Logical Labyrinths

Logical Labyrinths
Author: Raymond Smullyan
Publisher: CRC Press
Total Pages: 332
Release: 2008-12-22
Genre: Games & Activities
ISBN: 143986537X

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

Mathematical Labyrinths. Pathfinding

Mathematical Labyrinths. Pathfinding
Author: Boris Pritsker
Publisher: World Scientific
Total Pages: 324
Release: 2021-01-04
Genre: Mathematics
ISBN: 9811228256

Mathematical Labyrinths. Pathfinding provides an overview of various non-standard problems and the approaches to their solutions. The essential idea is a framework laid upon the reader on how to solve nonconventional problems — particularly in the realm of mathematics and logic. It goes over the key steps in approaching a difficult problem, contemplating a plan for its solution, and discusses set of mental models to solve math problems.The book is not a routine set of problems. It is rather an entertaining and educational journey into the fascinating world of mathematical reasoning and logic. It is about finding the best path to a solution depending on the information given, asking and answering the right questions, analyzing and comparing alternative approaches to problem solving, searching for generalizations and inventing new problems. It also considers as an important pedagogical tool playing mathematical and logical games, deciphering mathematical sophisms, and interpreting mathematical paradoxes.It is suitable for mathematically talented and curious students in the age range 10-20. There are many 'Eureka'- type, out of the ordinary, fun problems that require bright idea and insight. These intriguing and thought-provoking brainteasers and logic puzzles should be enjoyable by the audience of almost any age group, from 6-year-old children to 80-year-old and older adults.

A First Course in Logic

A First Course in Logic
Author: Mark Verus Lawson
Publisher: CRC Press
Total Pages: 250
Release: 2018-12-07
Genre: Mathematics
ISBN: 1351175378

A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists. There are three components to this course: propositional logic; Boolean algebras; and predicate/first-order, logic. Logic is the basis of proofs in mathematics — how do we know what we say is true? — and also of computer science — how do I know this program will do what I think it will? Surprisingly little mathematics is needed to learn and understand logic (this course doesn't involve any calculus). The real mathematical prerequisite is an ability to manipulate symbols: in other words, basic algebra. Anyone who can write programs should have this ability.

A Beginner's Further Guide To Mathematical Logic

A Beginner's Further Guide To Mathematical Logic
Author: Raymond M Smullyan
Publisher: World Scientific Publishing Company
Total Pages: 288
Release: 2016-11-11
Genre: Mathematics
ISBN: 9814733016

'A wealth of examples to which solutions are given permeate the text so the reader will certainly be active.'The Mathematical GazetteThis is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a 'fein' chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a 'decision machine.' Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.

Big Book of Mazes and Labyrinths

Big Book of Mazes and Labyrinths
Author: Walter Shepherd
Publisher: Courier Corporation
Total Pages: 129
Release: 1973-01-01
Genre: Games & Activities
ISBN: 0486229513

The path least traveled makes all the difference in this volume, especially when you find yourself crossing bridges, escaping from caves, lighting firecrackers, spelling out passwords, and untangling snakes. These 50 challenges include classic, solid, and ripple mazes, along with short-path and avoidance labyrinths and other intriguing problems. Solutions.

A Beginner's Guide to Mathematical Logic

A Beginner's Guide to Mathematical Logic
Author: Raymond M. Smullyan
Publisher: Courier Corporation
Total Pages: 292
Release: 2014-03-19
Genre: Mathematics
ISBN: 0486782972

Combining stories of great writers and philosophers with quotations and riddles, this original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2014 edition.

The Quantum Labyrinth

The Quantum Labyrinth
Author: D.J. Hoekzema
Publisher: Springer Science & Business Media
Total Pages: 287
Release: 2012-12-06
Genre: Science
ISBN: 9401117772

At the outset of the research leading to this book I held a position somewhere close to 'the standard Copenhagen interpretation' of QM. I was strongly attracted to, in particular, the philosophy of Niels Bohr. However, being aware of some of the problematic sides and ambiguities of his views and of new developments which have taken place in QM after his time, the main challenge would be to develop a more up to date version version of his approach and express it in a philosophically unobjectionable way. Traces of this original attitude can still be found in views I hold nowadays. For instance, I think that I now know a satisfactory and correct way of dealing with features like 'complementarity', and I still see this as a relevant subject. In many other respects, however, there have been major changes in my position. In fact, during certain stages of my research my views simply started moving and kept on doing so at an irritating pace and for uncomfortably long periods of time. I learned, for example that at least some of the classical ideas about theory structure are much better than I had realized, and cannot just be pushed aside for anything even as impressive as empirical success.

Labyrinths

Labyrinths
Author: Jorge Luis Borges
Publisher: New Directions Publishing
Total Pages: 292
Release: 1964
Genre: Fiction
ISBN: 9780811200127

Forty short stories and essays have been selected as representative of the Argentine writer's metaphysical narratives.

Four Lives

Four Lives
Author: Raymond M. Smullyan
Publisher: Courier Corporation
Total Pages: 353
Release: 2014-03-19
Genre: Mathematics
ISBN: 048649067X

" This 'best of' collection of works by Raymond Smullyan features excerpts from his published writings, including logic puzzles, explorations of mathematical logic and paradoxes, retrograde analysis chess problems, jokes and anecdotes, and meditations on the philosophy of religion. In addition, numerous personal tributes salute this celebrated professor, author, and logic scholar who is also a magician and musician. "--

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

The Idea of the Labyrinth from Classical Antiquity through the Middle Ages
Author: Penelope Reed Doob
Publisher: Cornell University Press
Total Pages: 376
Release: 2019-03-15
Genre: Literary Criticism
ISBN: 1501738461

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.