Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterly fundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that arithmetic follows, purely logically, from a near definition. As Crispin Wright was the first to make clear, that means that Frege's logicism, long thought dead, might yet be viable. Heck probes the philosophical significance of the Theorem, using it to launch and then guide a wide-ranging exploration of historical, philosophical, and technical issues in the philosophy of mathematics and logic, and of their connections with metaphysics, epistemology, the philosophy of language and mind, and even developmental psychology. The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues. There are also new postscripts to five of the essays, which discuss changes of mind, respond to published criticisms, and advance the discussion yet further.
Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy. Part I of Reading Frege's Grundgesetze develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses his notorious 'Basic Law V' and attempts to secure its status as a law of logic. Part II examines the mathematical basis of Frege's logicism, explaining and exploring Frege's formal arguments. Heck argues that Frege himself knew that his proofs could be reconstructed so as to avoid Russell's Paradox, and presents Frege's arguments in a way that makes them available to a wide audience. He shows, by example, that careful attention to the structure of Frege's arguments, to what he proved, to how he proved it, and even to what he tried to prove but could not, has much to teach us about Frege's philosophy.
Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy. Part I of Reading Frege's Grundgesetze develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses his notorious 'Basic Law V' and attempts to secure its status as a law of logic. Part II examines the mathematical basis of Frege's logicism, explaining and exploring Frege's formal arguments. Heck argues that Frege himself knew that his proofs could be reconstructed so as to avoid Russell's Paradox, and presents Frege's arguments in a way that makes them available to a wide audience. He shows, by example, that careful attention to the structure of Frege's arguments, to what he proved, to how he proved it, and even to what he tried to prove but could not, has much to teach us about Frege's philosophy.
Modes of Presentation analyses a collection of problems, known as 'Frege's puzzle', resulting from how thinkers and speakers have a limited perspective on reference in thought and language. Heck argues that these puzzles have much to teach us both about the foundations of cognition and the nature of linguistic communication.
Written by clinicians, for clinicians, Cardiovascular Medicine and Surgery offers a comprehensive, authoritative, and multidisciplinary approach to this rapidly evolving field. Covering every area relevant to the daily practice of cardiovascular medicine, this new and innovative reference text, led by Drs. Debabrata Mukherjee and Richard A. Lange, brings together a stellar team of cardiovascular specialists from leading medical centers worldwide who focus on cutting-edge strategies for the clinical and surgical management of patients. Both medicine and surgery are highlighted in chapters along with follow-up care and changing technology to equip the clinician for optimal patient care. Highly structured and templated chapters cover pathogenesis, diagnosis, management, special considerations/limitations, follow-up care, and on-going and future research.
Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterly fundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that arithmetic follows, purely logically, from a near definition. As Crispin Wright was the first to make clear, that means that Frege's logicism, long thought dead, might yet be viable. Heck probes the philosophical significance of the Theorem, using it to launch and then guide a wide-ranging exploration of historical, philosophical, and technical issues in the philosophy of mathematics and logic, and of their connections with metaphysics, epistemology, the philosophy of language and mind, and even developmental psychology. The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues. There are also new postscripts to five of the essays, which discuss changes of mind, respond to published criticisms, and advance the discussion yet further.
Concentrating on the most important reactions used for organic synthesis, this upper-level textbook presents the material by reaction type. The final chapter discusses the planning and execution of multi-step synthesis.
Authored by the originator of the standard nomenclature for this spectrum of disorders, Congenital Heart Disease: A Clinical, Pathological, Embryological, and Segmental Analysis discusses the history, anatomic features, and physiologic consequences of CHD—in one authoritative resource. The Van Praagh approach to the segmental classification of CHD, developed and implemented by Dr. Richard Van Praagh in the 1960s at Boston Children’s Hospital, remains widely used today, facilitating communication among radiologists, cardiologists, surgeons, and pediatricians who are involved in the diagnosis, characterization, and management of this disease. This unique atlas offers complete coverage of the ubiquitous Van Praagh “language of CHD, including the signs, symptoms, and clinical manifestations of malpositioned, malformed, or absent cardiovascular chambers, vessels, and valves using traditional as well as state-of-the-art technology. Based upon the systematic, widely accepted Van Praagh system of three-part notation used to succinctly describe the visceroatrial situs, the orientation of the ventricular loop, and the position and relation of the great vessels. Demonstrates how the Van Praagh approach facilitates interpreting and reporting findings through cardiac imaging with CT, MR, and ultrasonography, including fetal cardiac imaging. Presents the pathologic anatomy that pediatric and adult cardiologists, radiologists, and echocardiographers need to understand in order to make accurate diagnoses in complex congenital heart disease; as well as the pathologic anatomy that interventionists, pediatric cardiac surgeons, and adult congenital heart surgeons need to know in order to manage their patients successfully. Features more than 550 high-quality images to help you visualize and recognize malformations. Shares the knowledge and expertise of a world-renowned authority on congenital heart disease—a master teacher and the originator of the Van Praagh segmental classification system. Explores the synergy between the various disciplines who manage patient care, including surgeons, radiologists, cardiologists, pathologists, and pediatricians. Enhanced eBook version included with purchase. Your enhanced eBook allows you to access all of the text, figures, and references from the book on a variety of devices.
Since 1975, Dr. Kenneth Swaiman’s classic text has been the reference of choice for authoritative guidance in pediatric neurology, and the 6th Edition continues this tradition of excellence with thorough revisions that bring you fully up to date with all that’s new in the field. Five new sections, 62 new chapters, 4 new editors, and a reconfigured format make this a comprehensive and clearly-written resource for the experienced clinician as well as the physician-in-training. Nearly 3,000 line drawings, photographs, tables, and boxes highlight the text, clarify key concepts, and make it easy to find information quickly. New content includes 12 new epilepsy chapters, 5 new cerebrovascular chapters, and 13 new neurooncology chapters, as well as new chapters on neuroimmunology and neuromuscular disorders, as well as chapters focused on clinical care (e.g., Counseling Families, Practice Guidelines, Transitional Care, Personalized Medicine, Special Educational Law, Outcome Measurements, Neurorehabilitation, Impact of Computer Resources, and Training Issues). Additional new chapters cover topics related to the developmental connectome, stem cell transplantation, and cellular and animal models of neurological disease. Greatly expanded sections to increase your knowledge of perinatal acquired and congenital disorders, neurodevelopmental disabilities, pediatric epilepsy, and nonepileptiform paroxysmal disorders and disorders of sleep. Coverage of new, emerging, or controversial topics includes developmental encephalopathies, non-verbal learning disorders, and the pharmacological and future genetic treatment of neurodevelopmental disabilities.
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