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Classical Mathematical Logic
In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.
Critical Thinking 5th edition
This fifth edition of Critical Thinking by the noted logician Richard L. Epstein is practical, engaging, and easy to teach. Students enjoy and understand it because it is clear and has hundreds of examples using a cast of characters who reason as we do every day. More than 1,000 exercises lead students to be able to reason well in their courses and their lives. Essay writing lessons and visual writing lessons, using the cast of characters, teach students that first comes clear thinking and then comes clear writing. A complete and comprehensive Instructor's Manual makes the text easy to teach and grade. New to this edition: chapters on explanations and reasoning in the sciences. • Over 1,000 examples and exercises from daily life. • A dozen original writing lessons fully integrated with the text. • Unique cartoon writing lessons help students apply critical thinking to non-verbal situations.
Propositional Logics
This book grew out of my confusion. If logic is objective, how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic that I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the idea that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from reasoning in our usual language is the stepping-stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning that has some objective value.
Critical Thinking
Featuring its own cast of characters, a personal and accessible tone, and carefully crafted in step by step units, Epstein's CRITICAL THINKING sets new standards of clarity for presenting subject matter. Extensively class tested, the text uses an enormous number of everyday examples and exercises to illuminate key points and ideas. It is the only text in philosophy in which students work with cartoons to convert the non-verbal into arguments and arrive at conceptual understanding. It is also the only text-workbook-instructor's manual system designed and constructed simultaneously to provide the most fully integrated learning and teaching system available.
Predicate Logic
The forms and scope of logic rest on assumptions of how language and reasoning connect to experience. In this volume an analysis of meaning and truth provides a foundation for studying modern propositional and predicate logics. Chapters on propositional logic, parsing propositions, and meaning, truth, and reference give a basis for criteria that can be used to judge formalizations of ordinary language arguments. Over 120 worked examples of formalizations of propositions and arguments illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, functions, and second-order logic. The chapter on second-order logic illustrates how different conceptions of predicates and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things. Notable for its clarity of presentation, and supplemented by many exercises, this volume is suitable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formalizing reasoning.
How to Reason
Too often we're guided by what we last heard, by our friends' approval, by impulse—our desires, our fears. Without reflection. Without even stopping to think. In this book you'll learn how to reason and find your way better in life. You'll learn to see the consequences of what you and others say and do. You'll learn to see the assumptions that you and others make. You'll learn how to judge what you should believe. These are the skills we all need to make good decisions. Illustrations using a cast of cartoon characters make the concepts memorable. And many exercises will help you to check your understanding. Truly a book for all—from high school to graduate school, from auto repair to managing a company. "How to Reason" will help you find a way in life that is clearer and not buffetted by the winds of nonsense and fear.
An Introduction to Formal Logic: Second Edition
• Intended for a course for students in philosophy, mathematics, linguistics, or computer science, and excellent for self-study. • Motivation is given for each formal concept and each step in building a formal logic in terms of formalizing reasoning. Summaries are given at important junctures in the book to keep students aware of what they are doing and where they are going. • Criteria of formalization are developed and applied to formalizing ordinary language reasoning in an example-analysis format. • More than 300 worked examples. • More than 500 exercises with answers available on the web.
The Pocket Guide to Critical Thinking
Not everyone knows how to think critically. THE POCKET GUIDE TO CRITICAL THINKING is the new standard for reasoning well and making smart choices. Inside, you'll discover tips and secrets that not only help you get better grades, it gives you the tools you'll need for success in career and relationships. And with its easy-to-use format and review tools, this reasoning textbook is the one you'll use again and again.
Critical Thinking
Featuring its own cast of characters, a personal and accessible tone, and carefully crafted in step-by-step units, this book sets a new standard of clarity for presenting the subject matter. Extensively class-tested, the text uses an enormous number of everyday examples and exercises to illuminate key points and ideas. It is the only text in philosophy in which students work with cartoons to convert the non-verbal into arguments and arrive at conceptual understanding. It is also the only text-workbook-instructor's manual system designed and constructed simultaneously to provide the most fully integrated learning and teaching system available.
