Elements Of Intuitionism
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Elements Of Intuitionism
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Author : Michael Dummett
language : en
Publisher: Oxford University Press
Release Date : 2000
Elements Of Intuitionism written by Michael Dummett and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. Readers are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism.
Principles Of Intuitionism
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Author : Anne S. Troelstra
language : en
Publisher: Springer
Release Date : 2006-11-14
Principles Of Intuitionism written by Anne S. Troelstra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Mathematical Intuitionism And Intersubjectivity
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Author : Tomasz Placek
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-06-30
Mathematical Intuitionism And Intersubjectivity written by Tomasz Placek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-30 with Science categories.
In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being. Brouwer attacked the main currents of the philosophy of mathematics: the formalists and the Platonists. In tum, both these schools began viewing intuitionism as the most harmful party among all known philosophies of mathematics. That was the origin of the now-90-year-old debate over intuitionism. As both sides have appealed in their arguments to philosophical propositions, the discussions have attracted the attention of philosophers as well. One might ask here what role a philosopher can play in controversies over mathematical intuitionism. Can he reasonably enter into disputes among mathematicians? I believe that these disputes call for intervention by a philo sopher. The three best-known arguments for intuitionism, those of Brouwer, Heyting and Dummett, are based on ontological and epistemological claims, or appeal to theses that properly belong to a theory of meaning. Those lines of argument should be investigated in order to find what their assumptions are, whether intuitionistic consequences really follow from those assumptions, and finally, whether the premises are sound and not absurd. The intention of this book is thus to consider seriously the arguments of mathematicians, even if philosophy was not their main field of interest. There is little sense in disputing whether what mathematicians said about the objectivity and reality of mathematical facts belongs to philosophy, or not.
Mathematical Intuitionism
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Author : Carl J. Posy
language : en
Publisher: Cambridge University Press
Release Date : 2020-11-12
Mathematical Intuitionism written by Carl J. Posy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-12 with Science categories.
L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism - from elementary number theory through to Brouwer's uniform continuity theorem - and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth.
Mathematical Intuitionism
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Author : Al'bert Grigor'evi_ Dragalin
language : en
Publisher: American Mathematical Soc.
Release Date : 1988-12-31
Mathematical Intuitionism written by Al'bert Grigor'evi_ Dragalin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-31 with Mathematics categories.
In the area of mathematical logic, a great deal of attention is now being devoted to the study of nonclassical logics. This book intends to present the most important methods of proof theory in intuitionistic logic and to acquaint the reader with the principal axiomatic theories based on intuitionistic logic.
Mathematical Intuitionism
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Author : Carl J. Posy
language : en
Publisher: Cambridge University Press
Release Date : 2020-11-12
Mathematical Intuitionism written by Carl J. Posy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-12 with Science categories.
L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth.
One Hundred Years Of Intuitionism 1907 2007
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Author : Mark van Atten
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-09
One Hundred Years Of Intuitionism 1907 2007 written by Mark van Atten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-09 with Science categories.
Intuitionism is one of the main foundations for mathematics proposed in the twentieth century and its views on logic have also notably become important with the development of theoretical computer science. This book reviews and completes the historical account of intuitionism. It also presents recent philosophical work on intuitionism and gives examples of new technical advances and applications. It brings together 21 contributions from today's leading authors on intuitionism.
The Good In The Right
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Author : Robert Audi
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
The Good In The Right written by Robert Audi and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Philosophy categories.
This book represents the most comprehensive account to date of an important but widely contested approach to ethics--intuitionism, the view that there is a plurality of moral principles, each of which we can know directly. Robert Audi casts intuitionism in a form that provides a major alternative to the more familiar ethical perspectives (utilitarian, Kantian, and Aristotelian). He introduces intuitionism in its historical context and clarifies--and improves and defends--W. D. Ross's influential formulation. Bringing Ross out from under the shadow of G. E. Moore, he puts a reconstructed version of Rossian intuitionism on the map as a full-scale, plausible contemporary theory. A major contribution of the book is its integration of Rossian intuitionism with Kantian ethics; this yields a view with advantages over other intuitionist theories (including Ross's) and over Kantian ethics taken alone. Audi proceeds to anchor Kantian intuitionism in a pluralistic theory of value, leading to an account of the perennially debated relation between the right and the good. Finally, he sets out the standards of conduct the theory affirms and shows how the theory can help guide concrete moral judgment. The Good in the Right is a self-contained original contribution, but readers interested in ethics or its history will find numerous connections with classical and contemporary literature. Written with clarity and concreteness, and with examples for every major point, it provides an ethical theory that is both intellectually cogent and plausible in application to moral problems.
Interpolation And Definability
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Author : Dov M. Gabbay
language : en
Publisher: Clarendon Press
Release Date : 2005-05-12
Interpolation And Definability written by Dov M. Gabbay and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-12 with Mathematics categories.
This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.
The Intuitionist
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Author : Colson Whitehead
language : en
Publisher: Hachette UK
Release Date : 2017-05-04
The Intuitionist written by Colson Whitehead and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-04 with Fiction categories.
Verticality, architectural and social, is at the heart of Colson Whitehead's first novel that takes place in an unnamed high-rise city that combines twenty-first-century engineering feats with nineteenth-century pork-barrel politics. Elevators are the technological expression of the vertical ideal, and Lila Mae Watson, the city's first black female elevator inspector, is its embattled token of upward mobility.When Number Eleven of the newly completed Fanny Briggs Memorial Building goes into deadly free-fall just hours after Lila Mae has signed off on it, using the controversial 'Intuitionist' method of ascertaining elevator safety, both Intuitionists and Empiricists recognize the set-up, but may be willing to let Lila Mae take the fall in an election year. As Lila Mae strives to exonerate herself in this urgent adventure full of government spies, underworld hit men, and seductive double agents, behind the action, always, is the Idea. Lila Mae's quest is mysteriously entwined with existence of heretofore lost writings by James Fulton, father of Intuitionism, a giant of vertical thought. If she is able to find and reveal his plan for the perfect, next-generation elevator, the city as it now exists may instantly become obsolescent.