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Author: Stewart Shapiro
Publisher: Clarendon Press
ISBN: 0191524018
Category : Mathematics
Languages : en
Pages : 302
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Book Description
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.
Author: Stewart Shapiro
Publisher: Clarendon Press
ISBN: 0191524018
Category : Mathematics
Languages : en
Pages : 302
Get Book Here
Book Description
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.
Author: Stewart Shapiro
Publisher: Oxford University Press, USA
ISBN: 0198533918
Category : Mathematics
Languages : en
Pages : 298
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Book Description
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.
Author: Joseph Margolis
Publisher: Bloomsbury Publishing
ISBN: 1441167285
Category : Philosophy
Languages : en
Pages : 305
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Book Description
In this remarkable book, Joseph Margolis, one of America's leading and most celebrated philosophers, examines the relationship between two apparently contradictory philosophical tendencies - realism and relativism. In order to examine the relationship between the two, Margolis establishes a taxomony of different kinds of realism and different kinds of relativism. Drawing on both the analytic and Continental traditions, he examines (from a pragmatic point of view) the various relationships between these two tendencies in the light of two major developments in modern philosophy - the concern for praxis and the concern for historicity. Twenty years after it was first published to great acclaim, Margolis has updated Pragmatism Without Foundations in the light of his most recent work and the development of pragmatism in the intellectual world. This second edition includes an updated preface and a brand new epilogue addressing these developments and their implications for his earlier work.
Author: Donald J. Herzog
Publisher: Cornell University Press
ISBN: 1501723014
Category : Political Science
Languages : en
Pages : 269
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Book Description
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.
Author: William Maker
Publisher: State University of New York Press
ISBN: 1438411758
Category : Philosophy
Languages : en
Pages : 316
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Book Description
Author: Stefano Gattei
Publisher: Routledge
ISBN: 1134182953
Category : Philosophy
Languages : en
Pages : 154
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Book Description
Rectifying misrepresentations of Popperian thought with a historical approach to Popper’s philosophy, Gattei reconstructs the logic of Popper’s development to show how one problem and its tentative solution led to a new problem.
Author: John T. Baldwin
Publisher: Cambridge University Press
ISBN: 1107189217
Category : Mathematics
Languages : en
Pages : 365
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Book Description
Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.
Author: Timothy J. McGrew
Publisher: Rowman & Littlefield
ISBN: 9780822630425
Category : Philosophy
Languages : en
Pages : 178
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Book Description
Contemporary epistemology has been moving away from classical foundationalism--the thesis that our empirical knowledge is grounded in perceptual beliefs we know with certainty. McGrew reexamines classical foundationalism and offers a compelling reconstruction and defense of empirical knowledge grounded in perceptual certainty. He articulates and defends a new version of foundationalism and demonstrates how it meets all the standard criticisms. The book offers substantial rebuttals of the arguments of Kuhn and Rorty and demonstrates the value of the classical analytic approach to philosophy. Foundations will interest philosophers of science, language, and the mind.
Author: Randal Rauser
Publisher: Oxford University Press, USA
ISBN: 0199214603
Category : Philosophy
Languages : en
Pages : 324
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Book Description
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.
Author: Ernest Sosa
Publisher: Cambridge University Press
ISBN: 9780521396431
Category : Philosophy
Languages : en
Pages : 318
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Book Description
Ernest Sosa collects essays, written over the last 25 years, on the scope and nature of human knowledge.
