Download or read book Discovery of Deduction written by and published by . This book was released on 2009-01-15 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Discovery of Deduction written by Joelle Hodge and published by . This book was released on 2010-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to formal, deductive logic using Socratic dialogue and discussion.
Download or read book The Logic of Scientific Discovery written by Karl Popper and published by Routledge. This book was released on 2005-11-04 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.
Download or read book Deduction Systems written by Rolf Socher-Ambrosius and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of mechanizing deductive reasoning can be traced all the way back to Leibniz, who proposed the development of a rational calculus for this purpose. But it was not until the appearance of Frege's 1879 Begriffsschrift-"not only the direct ancestor of contemporary systems of mathematical logic, but also the ancestor of all formal languages, including computer programming languages" ([Dav83])-that the fundamental concepts of modern mathematical logic were developed. Whitehead and Russell showed in their Principia Mathematica that the entirety of classical mathematics can be developed within the framework of a formal calculus, and in 1930, Skolem, Herbrand, and Godel demonstrated that the first-order predicate calculus (which is such a calculus) is complete, i. e. , that every valid formula in the language of the predicate calculus is derivable from its axioms. Skolem, Herbrand, and GOdel further proved that in order to mechanize reasoning within the predicate calculus, it suffices to Herbrand consider only interpretations of formulae over their associated universes. We will see that the upshot of this discovery is that the validity of a formula in the predicate calculus can be deduced from the structure of its constituents, so that a machine might perform the logical inferences required to determine its validity. With the advent of computers in the 1950s there developed an interest in automatic theorem proving.
Download or read book The Art of Argument written by Aaron Larsen and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Junior high aged students will argue (and sometimes quarrel), but they won't argue well without good training. Young teens are also targeted by advertisers with a vengeance. From billboards to commercials to a walk down the mall, fallacious arguments are everywhere you look. The Art of Argument was designed to teach the argumentative adolescent how to reason with clarity, relevance and purpose at a time when he has a penchant for the why and how. It is designed to equip and sharpen young minds as they live, play, and grow in this highly commercial culture. This course teaches students to recognize and identify twenty-eight informal fallacies, and the eye-catching text includes over sixty slick and clever, ?phony advertisements? for items from blue jeans to pick-up trucks, which apply the fallacies to a myriad of real life situations.
Download or read book Discovery of Our Galaxy written by Charles A. Whitney and published by Knopf. This book was released on 2012-06-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about the mystery and the passion, the imagination, religion, and poetry, the philosophy, the intellectual flights—and, above all, the people—that have created the science of astronomy, from Thales of Miletus predicting eclipses in the sixth century B.C. to today’s scientists probing the cosmic significance of the mysterious “black holes” discovered in 1970. With authority and charm, the distinguished Harvard astronomer Charles A. Whitney here re-creates the lives and temperaments of the great astronomers and retraces the ingenious arguments, the feats of observation and deduction, and the leaps of intuition by which they have gradually unveiled a picture of the universe and have brought us to an understanding of our own planet’s place in it. Among them: KEPLER, searching the solar system for visible evidence of the transcendent order he believed in GALILEO, constructing the first telescope and proposing the concept of universal gravitation NEWTON, paragon of logic, paradoxically driven by an unshakable belief in himself as God’s appointed prophet to create a world of mathematical certainty and thus expose the wonder of his Father in Heaven WILLIAM HERSCHEL, the nineteenth-century German who may well be considered the father of modern astronomy, first man to chart the nebulae EDWIN HUBBLE, in the present century, discovering and exploring galaxies beyond our own Finally, Professor Whitney makes clear for the layman the fascinating problems astronomers wrestle with today: the mysterious nature of quasars, strange cosmic bodies discovered in 1963; the unknown forces behind cataclysmic explosions recently glimpsed in other galaxies; the elusive nature of “interstellar dust”; the eternal question of how it all began.
Download or read book The Argument Builder written by Shelly Johnson and published by . This book was released on 2008-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The argument builder will train you to build compelling and persuasive arguments, through a blend of logic and rhetoric. You will first study the logical structure of good, clear arguments. Then, you will study how to use the various elements of argumentation, such as examples, analogy, comparison, testimony, and statistics, combining them to construct your own sound and effective arguments. You will also learn about the fallacies often committed when using these elements and how to avoid them in your own arguments.
Download or read book The Shaping of Deduction in Greek Mathematics written by Reviel Netz and published by Cambridge University Press. This book was released on 2003-09-18 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice.
