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Forever Undecided

Author: Raymond M. Smullyan

Publisher: Knopf

Published: 2012-07-04

Total Pages: 286

ISBN-13: 0307962466

Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!

Undecided

Author: Barbara Bailey Kelley

Publisher: ReadHowYouWant.com

Published: 2011

Total Pages: 410

ISBN-13: 1459619331

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Large Print.

Possible Worlds

Author: Rod Girle

Publisher: McGill-Queen's Press - MQUP

Published: 2003

Total Pages: 226

ISBN-13: 0773526676

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Satan, Cantor, And Infinity And Other Mind-bogglin

Author: Raymond M. Smullyan

Publisher: Knopf

Published: 2012-05-30

Total Pages: 281

ISBN-13: 0307819825

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More than two hundred new and challenging logic puzzles—the simplest brainteaser to the most complex paradoxes in contemporary mathematical thinking—from our topmost puzzlemaster (“the most entertaining logician who ever lived,” Martin Gardner has called him). Our guide to the puzzles is the Sorcerer, who resides on the Island of Knights and Knaves, where knights always tell the truth and knaves always lie, and he introduces us to the amazing magic—logic—that enables to discover which inhabitants are which. Then, in a picaresque adventure in logic, he takes us to the planet Og, to the Island of Partial Silence, and to a land where metallic robots wearing strings of capital letters are noisily duplicating and dismantling themselves and others. The reader’s job is to figure out how it all works. Finally, we accompany the Sorcerer on an alluring tour of Infinity which includes George Cantor’s amazing mathematical insights. The tour (and the book) ends with Satan devising a diabolical puzzle for one of Cantor’s prize students—who outwits him! In sum: a devilish magician’s cornucopia of puzzles—a delight for every age and level of ability.

My Life Undecided

Author: Jessica Brody

Publisher: Farrar, Straus and Giroux (BYR)

Published: 2011-06-07

Total Pages: 320

ISBN-13: 9781429940993

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PLEASE READ THIS! MY LIFE DEPENDS ON IT! Okay, maybe that was a bit melodramatic, but I'm sorry, I'm feeling a bit melodramatic at the moment. Here's the deal. My name is Brooklyn Pierce, I'm fifteen years old, and I am decisionally challenged. Seriously, I can't remember the last good decision I made. I can remember plenty of crappy ones though. Including that party I threw when my parents were out of town that accidentally burned down a model home. Yeah, not my finest moment, for sure. But see, that's why I started a blog. To enlist readers to make my decisions for me. That's right. I gave up. Threw in the towel. I let someone else decide which book I read for English. And whether or not I accepted an invitation to join the debate team from that cute-in-a-dorky-sort-of-way guy who gave me the Heimlich maneuver in the cafeteria. (Note to self: chew the melon before swallowing it.) I even let them decide who I dated! Well, it turns out there are some things in life you simply can't choose or have chosen for you—like who you fall in love with. And now everything's more screwed up than ever. But don't take my word for it. Read the book and decide for yourself. You'll laugh, you'll cry, you'll scream in frustration. Or maybe that's just me. After all, it's my life.

Theoretical Aspects of Reasoning About Knowledge

Author: Joseph Y. Halpern

Publisher: Morgan Kaufmann

Published: 2014-05-12

Total Pages: 416

ISBN-13: 1483214419

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Theoretical Aspects of Reasoning About Knowledge: Proceedings of the 1986 Conference focuses on the principles, methodologies, approaches, and concepts involved in reasoning about knowledge. The selection first provides an overview of reasoning about knowledge, varieties of self-reference, and pegs and alecs. Topics covered include data semantics, partial objects and identity, circumstance, self, and causal connection, structure of circumstance, varieties and limits of self-reference, problem of logical omniscience, and knowledge, communication, and action. The book then explores reasoning about knowledge in artificial intelligence; synthesis of digital machines with provable epistemic properties; and a first order theory of planning, knowledge, and action. The publication ponders on the consistency of syntactical treatments of knowledge, foundations of knowledge for distributed systems, knowledge and implicit knowledge in a distributed environment, and the logic of distributed protocols. Topics include formal syntax and semantics, structure of models, message-based knowledge worlds, changing the class of messages, implicit knowledge in message-based knowledge worlds, conservation and implicit knowledge, and distributed protocols. The selection is a dependable source of data for researchers interested in the theoretical aspects of reasoning about knowledge.

Mathematics, Models, and Modality

Author: John P. Burgess

Publisher: Cambridge University Press

Published: 2008-02-21

Total Pages: 253

ISBN-13: 113947054X

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John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy of mathematics, logic, and philosophy of language.

Forever Undecided

Author: Raymond M. Smullyan

Publisher: Alfred a Knopf Incorporated

Published: 1987

Total Pages: 257

ISBN-13: 9780394549439

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Collects a variety of mathematics and logic puzzles, some based on the theorems of the mathematician Kurt Godel

Mathematical Intuitionism

Author: Carl J. Posy

Publisher: Cambridge University Press

Published: 2020-11-12

Total Pages: 116

ISBN-13: 1108593259

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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.

Eternal Youth and the Myth of Deconstruction

Author: Bret Alderman

Publisher: Taylor & Francis

Published: 2023-12-06

Total Pages: 235

ISBN-13: 1003805442

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In Eternal Youth and the Myth of Deconstruction, Bret Alderman puts forth a compelling thesis: Deconstruction tells a mythic story. Through an attentive examination of multiple texts and literary works, he elucidates this story in psychological and philosophical terms. Deconstruction, the method of philosophical and literary analysis originated by Jacques Derrida, arises from what Carl Jung called “a kind of readiness to produce over and over again the same or similar mythical ideas.” In the case of deconstruction, such ideas bear a striking resemblance to a figure that Jungian and Post-Jungian writers refer to as the puer aeternus or eternal youth. To make his case, in addition to a careful analysis of numerous Derridean texts, he offers readings of literary works by Milan Kundera, J.M. Barrie, Dante, Apuleius, and others. These texts help illustrate that deconstruction’s preoccupations over questions of presence, deferral, authority, limits, time, and representation are also recurrent issues for the eternal youth as described by Marie-Louise Von Franz and James Hillman. Judith Butler’s deconstruction of sex and gender reflects similar patterns, and she features in this work as a contemporary exemplar of the deconstructive approach. Eternal Youth and the Myth of Deconstruction will be a compelling read for both students and teachers of depth psychology and continental philosophy. The clarity of its style will be appealing to advanced scholars and educated laypersons alike.