Foundations without Foundationalism
Foundations without Foundationalism

Author: Stewart Shapiro

Publisher: Clarendon Press

Published: 1991-09-19

Total Pages: 302

ISBN-13: 0191524018

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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.

Foundations Without Foundationalism
Foundations Without Foundationalism

Author: Stewart Shapiro

Publisher: Oxford University Press, USA

Published: 1991-09-19

Total Pages: 298

ISBN-13: 0198533918

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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.

Without Foundations
Without Foundations

Author: Donald J. Herzog

Publisher: Cornell University Press

Published: 2018-03-15

Total Pages: 297

ISBN-13: 1501723014

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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.

Karl Popper's Philosophy of Science
Karl Popper's Philosophy of Science

Author: Stefano Gattei

Publisher: Routledge

Published: 2008-10-16

Total Pages: 154

ISBN-13: 1134182953

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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.

Theology in Search of Foundations
Theology in Search of Foundations

Author: Randal Rauser

Publisher: Oxford University Press, USA

Published: 2009-08-20

Total Pages: 324

ISBN-13: 0199214603

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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.

Pragmatism without Foundations 2nd ed
Pragmatism without Foundations 2nd ed

Author: Joseph Margolis

Publisher: Bloomsbury Publishing

Published: 2007-04-26

Total Pages: 305

ISBN-13: 1441167285

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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.

Epistemic Friction
Epistemic Friction

Author: Gila Sher

Publisher: Oxford University Press

Published: 2016-06-23

Total Pages: 320

ISBN-13: 0191081299

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Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this 'classical' project. The book challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine's revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to robust norms of both veridicality and conceptualization. The correspondence theory is at once robust, universal, and flexible, allowing multiple patterns of correspondence, including complex and indirect patterns. Logic's systematic grounding brings it in line with other disciplines without neglecting its strong necessity, generality, and normativity, which are explained by its semantic formality.

The Foundations of Knowledge
The Foundations of Knowledge

Author: Timothy J. McGrew

Publisher: Rowman & Littlefield

Published: 1995

Total Pages: 178

ISBN-13: 9780822630425

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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.