Paradoxes of Appearing
Paradoxes of Appearing

Author: Michael Asgaard Andersen

Publisher: Lars Muller Publishers

Published: 2009

Total Pages: 212

ISBN-13:

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The book contains a collection of essays by scholars and artists from a range of different fields including art, art history, architectural theory and philosophy. The essays are based on papers given at a symposium in Copenhagen in June 2008 and refer to the following considerations: When spectators confront and designers invent works of art and architecture, vital questions regarding their appearance arise. Based on multiple discourses on these subjects, contemporary positions in art, architecture and philosophy draw up new challenges, especially with regard to the creative practices. Within and between these positions emerge potentials for modes of thinking and doing with a new sensitivity. Contributors include Michael Asgaard Andersen and Henrik Oxvig, Renaud Barbaras, Andrew Benjamin, Olafur Eliasson, Sanford Kwinter, David Leatherbarrow, Martin Seel, David Summers, and Sven-Olov Wallenstein.

Sleight of Mind
Sleight of Mind

Author: Matt Cook

Publisher: MIT Press

Published: 2021-08-03

Total Pages: 369

ISBN-13: 0262542293

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This “fun, brain-twisting book . . . will make you think” as it explores more than 75 paradoxes in mathematics, philosophy, physics, and the social sciences (Sean Carroll, New York Times–bestselling author of Something Deeply Hidden). Paradox is a sophisticated kind of magic trick. A magician’s purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn’t require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts—and how reason can dispel the illusion of contradiction. The journey begins with “a most ingenious paradox” from Gilbert and Sullivan’s Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world—and much more.

On the Brink of Paradox
On the Brink of Paradox

Author: Agustin Rayo

Publisher: MIT Press

Published: 2019-04-02

Total Pages: 321

ISBN-13: 0262039419

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An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

Surprised by Paradox
Surprised by Paradox

Author: Jen Pollock Michel

Publisher: InterVarsity Press

Published: 2019-05-14

Total Pages: 221

ISBN-13: 083087092X

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In a world filled with ambiguity, we want faith to act like an orderly set of truth-claims to solve the problems that life throws at us. While there are certainties in Christian faith, at the heart of the Christian story is also paradox, and Jen Pollock Michel helps readers imagine a Christian faith open to mystery. Jesus invites us to abandon the polarities of either and or in order to embrace the difficult, wondrous dissonance of and.

Mathematical Fallacies and Paradoxes
Mathematical Fallacies and Paradoxes

Author: Bryan Bunch

Publisher: Courier Corporation

Published: 2012-10-16

Total Pages: 228

ISBN-13: 0486137937

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Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.

Paradoxes of Rationality and Cooperation
Paradoxes of Rationality and Cooperation

Author: Richmond Campbell

Publisher: UBC Press

Published: 1985

Total Pages: 378

ISBN-13: 0774802154

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This anthology, the first to bring together the most importantphilosophical essays on the paradoxes, analyses the concepts underlyingthe Prisoner's Dilemma and Newcomb's Problem and evaluates theproposed solutions. The relevant theories have been developed over thepast four decades in a variety of disciplines: mathematics, economics,psychology, political science, biology, and philosophy. And theproblems these paradoxes uncover can arise in many different forms: indebates over nuclear disarmament, labour-management disputes, maritalconflicts, Calvinist theology, and even in the evolution of diseasethrough the "cooperation" of microorganisms. Thepossibilities for application are virtually limitless.

The Outer Limits of Reason
The Outer Limits of Reason

Author: Noson S. Yanofsky

Publisher: MIT Press

Published: 2016-11-04

Total Pages: 419

ISBN-13: 026252984X

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This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review 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 intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. 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 • statements that are true but cannot be proven 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.

The Three Paradoxes
The Three Paradoxes

Author: Paul Hornschemeier

Publisher: Fantagraphics Books

Published: 2007-07-02

Total Pages: 81

ISBN-13: 1560976535

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The Three Paradoxes is an intricate and complex autobiographical comic by one of the most talented and innovative young cartoonists today. The story begins with a story inside the story: the cartoon character Paul Hornschemeier is trying to finish a story called "Paul and the Magic Pencil." Paul has been granted a magical implement, a pencil, and is trying to figure out what exactly it can do. He isn't coming up with much, but then we zoom out of this story to the creator, Paul, whose father is about to go on a walk to turn off the lights in his law office in the center of the small town. Abandoning the comic strip temporarily, Paul leaves with his camera, in order to fulfill a promise to his girlfriend that he would take pictures of the places that affected him as a child. Each "chapter" of the story is drawn in a completely different style, with strikingly unique production and color themes, and yet, somehow, despite (or perhaps because of) this non-linear progression, it all comes together as one story: a story questioning change, progress, and worth within the author's life.

Learning from Lying
Learning from Lying

Author: Julia Luisa Abramson

Publisher: University of Delaware Press

Published: 2005

Total Pages: 212

ISBN-13: 9780874139006

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"Learning from Lying narrates a new literary history as seen through the lens of mystification. Beginning with an examination of mystification's elaboration during the century of Enlightenment, the book accounts for mystification's distinctiveness relative to other deceptive forms, particularly forgery, and provides a timely intervention in current debates about the study of fakes. Readings of works by Denis Diderot, Prosper Merimee, and Wolfgang Hildesheimer follow out the cosmopolitan roots of the genre in the Republic of Letters and show how it theorizes literature through practical experiment. For when textual imitation is revealed, it unveils the necessary collusion between reader and writer that allows literature to exist as such."--BOOK JACKET.

Saving Truth From Paradox
Saving Truth From Paradox

Author: Hartry Field

Publisher: OUP Oxford

Published: 2008-03-06

Total Pages: 432

ISBN-13: 0191528161

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Saving Truth from Paradox is an ambitious investigation into paradoxes of truth and related issues, with occasional forays into notions such as vagueness, the nature of validity, and the Gödel incompleteness theorems. Hartry Field presents a new approach to the paradoxes and provides a systematic and detailed account of the main competing approaches. Part One examines Tarski's, Kripke’s, and Lukasiewicz’s theories of truth, and discusses validity and soundness, and vagueness. Part Two considers a wide range of attempts to resolve the paradoxes within classical logic. In Part Three Field turns to non-classical theories of truth that that restrict excluded middle. He shows that there are theories of this sort in which the conditionals obey many of the classical laws, and that all the semantic paradoxes (not just the simplest ones) can be handled consistently with the naive theory of truth. In Part Four, these theories are extended to the property-theoretic paradoxes and to various other paradoxes, and some issues about the understanding of the notion of validity are addressed. Extended paradoxes, involving the notion of determinate truth, are treated very thoroughly, and a number of different arguments that the theories lead to "revenge problems" are addressed. Finally, Part Five deals with dialetheic approaches to the paradoxes: approaches which, instead of restricting excluded middle, accept certain contradictions but alter classical logic so as to keep them confined to a relatively remote part of the language. Advocates of dialetheic theories have argued them to be better than theories that restrict excluded middle, for instance over issues related to the incompleteness theorems and in avoiding revenge problems. Field argues that dialetheists’ claims on behalf of their theories are quite unfounded, and indeed that on some of these issues all current versions of dialetheism do substantially worse than the best theories that restrict excluded middle.