of Adam Smith and David Hume offer illuminating examples of successful justifications. Basing their political conclusions on social contexts, not on abstract principles, Hume and Smith develop creative solutions to given problems.

Philosophy without Foundations

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Author :
Release : 1994-10-11
Genre : Philosophy
Kind : eBook
Book Rating : 758/5 ( reviews)

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Book Synopsis Philosophy without Foundations by : William Maker

Download or read book Philosophy without Foundations written by William Maker. This book was released on 1994-10-11. Available in PDF, EPUB and Kindle. Book excerpt:

Theology in Search of Foundations

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Release : 2009-08-20
Genre : Philosophy
Kind : eBook
Book Rating : 603/5 ( reviews)

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Book Synopsis Theology in Search of Foundations by : Randal Rauser

Download or read book Theology in Search of Foundations written by Randal Rauser. This book was released on 2009-08-20. Available in PDF, EPUB and Kindle. Book excerpt: A pithy account of theological rationality, justification and knowledge that avoids the twin pitfalls of modern rationalism and postmodern irrationalism. This lively and accessible survey debates with the ideas of key theological and philosophical thinkers, past and present, providing a fresh understanding of theology as a discipline.

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