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.
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 basic theme here is the analysis of formal logic in terms of what metaphysical assumptions we need when we develop the formal systems we use. The essays together give a perspective of formal logic as part of the art of reasoning well. The essays are • Possibilities and Valid Inferences, • A General Framework for Semantics for Propositional Logics, • Why Are There So Many Logics? • Truth and Reasoning, • On Translations, • Reflections on Temporal and Modal Logic, • The Timelessness of Classical Predicate Logic, • Events in the Metaphysics of Predicate Logic, • Categoricity with Minimal Metaphysics, • Reflections on Gödel's Theorems, • On the Error in Frege's Proof that Names Denote, and • Postscript: Logic as the Art of Reasoning Well.
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.
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 question addressed in this volume is how we can justify our beliefs through reasoning. The first essay, "Arguments," investigates what it is that we call true or false and how we reason toward truths through arguments. A general theory of argument analysis is set out on the basis of what we can assume about those with whom we reason. The next essay, "Fallacies," explains how the classification of an argument as a fallacy can be used within that general approach. In contrast, there is no agreement on what the terms "induction" and "deduction" mean, and they are not useful in evaluating arguments, as shown in "Induction and Deduction." In reasoning to truths, in the end we must take some claims as basic, not requiring any justification for accepting them. How we choose those claims and how they affect our reasoning is examined in "Base Claims." The essay "Analogies" considers how comparisons can be used as the basis of arguments, arguing from similar situations to similar conclusions. An important use of analogies is in reasoning about the mental life of other people and things, which is examined in "Subjective Claims," written with Fred Kroon and William S. Robinson. "Generalizing" examines how to argue from part of a collection or mass to the whole or a larger part. The question there is whether we are ever justified in accepting such an argument as good. "Probabilities" sets out the three main ways probability statements have been interpreted: the logical relation view, the frequency view, and the subjective degree of belief view. Each of those is shown to be inadequate to make precise the scale of plausibility of claims and the scale of the likelihood of a possibility. Many discussions of how to reason well and what counts as good reason are given in terms of who or what is rational. In the final essay, "Rationality," it's shown that what we mean by the idea of someone being rational is of very little use in evaluating reasoning or actions. This volume is meant to give a clearer idea of how to reason well, setting out methods of evaluation that are motivated in terms of our abilities and interests. At the ground of our reasoning, though, are metaphysical assumptions, too basic and too much needed in our reasoning for us to justify them through reasoning. But we can try to uncover those assumptions to see how they are important and what depends on them.
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.
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.
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.
This book 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.
• 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.
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. ** Claims. Arguments. Fallacies. Analogies. Generalizing. Cause and Effect. Explanations. These are clearly set out with hundreds of examples from daily life showing how to use them. 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. ******* In Reasoning in the Sciences, you'll learn how to use your reasoning skills to understand how scientists make definitions, what an experiment is, what can go wrong with an experiment, how scientists reason with models and theories, what counts as a good explanation in science, and how to distinguish science from magic, religion, and fraud. No background in science is needed, just a healthy appetitite for learning.
This series of volumes is meant to extend the scope of what we can formalize in classical predicate logic, and in doing so see the limitations of what can be done. The first section of this volume presents classical predicate logic with equality. In the second section, that logic is extended to formalize reasoning that involves adverbs and relative adjectives by viewing those as modifiers of simpler predicates. What is normally taken to be an atomic predicate, such as "barking loudly", can then have internal structure. Reasoning that involves conjunctions of terms, as in "Tom and Dick lifted the table", conjunctions of modifiers, conjunctions of predicates, and disjunctions of predicates can also be formalized by viewing them as part of the internal structure of atomic predicates. Many questions about the nature of formalizing arise in doing this. The internal structure of names is the topic of the third and last section. Names for functions are used in classical predicate logic to form complex names. In our ordinary reasoning we also use descriptions to form functions, such as "the wife of", and descriptions to form names, such as "the cat that scratched Zoe". To reason with those we can take account of their internal structure by dropping the assumption that every name must refer to a specific thing. The formal systems that are developed here are meant to help us understand how to reason well. Many worked examples show how to use them. Those examples also uncover limitations of the formal work. Throughout this series of volumes, the work proceeds by abstracting and creating formal models to formalize reasoning. By paying attention to the process of abstracting we gain insight into why we consider some reasoning to be good and some reasoning bad, and insight also into the deeper assumptions we make about the world on which our judgments rely.
