Logical LabyrinthsLogical Labyrinths

This book features a unique approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought.

Author: Raymond Smullyan

Publisher: A K Peters/CRC Press

ISBN: 1568814437


Page: 275

View: 742

This book features a unique approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought. It serves as a bridge from the author’s puzzle books to his technical writing in the fascinating field of mathematical logic. Using the logic of lying and truth-telling, the author introduces the readers to informal reasoning preparing them for the formal study of symbolic logic, from propositional logic to first-order logic, a subject that has many important applications to philosophy, mathematics, and computer science. The book includes a journey through the amazing labyrinths of infinity, which have stirred the imagination of mankind as much, if not more, than any other subject.

Logical LabyrinthsLogical Labyrinths

Labyrinths Raymond M. Smullyan This book features a unique approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought . It serves as a bridge from the ...

Author: Raymond Smullyan

Publisher: CRC Press

ISBN: 9781439865378


Page: 275

View: 117

This book features a unique approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought. It serves as a bridge from the author's puzzle books to his technical writing in the fascinating field of mathematical logic. Using the logic of lying and truth-telling, the au

A Beginner s Guide to Mathematical LogicA Beginner s Guide to Mathematical Logic

... and tableaux logical consequence, a formula being a logical consequence of a set of formulas, definition logical implication and logical equivalence, definitions in terms of interpretations of Propositional Logic Logical Labyrinths, ...

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 9780486492377


Page: 292

View: 838

Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. Dover (2014) original publication. See every Dover book in print at www.doverpublications.com

The Idea of the Labyrinth from Classical Antiquity through the Middle AgesThe Idea of the Labyrinth from Classical Antiquity through the Middle Ages

The safest and surest course is to rise above the labyrinths of earthly creation and human reasonings to glimpse God the ... she creates a kind of logical labyrinth with her difficult circular argument proving that evil does not exist.

Author: Penelope Reed Doob

Publisher: Cornell University Press

ISBN: 9781501738463


Page: 376

View: 644

Ancient and medieval labyrinths embody paradox, according to Penelope Reed Doob. Their structure allows a double perspective—the baffling, fragmented prospect confronting the maze-treader within, and the comprehensive vision available to those without. Mazes simultaneously assert order and chaos, artistry and confusion, articulated clarity and bewildering complexity, perfected pattern and hesitant process. In this handsomely illustrated book, Doob reconstructs from a variety of literary and visual sources the idea of the labyrinth from the classical period through the Middle Ages. Doob first examines several complementary traditions of the maze topos, showing how ancient historical and geographical writings generate metaphors in which the labyrinth signifies admirable complexity, while poetic texts tend to suggest that the labyrinth is a sign of moral duplicity. She then describes two common models of the labyrinth and explores their formal implications: the unicursal model, with no false turnings, found almost universally in the visual arts; and the multicursal model, with blind alleys and dead ends, characteristic of literary texts. This paradigmatic clash between the labyrinths of art and of literature becomes a key to the metaphorical potential of the maze, as Doob's examination of a vast array of materials from the classical period through the Middle Ages suggests. She concludes with linked readings of four "labyrinths of words": Virgil's Aeneid, Boethius' Consolation of Philosophy, Dante's Divine Comedy, and Chaucer's House of Fame, each of which plays with and transforms received ideas of the labyrinth as well as reflecting and responding to aspects of the texts that influenced it. Doob not only provides fresh theoretical and historical perspectives on the labyrinth tradition, but also portrays a complex medieval aesthetic that helps us to approach structurally elaborate early works. Readers in such fields as Classical literature, Medieval Studies, Renaissance Studies, comparative literature, literary theory, art history, and intellectual history will welcome this wide-ranging and illuminating book.

Plato s LabyrinthPlato s Labyrinth

This is why the Parmenides is a logical labyrinth where following each path first to the right leads to a dead-end, and then going back and following each path to the left also leads to a dead-end. It is a labyrinth of logic, ...

Author: Aakash Singh Rathore

Publisher: Taylor & Francis

ISBN: 9781351190695


Page: 174

View: 410

This original and stimulating study of Plato's Socratic dialogues rereads and reinterprets Plato's writings in terms of their dialogical or dramatic form. Taking inspiration from the techniques of Umberto Eco, Jacques Derrida, and Leo Strauss, Aakash Singh Rathore presents the Socratic dialogues as labyrinthine texts replete with sophistries and lies that mask behind them important philosophical and political conspiracies. Plato's Labyrinth argues that these conspiracies and intrigues are of manifold kinds – in some, Plato is masterminding the conspiracy; in others, Socrates, or the Sophists, are the victims of the conspiracies. With supplementary forays ('intermissions') into the world of Xenophon and the Sophists, the complex and evolving series of overlapping arguments that the book lays out unfold within an edgy and dramatic narrative. Presenting innovative readings of major texts – Plato's Parmenides, Republic, Symposium and Meno as also Homer's Odyssey – this work is an ambitious attempt to synthesize philological, political, historical and philosophical research into a classical text-centred study that is at once of urgent contemporary relevance. This book aims to revitalize the study of ancient Greek thought in all its diverse disciplinary richness and will interest students and scholars across the social sciences and humanities, especially those in philosophy, Greek and classical studies, language and literature, politics, media and culture studies, theatre and performance studies, and history.

Meaningful GamesMeaningful Games

Logical labyrinths. Wellesley, MA: A. K. Peters. Soames, Scott. 2003. Philosophical analysis in the twentieth century. Vol. I: The Dawn of Analysis. Princeton, NJ: Princeton University Press. Strawson, P. F. 1950. On referring.

