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Author: Michael Shenefelt Publisher: Columbia University Press ISBN: 0231161050 Category : Philosophy Languages : en Pages : 352
Book Description
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.
Author: Michael Shenefelt Publisher: Columbia University Press ISBN: 0231161050 Category : Philosophy Languages : en Pages : 352
Book Description
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.
Author: Orna Harari Publisher: Springer Science & Business Media ISBN: 9781402027871 Category : Philosophy Languages : en Pages : 180
Book Description
This book examines a fundamental problem in Aristotle’s Posterior Analytics: what is the role of syllogistic logic in the theory of demonstrative knowledge? The answer to this question is sought in Aristotle’s metaphysical theory and his conception of substance. This interpretation challenges the traditional interpretation that approaches Aristotle’s theory of demonstration from the standpoint of scientific practice. It is argued, in this book, that the Posterior Analytics’ main objective is to articulate the notion of knowledge, viewed here as a conceptualisation, rather than analysing the structure and methods of scientific explorations. The original interpretation offered in this book sheds fresh light on issues, such as the conceptual difference between Aristotle’s logic and modern logic, the relationship between Aristotle’s logic and Greek mathematics, and the differences between the Aristotelian and modern notions of knowledge and proof. In attempting to present a comprehensive interpretation of one of the most difficult works in the Aristotelian corpus, this book is of major importance first and foremost for Aristotelian scholars and historians of Greek philosophy; the historical character of the analysis offered here makes it relevant also to historians of Greek mathematics, historians of logic, historians of science in general, and philosophers of sciences.
Author: Harris Kwong Publisher: Open SUNY Textbooks ISBN: 9781942341161 Category : Mathematics Languages : en Pages : 298
Book Description
A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills.
Author: Uwe Meixner Publisher: Walter de Gruyter ISBN: 3110326892 Category : Philosophy Languages : en Pages : 379
Book Description
This book presents a comprehensive, non-model-theoretic theory of ontic necessity and possibility within a formal (and formalized) ontology consisting of states of affairs, properties, and individuals. Its central thesis is that all modalities are reducible to intrinsic (or "logical") possibility and necessity if reference is made to certain states of affairs, called "bases of necessity." The viability of this Bases-Theory of Modality is shown also in the case of conditionals, including counterfactual conditionals. Besides the ontological aspects of the philosophy of modality, also the epistemology of modality is treated in the book. It is shown that the Bases-Theory of Modality provides a satisfactory solution to the epistemological problem of modality. In addition to developing that theory, the book includes detailed discussions of positions in the philosophy of modality maintained by Alvin Plantinga, David Lewis, Charles Chihara, Graeme Forbes, David Armstrong, and others. Among the themes treated are: possibilism vs. actualism; the theory of essences; conceivability and possibility; the nature of possible worlds; the nature of logical, nomological, and metaphysical possibility and necessity.
Author: Antonella Cupillari Publisher: Academic Press ISBN: 0123822173 Category : Mathematics Languages : en Pages : 297
Book Description
Annotation The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.Jumps right in with the needed vocabulary-gets students thinking like mathematicians from the beginningOffers a large variety of examples and problems with solutions for students to work through on their ownIncludes a collection of exercises without solutions to help instructors prepare assignmentsContains an extensive list of basic mathematical definitions and concepts needed in abstract mathematics.
Author: Martin Aigner Publisher: Springer Science & Business Media ISBN: 3662223430 Category : Mathematics Languages : en Pages : 194
Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author: P.D. Magnus Publisher: Good Press ISBN: Category : Philosophy Languages : en Pages : 162
Book Description
Forallx is an introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading. This book treats symbolization, formal semantics, and proof theory for each language. The discussion of formal semantics is more direct than in many introductory texts. Although forall x does not contain proofs of soundness and completeness, it lays the groundwork for understanding why these are things that need to be proven. Contents: What is logic? Sentential logic Truth tables Quanti ed logic Formal semantics Proofs Other symbolic notation Solutions to selected exercises
Author: GMAC (Graduate Management Admission Council) Publisher: John Wiley & Sons ISBN: 1394260024 Category : Study Aids Languages : en Pages : 887
Book Description
GMAT Official Guide 2024-2025: Includes Book + Online Question Bank + Digital Flashcards + Mobile App Power up your prep with the GMAT Official Guide, the only study guide that features real exam questions. You'll get exclusive tips and tricks directly from the exam creators and gain access to 900+ practice questions to set you up for success on test day. Highlights: Updated Data Insights, Quantitative Review and Verbal Review chapters to master each section of the GMAT Focus Edition Access to an Online Question Bank to create custom practice sets by questions type and difficulty level so that you can plan your individual practice Exclusive access to online diagnostic evaluations to discover your strengths and focus areas Detailed answer explanations to master the reasoning behind the answers New! Get exclusive exam preparation tips from test prep organizations Use this guide to: Master the exam structure and excel in each section Understand key concepts with review chapters Gain confidence in all question types (featuring 100+ new questions!) Review detailed explanations to understand correct and incorrect answers New! Practice with two-part analysis questions in the book PLUS! Focus your studying with the Online Question Bank – Bonus: included with purchase! Tailor your practice by building practice sets targeting question type and difficulty Discover your strengths and weaknesses with diagnostic quizzes Track your focus areas and progress with key metrics Reinforce concepts with flashcards and engaging games Challenge yourself with timed practice Use digital flashcards to master key concepts, also accessible on the mobile app The Online Question Bank is accessible through your mba.com account.
Author: Michael Shenefelt
Author: Michael Shenefelt
Author: Craig DeLancey
Author: Orna Harari
Author: S. Barry Cooper
Author: Harris Kwong
Author: Uwe Meixner
Author: Antonella Cupillari
Author: Martin Aigner
Author: P.D. Magnus
Author: GMAC (Graduate Management Admission Council)