Time and Space in Formal Logic begins with an analysis of assumptions about how logic and language relate. Then in the first section, times are taken to be established by true propositions, and those are related as before and after with temporal propositional connectives. In the second section, times are treated as things that can be picked out and counted, leading to a predicate logic that allows for quantification over times. In the third section, locations in space are also treated as things that can be picked out and counted, leading to a predicate logic that allows for quantification over both times and locations. Many applications of the formal systems to formalizing ordinary language propositions and inferences clarify better the assumptions we make in reasoning taking account of time and space by making those precise in the formal systems. Appendices on events, branching times, intentions, and descriptive names add to the scope of the work.
We prove two main results: (1) [lowercase Greek]Omega + 1 is an initial segment of the degrees ([less-than or equal to]≤ a̲ for any r.e. a̲ [not equal to] 0̲ , and (2) given any 0̲ [less than] a̲ [less than] h̲ where a̲ and h̲ are r.e. and h̲ is high, there is a minimal degree m̲ [less than] h̲ such that m̲ [set-theoretic union] a̲ = h̲.
For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.
Principles of Neurosurgery, by Drs. Richard G. Ellenbogen, Saleem I. Abdulrauf and Laligam N Sekhar, provides a broad overview of neurosurgery ideal for anyone considering or training in this specialty. From general principles to specific techniques, it equips you with the perspectives and skills you need to succeed. Comprehensive without being encyclopedic, this new edition familiarizes you with the latest advances in the field—neuroimaging, the medical and surgical treatment of epilepsy, minimally invasive techniques, and new techniques in position and incisions—and shows you how to perform key procedures via an online library of surgical videos at www.expertconsult.com. No other source does such an effective job of preparing you for this challenging field! Get comprehensive coverage of neurosurgery, including pre- and post- operative patient care, neuroradiology, pediatric neurosurgery, neurovascular surgery, trauma surgery, spine surgery, oncology, pituitary adenomas, cranial base neurosurgery, image-guided neurosurgery, treatment of pain, epilepsy surgery, and much more. Gain a clear visual understanding from over 1,200 outstanding illustrations—half in full color—including many superb clinical and operative photographs, surgical line drawings, and at-a-glance tables. Apply best practices in neuroimaging techniques, minimally invasive surgery, epilepsy surgery, and pediatric neurosurgery. Master key procedures by watching experts perform them in a video library online at www.expertconsult.com, where you can also access the fully searchable text, an image gallery, and links to PubMed. Keep up with recent advances in neurosurgery with fully revised content covering neuroimaging, the medical and surgical treatment of epilepsy, minimally invasive techniques, new techniques in position and incisions, deep brain stimulation, cerebral revascularization, and treatment strategies for traumatic brain injury in soldiers. Apply the latest guidance from new chapters on Cerebral Revascularization, Principles of Modern Neuroimaging, Principles of Operative Positioning, Pediatric Stroke and Moya-Moya, Anomalies of Craniovertebral Junction, and Degenerative Spine Disease. Tap into truly global perspectives with an international team of contributors led by Drs. Richard G. Ellenbogen and Saleem I. Abdulrauf. Find information quickly and easily thanks to a full-color layout and numerous detailed illustrations.
This handy book is a summary and guide to the art of reasoning well in academic pursuits and in everyday life. The Second Edition of Epstein's comprehensive text, CRITICAL THINKING, set a new standard of pedagogical excellence and provided a well-integrated approach to the subject. This brief "pocket guide" provides the same benefits in a trimmed-down fashion, covering the essentials. This latest edition includes revised examples that are more inter-disciplinary in scope.
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 but can lead to better research in science and mathematics. First comes clear thinking, then comes clear research and clear writing. The essays: • Background • Models and Theories • Experiments • Mathematics as the Art of Abstraction.
Conventional gestures are those movements we make, such as waving hello and shaking hands, that are part of a learned, shared, symbolic system. In this book Richard L. Epstein working with the illustrator Alex Raffi examines how such gestures mean and how we can study them. Drawing on their collection of over 400 American gestures, available on the Advanced Reasoning Forum website, they examine problems of methodology and the nature of gestures in relation to the work of others who have studied and collected gestures from various cultures. An extensive annotated bibliography describes and comments on virtually all known collections of conventional gestures.