Author: Robin Clark

Publisher: MIT Press

ISBN: 9780262297868


Page: 373

View: 489

An engaging introduction to the use of game theory to study lingistic meaning. In Meaningful Games, Robin Clark explains in an accessible manner the usefulness of game theory in thinking about a wide range of issues in linguistics. Clark argues that we use grammar strategically to signal our intended meanings: our choices as speaker are conditioned by what choices the hearer will make interpreting what we say. Game theory—according to which the outcome of a decision depends on the choices of others—provides a formal system that allows us to develop theories about the kind of decision making that is crucial to understanding linguistic behavior. Clark argues the only way to understand meaning is to grapple with its social nature—that it is the social that gives content to our mental lives. Game theory gives us a framework for working out these ideas. The resulting theory of use will allow us to account for many aspects of linguistic meaning, and the grammar itself can be simplified. The results are nevertheless precise and subject to empirical testing. Meaningful Games offers an engaging and accessible introduction to game theory and the study of linguistic meaning. No knowledge of mathematics beyond simple algebra is required; formal definitions appear in special boxes outside the main text. The book includes an extended argument in favor of the social basis of meaning; a brief introduction to game theory, with a focus on coordination games and cooperation; discussions of common knowledge and games of partial information; models of games for pronouns and politeness; and the development of a system of social coordination of reference.

Sociative Logics and Their Applications Essays by the Late Richard SylvanSociative Logics and Their Applications Essays by the Late Richard Sylvan

extension of the logic of reason-for which includes full comprehension principles, ... This leads us through many little investigated logical labyrinths, through significant parts of scientific, legal and practical reasoning.

Author: Dominic Hyde

Publisher: Routledge

ISBN: 9781351723725


Page: 441

View: 782

This title was first published in 2003. Richard Sylvan died in 1996, he had made contributions to many areas of philosophy, such as, relevant and paraconsistent logic, Meinongianism and metaphysics and environmental ethics. One of his "trademarks" was the taking up of unpopular views and defending them. To Richard Sylvan ideas were important, wether they were his or not. This is a book of ideas, based on a collection of work found after his death, a chance for readers to see his vision of his projects. This collected works represents material drafted between 1982 and 1996, and the theme is that a small band of logics, namely pararelevant logics, offer solutions to many problems, puzzles and paradoxes in the philosophy of science.

Math Makes Sense Math Makes Sense

(2009) Logical Labyrinths ISBN 9781568814438, A K Peters • (2013) The Godelian Puzzle Book: Puzzles, Paradoxes and Proofs ISBN 0486497054 Vakil, R. 1996. A Mathematical Mosaic: Patterns and Problem Solving. Burlington, Ontario: Brendan ...

Author: Ana Helvia Quintero

Publisher: World Scientific

ISBN: 9781783268665


Page: 292

View: 366

The methods for teaching mathematics usually follow the structure of mathematics. The problem with this is that the structure of mathematics took centuries of elaboration to develop and is not the same as how one originally experiences mathematics. Based on research of how mathematics is actually learned, this book presents an innovative approach for teaching mathematics that will engage pupils and can have lifelong benefits for how they take on board more advanced mathematical topics. Math Makes Sense! makes use of the realistic mathematics education (RME) philosophy, which bridges the gap between informal mathematics learning (such as in day-to-day life) and more formal teaching in school. Many real-life situations as examples for learning are included, as well as different mathematical and logic puzzles that will stimulate learning and foster understanding. The ideas presented are not confined to one national curriculum and so can be helpful worldwide to teachers/ instructors (both in practice and those still in training), private tutors, homeschooling parents, and educational researchers. Contents:PrefaceAcknowledgmentsAbout the AuthorsFostering the Learning of MathematicsConstruction of Concepts and Mathematical InterpretationsNumberingAddition and SubtractionMultiplication and DivisionFractions, Decimals, and PercentagesMeasurementExploring SpaceProbability and StatisticsPatterns, Relations, and FunctionsThe Joy of PuzzlesTechnology: A Tool for Analysis and InterpretationAssessmentConcluding Remarks Readership: Teachers, trainee teachers, researchers interested in mathematics education, homeschool parents, and parents with children in primary/ elementary school. Key Features:This book is grounded on solid mathematics learning research, as well as on the authors' own observations in the classroom, and so combines theoretical knowledge with practiceWritten in an accessible mannerGives educators ideas which they can easily implement in the classroom

Glimpses into the World of MathematicsGlimpses into the World of Mathematics

The lady or the tiger?: and other logic puzzles. Dover Publications. Smullyan, R. 2009b. Satan, Cantor and infinity: mind-boggling puzzles. Dover Publications. Smullyan, R. 2009c. Logical labyrinths. A K Peters, Wellesley, Massachusetts ...

Author: Szymon Chlebowski

Publisher: LIT Verlag Münster

ISBN: 9783643913654



View: 955

Essays collected in this volume deal with various problems from the philosophy of mathematics. What connects them are two questions: how mathematics is created and how it is acquired. In 'Three Worlds of Mathematics' we are familiarized with David Tall's ideas pertaining to the embodied, symbolic and formal worlds of mathematics. In 'Basic Ideas of Intuitionism', we focus on an epistemological approach to mathematics which is distinctive to constructive mathematics. The author focuses on the computational content of intuitionistic logic and shows how it relates to functional programming. 'The Brave Mathematical Ant' carefully selects mathematical puzzles related to teaching experiences in a way that the solution requires creativity and is not obtainable by following an algorithm. Moreover the solution gives us some new insight into the underlying idea. 'Degrees Of Accessibility Of Mathematical Objects' discusses various criteria which can be used to judge accessibility of mathematical objects. We find logical complexity, range of applications, existence of a physical model as well as aesthetic values.