An exploration of the scientific limits of knowledge that challenges our deep-seated beliefs about our universe, our rationality, and ourselves.
Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.
Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.
Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
Автор: Petr Hajek Название: Metamathematics of First-Order Arithmetic ISBN: 1107168414 ISBN-13(EAN): 9781107168411 Издательство: Cambridge Academ Рейтинг: Цена: 16743.00 р. 23918.00-30% Наличие на складе: Есть (1 шт.) Описание: This much-needed monograph on the metamathematics of first-order arithmetic pays particular attention to subsystems (fragments) of Peano arithmetic and gives the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness.
Автор: Netz, Reviel (stanford University, California) Название: New history of greek mathematics ISBN: 1108833845 ISBN-13(EAN): 9781108833844 Издательство: Cambridge Academ Рейтинг: Цена: 5542.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A comprehensive history of Greek mathematics (pure and applied, including the history of astronomy) from its beginnings to its legacy in Byzantium, Islamic science and the scientific revolution. Explores comparative and sociological perspectives and engages the reader with joy of encountering some of the finest mathematics ever created.
Автор: Russell Bertrand Название: Principles of Mathematics ISBN: 0415487412 ISBN-13(EAN): 9780415487412 Издательство: Taylor&Francis Рейтинг: Цена: 3061.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A precursor to Russell`s famous Principa Mathematica, this is one of the most original and comprehensive treatises on the logical foundation of mathematics available today.
Автор: Brown Название: Platonism, Naturalism, and Mathematical Knowledge ISBN: 1138809772 ISBN-13(EAN): 9781138809772 Издательство: Taylor&Francis Рейтинг: Цена: 9033.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.
Автор: Russell Marcus, Mark McEvoy Название: An Historical Introduction to the Philosophy of Mathematics: A Reader ISBN: 1472525671 ISBN-13(EAN): 9781472525673 Издательство: Bloomsbury Academic Рейтинг: Цена: 5780.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.
Автор: Bolzano Название: Paradoxes of the Infinite (Routledge Revivals) ISBN: 0415749778 ISBN-13(EAN): 9780415749770 Издательство: Taylor&Francis Рейтинг: Цена: 6430.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19th century: Dr Bernard Bolzano's Paradoxien. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction to the masterpiece, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.
Автор: Chubb Название: Logic and Algebraic Structures in Quantum Computing ISBN: 110703339X ISBN-13(EAN): 9781107033399 Издательство: Cambridge Academ Рейтинг: Цена: 21226.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this international cross-disciplinary collaboration, leading experts explore connections across their respective fields. The book offers an insight into the fundamental questions in quantum theory and logic, which will appeal to many researchers and graduate students including logicians, mathematicians, computer scientists, and physicists.
Автор: Dieter Probst, Peter Schuster Название: Concepts of Proof in Mathematics, Philosophy, and Computer Science ISBN: 1501510800 ISBN-13(EAN): 9781501510809 Издательство: Walter de Gruyter Цена: 20446.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
Автор: Burhanuddin Baki Название: Badiou`s Being and Event and the Mathematics of Set Theory ISBN: 1474288006 ISBN-13(EAN): 9781474288002 Издательство: Bloomsbury Academic Рейтинг: Цена: 6551.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Alain Badiou's Being and Event continues to impact philosophical investigations into the question of Being. By exploring the central role set theory plays in this influential work, Burhanuddin Baki presents the first extended study of Badiou's use of mathematics in Being and Event. Adopting a clear, straightforward approach, Baki gathers together and explains the technical details of the relevant high-level mathematics in Being and Event. He examines Badiou's philosophical framework in close detail, showing exactly how it is 'conditioned' by the technical mathematics. Clarifying the relevant details of Badiou's mathematics, Baki looks at the four core topics Badiou employs from set theory: the formal axiomatic system of ZFC; cardinal and ordinal numbers; Kurt Godel's concept of constructability; and Cohen's technique of forcing. Baki then rebuilds Badiou's philosophical meditations in relation to their conditioning by the mathematics, paying particular attention to Cohen's forcing, which informs Badiou's analysis of the event. Providing valuable insights into Badiou's philosophy of mathematics, Badiou's Being and Event and the Mathematics of Set Theory offers an excellent commentary and a new reading of Badiou's most complex and important work.
Автор: Russell Marcus, Mark McEvoy Название: An Historical Introduction to the Philosophy of Mathematics: A Reader ISBN: 1472525345 ISBN-13(EAN): 9781472525345 Издательство: Bloomsbury Academic Рейтинг: Цена: 28908.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.
Автор: Tieszen, Richard Название: After Godel ISBN: 0199680612 ISBN-13(EAN): 9780199680610 Издательство: Oxford Academ Рейтинг: Цена: 7073.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Richard Tieszen analyzes, develops, and defends the writings of Kurt Goedel (1906-1978) on the philosophy and foundations of mathematics and logic. Goedel`s relation to the work of Plato, Leibniz, Husserl, and Kant is examined, and a new type of platonic rationalism that requires rational intuition, called `constituted platonism`, is proposed.
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