The trusted landmark cardiology resource—thoroughly updated to reflect the latest clinical perspectives Includes DVD with image bank A Doody's Core Title ESSENTIAL PURCHASE for 2011! 5 STAR DOODY'S REVIEW! "This is an outstanding choice for those who strive for a firm foundation in cardiovascular medicine, as well as an up-to-date and user-friendly source that addresses every discipline in the field. The updates and enhancements to this edition have made the book easier to use."--Doody's Review Service Through thirteen editions, Hurst’s the Heart has always represented the cornerstone of current scholarship in the discipline. Cardiologists, cardiology fellows, and internists from across the globe have relied on its unmatched authority, breadth of coverage, and clinical relevance to help optimize patient outcomes. The thirteenth edition of Hurst’s the Heart continues this standard-setting tradition with 19 new chapters and 59 new authors, each of whom are internationally recognized as experts in their respective content areas. Featuring an enhanced, reader-friendly design, the new edition covers need-to-know clinical advances, as well as issues that are becoming increasingly vital to cardiologists worldwide. As in previous editions, you will find the most complete overview of cardiology topics available—plus a timely new focus on evidence-based medicine, health outcomes, and health quality. New Features 1548 full-color illustrations and 578 tables Companion DVD with image bank includes key figures and tables from the text The Cardiovascular Disease: Past, Present, and Future section includes a new chapter on assessing and improving quality of care in cardiovascular medicine The section on the scientific foundations of cardiovascular medicine has been thoroughly revised 2 new chapters in the section on the evaluation of the patient detail the process of effective diagnostic decision making based on technology, clinical trials, and practice guidelines A new chapter in the section on heart failure details cardiac transplantation The sections on primary heart disease include new chapters on topics such as preventive strategies for coronary artery disease and updated pharmacologic strategies for acute coronary syndromes The section on cardiopulmonary disease features new chapters on chronic cor pulmonale and sleep disorder breathing and its relationship to cardiovascular disease The section on valvular heart disease has four of the six chapter completely rewritten by new authors who are authorities in the field The final six sections feature new chapters on the environment and heart disease, surgical treatment of carotid and peripheral vascular disease and cost effective strategies in cardiology
Now in a new edition!--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".
An all-inclusive overview of cardiology in a trusted landmark reference A Doody's Core Title ESSENTIAL PURCHASE! 5 STAR DOODY'S REVIEW! "This well-organized textbook begins with a thoughtful discussion of cardiology's past and future. It presents readers with the foundations of cardiovascular medicine and the basics of cardiovascular evaluation. These initial chapters provide an excellent overview of topics in general cardiology from guidelines to newer diagnostic modalities such as MRI, CT, and PET. Subsequently, the book is organized to provide readers with a focused approach to other areas of cardiology from heart failure to electrophysiology and interventional cardiology." This is a very useful reference that compiles a vast amount of information on the diagnosis and management of cardiovascular diseases in one book. It continues to be one of best overall references in this field. -- Doody's Review Service Developed by a team of internationally renowned editors and authors, Hurst's The Heart is synonymous with the most comprehensive and current perspectives on treating the full range of heart problems. Inside, you'll get an incisive look at all the global advances in the diagnosis and management of cardiovascular disease, including the translation of basic science research into clinical applications. And integrated throughout are the latest treatment protocols, ACC/AHA and ESC treatment guidelines, as well as quick-reference tables and algorithms. NEW to this Edition: Stunning full-color illustrations Information from the COURAGE trial, covering the use and misuse of drug eluting stents Vital coverage of advances in the treatment of pulmonary hypertension and new information on hypertrophic cardiomyopathy Expert-authored chapters on coronary blood flow, stunning, and hibernation; race and ethnicity in cardiovascular disease; and cardiovascular physiology Up-to-date information on the diagnosis and management of heart failure Latest guidelines for the management of atrial fibrillation New advances in curative catheter ablation of arrhythmias Increased number of international contributors Expanded chapters on epidemiology, diagnosis, and treatment of hypertension
This supplement includes all of the exercises from CRITICAL THINKING 2e in an easy to hand in format. In addition, it includes many additional exercises not found in the book and has a section on critical reasoning applied to the law. An Instructor's Manual/Answer Key (0534580645), available to instructors, provides additional teaching support materials.
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