In this entertaining and challenging collection of logic puzzles, Raymond Smullyan - author of Forever Undecided - continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time. In the first part of the book, he transports us once again to that wonderful realm where knights, knaves, twin sisters, quadruplet brothers, gods, demons, and mortals either always tell the truth or always lie, and where truth-seekers are set a variety of fascinating problems. The section culminates in an enchanting and profound metapuzzle in which Inspector Craig of Scotland Yard gets involved in a search for the Fountain of Youth on the Island of Knights and Knaves. In the second part of To Mock a Mockingbird, we accompany the Inspector on a summer-long adventure into the field of combinatory logic (a branch of logic that plays an important role in computer science and artificial intelligence). His adventure, which includes enchanted forests, talking birds, bird sociologists, and a classic quest, provides for us along the way the pleasure of solving puzzles of increasing complexity until we reach the Master Forest and - thanks to Godel's famous theorem - the final revelation.

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

After putting forward the type of modal realism he favors, Lewis answers numerous objections that have been raised against it. These include an insistence that everything must be actual; paradoxes akin to those that confront naive set theory; arguments that modal realism leads to inductive skepticism, or to disregard for prudence and morality; and finally, sheer incredulity at a theory that disagrees so badly with common opinion. Lewis grants the weight of the last objection, but takes it to be outweighed by the benefits to systematic theory that acceptance of modal realism brings. He asks whether these same benefits might be gained more cheaply if we replace his many worlds by many merely 'abstract' representations; but concludes that all versions of this 'ersatz modal realism' are in serious trouble. In the final chapter, Lewis distinguishes various questions about trans-world identity, and argues that his 'method of counterparts' is preferable to alternative approaches.

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

With clear explanations and many examples drawn right out of day-to-day life, Paul Herrick untangles the complexities of logical theory in The Many Worlds of Logic. This new edition adds new chapters on informal logic and critical thinking. It also breaks out longer chapters from the previous edition into shorter, more focused chapters. Herrick has added many new explanations and examples; in each chapter, he covers the fundamentals completely before moving on to more challenging areas.

Features
* Difficult terms are highlighted and explained carefully
* End-of-chapter glossaries help students remember important terms
* Hundreds of examples demonstrate the application of concepts
* Hundreds of exercises help students learn logic by actually doing it
* Truth-trees in an appendix help students go beyond the basics

This book categorizes, identifies and explains the various techniques that are used repeatedly in all proofs and explains how to read proofs that arise in mathematical literature by understanding which techniques are used and how they are applied.

Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems.

This book introduces the beginning computer science student to some of the fundamental ideas and techniques used by computer scientists today, focusing on discrete structures, logic, and computability.