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Showing 1 - 6 of 6 matches in All Departments

The Arche Papers on the Mathematics of Abstraction (Hardcover, 2007 ed.): Roy T. Cook The Arche Papers on the Mathematics of Abstraction (Hardcover, 2007 ed.)
Roy T. Cook
R5,036 Discovery Miles 50 360 Ships in 10 - 15 working days

This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines.Gottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege's enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has recieved extensive attention and discussion, the present volume is unique in presenting a thorough going examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns). Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut - or cauchy-sequence-related abstraction principles...

Hilary Putnam on Logic and Mathematics (Hardcover, 1st ed. 2018): Geoffrey Hellman, Roy T. Cook Hilary Putnam on Logic and Mathematics (Hardcover, 1st ed. 2018)
Geoffrey Hellman, Roy T. Cook
R2,581 R1,802 Discovery Miles 18 020 Save R779 (30%) Ships in 12 - 17 working days

This book explores the research of Professor Hilary Putnam, a Harvard professor as well as a leading philosopher, mathematician and computer scientist. It features the work of distinguished scholars in the field as well as a selection of young academics who have studied topics closely connected to Putnam's work. It includes 12 papers that analyze, develop, and constructively criticize this notable professor's research in mathematical logic, the philosophy of logic and the philosophy of mathematics. In addition, it features a short essay presenting reminiscences and anecdotes about Putnam from his friends and colleagues, and also includes an extensive bibliography of his work in mathematics and logic. The book offers readers a comprehensive review of outstanding contributions in logic and mathematics as well as an engaging dialogue between prominent scholars and researchers. It provides those interested in mathematical logic, the philosophy of logic, and the philosophy of mathematics unique insights into the work of Hilary Putnam.

The Arche Papers on the Mathematics of Abstraction (Paperback, Softcover reprint of hardcover 1st ed. 2007): Roy T. Cook The Arche Papers on the Mathematics of Abstraction (Paperback, Softcover reprint of hardcover 1st ed. 2007)
Roy T. Cook
R5,004 Discovery Miles 50 040 Ships in 10 - 15 working days

This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Gottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege s enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has received extensive attention and discussion, the present volume is unique in presenting a thoroughgoing examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns). Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut- or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies. As a result, the volume provides a test of the scope and limits of the neo-logicist project, detailing what has been accomplished and outlining the desiderata still outstanding. All papers in the anthology have their origins in presentations at Arche events, thus providing a volume that is both a survey of the cutting edge in research on the technical aspects of abstraction and a catalogue of the work in this area that has been supported in various ways by Arche."

LEGO and Philosophy - Constructing Reality Brick By Brick (Paperback): William Irwin LEGO and Philosophy - Constructing Reality Brick By Brick (Paperback)
William Irwin; Edited by Roy T. Cook, Sondra Bacharach 1
R419 R338 Discovery Miles 3 380 Save R81 (19%) Ships in 12 - 17 working days

How profound is a little plastic building block? It turns out the answer is very ! 22 chapters explore philosophy through the world of LEGO which encompasses the iconic brick itself as well as the animated televisions shows, feature films, a vibrant adult fan base with over a dozen yearly conventions, an educational robotics program, an award winning series of videogames, hundreds of books, magazines, and comics, a team-building workshop program for businesses and much, much more. * Dives into the many philosophical ideas raised by LEGO bricks and the global multimedia phenomenon they have created * Tackles metaphysical, logical, moral, and conceptual issues in a series of fascinating and stimulating essays * Introduces key areas of philosophy through topics such as creativity and play, conformity and autonomy, consumption and culture, authenticity and identity, architecture, mathematics, intellectual property, business and environmental ethics * Written by a global group of esteemed philosophers and LEGO fans * A lively philosophical discussion of bricks, minifigures, and the LEGO world that will appeal to LEGO fans and armchair philosophers alike

The Yablo Paradox - An Essay on Circularity (Hardcover): Roy T. Cook The Yablo Paradox - An Essay on Circularity (Hardcover)
Roy T. Cook
R2,051 Discovery Miles 20 510 Ships in 12 - 17 working days

Roy T Cook examines the Yablo paradox-a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others later than it in the sequence-with special attention paid to the idea that this paradox provides us with a semantic paradox that involves no circularity. The three main chapters of the book focus, respectively, on three questions that can be (and have been) asked about the Yablo construction. First we have the Characterization Problem, which asks what patterns of sentential reference (circular or not) generate semantic paradoxes. Addressing this problem requires an interesting and fruitful detour through the theory of directed graphs, allowing us to draw interesting connections between philosophical problems and purely mathematical ones. Next is the Circularity Question, which addresses whether or not the Yablo paradox is genuinely non-circular. Answering this question is complicated: although the original formulation of the Yablo paradox is circular, it turns out that it is not circular in any sense that can bear the blame for the paradox. Further, formulations of the paradox using infinitary conjunction provide genuinely non-circular constructions. Finally, Cook turns his attention to the Generalizability Question: can the Yabloesque pattern be used to generate genuinely non-circular variants of other paradoxes, such as epistemic and set-theoretic paradoxes? Cook argues that although there are general constructions-unwindings-that transform circular constructions into Yablo-like sequences, it turns out that these sorts of constructions are not 'well-behaved' when transferred from semantic puzzles to puzzles of other sorts. He concludes with a short discussion of the connections between the Yablo paradox and the Curry paradox.

A Dictionary of Philosophical Logic (Hardcover): Roy T. Cook A Dictionary of Philosophical Logic (Hardcover)
Roy T. Cook
R2,584 R2,168 Discovery Miles 21 680 Save R416 (16%) Ships in 9 - 15 working days

This dictionary introduces undergraduate and post-graduate students in philosophy, mathematics, and computer science to the main problems and positions in philosophical logic. Coverage includes not only key figures, positions, terminology, and debates within philosophical logic itself, but issues in related, overlapping disciplines such as set theory and the philosophy of mathematics as well. Entries are extensively cross-referenced, so that each entry can be easily located within the context of wider debates, thereby providing a valuable reference both for tracking the connections between concepts within logic and for examining the manner in which these concepts are applied in other philosophical disciplines.

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