Download or read book Patterns of Discovery written by Norwood Russell Hanson and published by CUP Archive. This book was released on 1979 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book If A Then B written by Michael Shenefelt and published by Columbia University Press. This book was released on 2013-06-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: While logical principles seem timeless, placeless, and eternal, their discovery is a story of personal accidents, political tragedies, and broad social change. If A, Then B begins with logic's emergence twenty-three centuries ago and tracks its expansion as a discipline ever since. It explores where our sense of logic comes from and what it really is a sense of. It also explains what drove human beings to start studying logic in the first place. Logic is more than the work of logicians alone. Its discoveries have survived only because logicians have also been able to find a willing audience, and audiences are a consequence of social forces affecting large numbers of people, quite apart from individual will. This study therefore treats politics, economics, technology, and geography as fundamental factors in generating an audience for logic--grounding the discipline's abstract principles in a compelling material narrative. The authors explain the turbulent times of the enigmatic Aristotle, the ancient Stoic Chrysippus, the medieval theologian Peter Abelard, and the modern thinkers René Descartes, David Hume, Jeremy Bentham, George Boole, Augustus De Morgan, John Stuart Mill, Gottlob Frege, Bertrand Russell, and Alan Turing. Examining a variety of mysteries, such as why so many branches of logic (syllogistic, Stoic, inductive, and symbolic) have arisen only in particular places and periods, If A, Then B is the first book to situate the history of logic within the movements of a larger social world. If A, Then B is the 2013 Gold Medal winner of Foreword Reviews' IndieFab Book of the Year Award for Philosophy.
Download or read book An Introduction to Formal Logic written by Peter Smith and published by Cambridge University Press. This book was released on 2003-11-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
Download or read book Rethinking Logic Logic in Relation to Mathematics Evolution and Method written by Carlo Cellucci and published by Springer Science & Business Media. This book was released on 2013-10-09 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. trigger
Download or read book The Art of Scientific Discovery written by George Gore and published by . This book was released on 1878 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Dialogical Roots of Deduction written by Catarina Dutilh Novaes and published by Cambridge University Press. This book was released on 2020-12-17 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive account of the concept and practices of deduction covering philosophy, history, cognition and mathematical practice.
Download or read book Medical Reasoning written by Erwin B. Montgomery and published by Oxford University Press, USA. This book was released on 2018-11-14 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern medicine is one of humankind's greatest achievements.Yet today, frequent medical errors and irreproducibility in biomedical research suggest that tremendous challenges beset it. Understanding these challenges and trying to remedy them have driven considerable and thoughtful critical analyses, but the apparent intransigence of these problems suggests a different perspective is needed. Now more than ever, when we see options and opportunities for healthcare expanding while resources are diminishing, it is extremely important that healthcare professionals practice medicine wisely. In Medical Reasoning, neurologist Erwin B. Montgomery, Jr. offers a new and vital perspective. He begins with the idea that the need for certainty in medical decision-making has been the primary driving force in medical reasoning. Doctors must routinely confront countless manifestations of symptoms, diseases, or behaviors in their patients. Therefore, either there are as many different "diseases" as there are patients or some economical set of principles and facts can be combined to explain each patient's disease. The response to this epistemic conundrum has driven medicine throughout history: the challenge is to discover principles and facts and then to develop means to apply them to each unique patient in a manner that provides certainty. This book studies the nature of medical decision making systematically and rigorously in both an analytic and historical context, addressing medicine's unique need for certainty in the face of the enormous variety of diseases and in the manifestations of the same disease in different patients. The book also examines how the social, legal, and economic circumstances in which medical decision-making occurs greatly influence the nature of medical reasoning. Medical Reasoning is essential for those at the intersection of healthcare and philosophy.
Download or read book The Great Formal Machinery Works written by Jan von Plato and published by Princeton University Press. This book was released on 2017-08-02 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.
Download or read book Discovery of Grounded Theory written by Barney Glaser and published by Routledge. This book was released on 2017-07-05 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most writing on sociological method has been concerned with how accurate facts can be obtained and how theory can thereby be more rigorously tested. In The Discovery of Grounded Theory, Barney Glaser and Anselm Strauss address the equally Important enterprise of how the discovery of theory from data?systematically obtained and analyzed in social research?can be furthered. The discovery of theory from data?grounded theory?is a major task confronting sociology, for such a theory fits empirical situations, and is understandable to sociologists and laymen alike. Most important, it provides relevant predictions, explanations, interpretations, and applications. In Part I of the book, "Generation Theory by Comparative Analysis," the authors present a strategy whereby sociologists can facilitate the discovery of grounded theory, both substantive and formal. This strategy involves the systematic choice and study of several comparison groups. In Part II, The Flexible Use of Data," the generation of theory from qualitative, especially documentary, and quantitative data Is considered. In Part III, "Implications of Grounded Theory," Glaser and Strauss examine the credibility of grounded theory. The Discovery of Grounded Theory is directed toward improving social scientists' capacity for generating theory that will be relevant to their research. While aimed primarily at sociologists, it will be useful to anyone Interested In studying social phenomena?political, educational, economic, industrial? especially If their studies are based on qualitative data.
