This self-study guide is an introduction to the methods of reasoning that make science possible. Clear and accessible, with no background in science assumed, Reasoning in the Sciences presents over 700 worked examples and exercises with solutions covering everything from claims, definitions, and arguments to generalizing, cause and effect, explanations, models, and theories. This is a book that will help every student in their science courses.

Reasoning in the Sciences: A Self-Study Guide

Computers & Technology

Epstein, Richard L.

Programming Languages

Advanced Reasoning Forum

The classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".

Computability: Computable Functions, Logic, and the Foundations of Mathematics

Carnielli, Walter A.

Computer Science

A summary and guide to the art of reasoning well, this small book is a great aid to reasoning in daily life. Using everyday examples that relate to everyone's experiences, and with an extraordinary clarity of presentation, this Pocket Guide allows the reader to learn all the basic skills of how to reason well in a short, useful introduction. It is also the basic text for how to think clearly enough to write well. The Pocket Guide to Critical Thinking is a perfect supplement for any course, for self-study, or as a reference when writing.

The Pocket Guide to Critical Thinking, 3rd edition

Politics & Social Sciences

Kernberger, Carolyn

Philosophy

First comes clear thinking, then comes clear writing. The extraordinarily clear explanations in the Pocket Guide to Critical Thinking provide the essential skills to reason better-for classwork, for writing, and for use in everyday life. The book employs an abundance of engaging examples from everyday life that illustrate how to analyze arguments and make better decisions. The Pocket Guide is both the perfect supplement for any course that requires critical thinking, from the sciences to the humanities, and a practical aid for self-study or a reference source in writing. This extensively revised fourth edition has over 150 new examples and a new chapter on evaluating risks. Buyers of this book also get free access to hundreds of additional examples and exercises as well as further material for the sciences on the Critical Thinking Web Exchange at the Advanced Reasoning Forum website.

The Pocket Guide to Critical Thinking

This series of books presents the fundamentals of reasoning well, in a style accessible to both students and scholars.  The text of each essay presents a story, the main line of development of the ideas, while the footnotes and appendices place the research within a larger scholarly context.  The essays overlap, forming a unified analysis of reasoning, yet each essay is designed so that it may be read independently of the others.  The topic of this volume is the evaluation of reasoning about cause and effect, reasoning using conditionals, and reasoning that involves explanations.  The essay "Reasoning about Cause and Effect" sets out a way to analyze whether there is cause and effect in terms of whether an inference from a claim describing the purported cause to a claim describing the purported effect satisfies specific conditions.  Different notions of cause and effect correspond to placing different conditions on what counts as a good causal inference.  An application of that method in "The Directedness of Emotions" leads to a clearer understanding of the issue whether every emotion need be directed at something.  In the essay "Conditionals" various ways of analyzing reasoning with claims of the form "if . . . then . . ." are surveyed.  Some of those uses are meant to be judged as inferences that are not necessarily valid, and conditions are given for when we can consider such inferences to be good.  In "Explanations" verbal answers to a question why a claim is true are evaluated in terms of conditions placed on inferences from the explaining claims to the claim being explained. Recognizing that the direction of inference of such an explanation is the reverse of that for an argument with the very same claims is crucial in their evaluation.  Explanations in terms of functions and goals are also investigated.

Cause and Effect, Conditionals, Explanations

This series of books is meant to present the fundamentals of reasoning well in a clear manner accessible to both scholars and students. The body of each essay gives the main development of the subject, while the footnotes and appendices place the research within a larger scholarly context. The topic of this volume is the nature and evaluation of reasoning in science and mathematics. Science and mathematics can both be understood as proceeding by a method of abstraction from experience. Mathematics is distinguished from other sciences only in its greater abstraction and its demand for necessity in its inferences. That methodology of abstraction is the main focus here. The study of these subjects is not just of academic interest. First comes clear thinking, then comes clear research and clear writing. The essays: • Background • Models and Theories • Experiments • Mathematics as the Art of Abstraction

Reasoning in Science and Mathematics

This series of books presents the fundamentals of logic in a style accessible to both students and scholars. The text of each essay presents a story, the main line of development of the ideas, while the notes and appendices place the research within a larger scholarly context. The essays overlap, forming a unified analysis of logic as the art of reasoning well, yet each essay is designed so that it may be read independently. The topic of this volume is prescriptive reasoning. Descriptive claims say how the world is, was, or will be; prescriptive claims say how the world should be. We have fairly clear rules for reasoning with descriptive claims. The goal of the first essay, "Reasoning with Prescriptive Claims," is to clarify how to reason with prescriptive ones. The first step in doing so is to justify our viewing prescriptions as true or false. That justification is part of a general approach to reasoning in which many kinds of personal evaluations are taken to be true-false divisions. That view has been implicit if not explicit in analyses of reasoning from formal logic through argument analysis. in "Truth and Reasoning" I set out reasons for adopting that methodology. Theories, too, seem to be descriptive or prescriptive. Some say how the world is, others how the world should be. Yet, as shown in "Prescriptive Theories?," on close examination the distinction evaporates. Unless, that is, one says that certain theories about values use an entirely different notion of truth than is used in science and is codified in our usual methods of reasoning. Absent that, there seems to be no justification for constructing and evaluating what are typically thought of as prescriptive theories differently from descriptive ones. Many discussions of how to evaluate prescriptive claims are given in terms of what is rational or irrational to do. In the final essay, "Rationality," what we mean by the idea of someone being rational is investigated and the limitations of that label in evaluating reasoning or actions is shown.

Prescriptive Reasoning

Propositional Logics presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum. As the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.

Propositional Logics Third Edition

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.

Predicate Logic

Featuring its own cast of illustrated 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 the subject matter. Extensively classroom tested, the text uses over one thousand everyday examples and exercises to illuminate key points and ideas. It is the only text on critical thinking in which students work with illustrations 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 by one author to provide the most fully integrated learning and teaching system available.

Critical Thinking Third Edition

Richard L. Epstein

Carolyn Kernberger

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Books by Advanced Reasoning Forum