Showing posts with label mathematical logic. Show all posts
Showing posts with label mathematical logic. Show all posts

Introduction to Logic Review

Introduction to Logic
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For the beginner, there's no better book to begin one's excursion into logic, both deductive and inductive, formal and informal, syllogistic and mathematical, propositional as well as predicate calculus. There is excellent competition, such as Bates' Introduction to Logic and Lemmon's book by the same name. But these books are limited in their scope, and not always as didactic and insightful as the Copi work. This book is certainly not exhaustive of all logical norms and forms, but it is quite comprehensive. I know of no other book which is so thoroughly diversified in the treatment of all logical styles and methods, and which does so with greater clarity and elegance of style. I wish this had been my textbook upon taking formal logic courses years ago; it is clearly superior to literally dozens of others that are either too simplistic or over the head of most beginning logicians.

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Easy-to-read, visually appealing, and chock full of real-world applications, this most complete and authoritative book on introductory logic fully prepares users to understand, recognize, and apply classical syllogistic logic and the more powerful techniques of modern symbolic logic-explaining all concepts and techniques clearly, accurately, and thoroughly, and bringing them to life using a wealth of real-life examples of lively arguments and explanations drawn from a wide variety of sources to help demonstrate the application of logical principles by serious writers and thinkers trying to solve real problems in a wide range of fields.Includes full chapters on basic logical concepts, the uses of language, definitions, fallacies, categorical propositions, categorical syllogisms, arguments in ordinary language, symbolic logic, methods of deduction, quantification theory, analogy and probable inference, Mill's Methods of experimental inquiry, science and hypothesis, and probability. Reformulates key logical issues, and presents a more detailed account of the concept of logical equivalence, distinguishing it more clearly from the truth-functional connectives. Includes sidebars containing additional, enriching information; many new illustrations taken from contemporary research I the physical and biological science; and a plethora of exercises.For anyone searching for a top-notch, easy-to-understand introduction to logic.--This text refers to an out of print or unavailable edition of this title.

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Thinking about Mathematics: The Philosophy of Mathematics Review

Thinking about Mathematics: The Philosophy of Mathematics
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Anybody who's interested in why mathematics might have the least bit to do with philosophy will be interested in this book. To many the philosophy of mathematics may seem too specialized and peripheral to be of much interest. But such is not the case. The philosophy of math is intricately intertwined with many of the classic epistemological questions that I have never seen satisfactory answers to. This book will force you to think about things you have never considered before. Why does mathematics 'just happen' to describe empirical studies so well if mathematics is solely logical and in the head? Or is mathematics empirical and merely charading as necessary logical truth? These questions will be brought up in the book and the different answers given from the different philisophical sides.
Some of the book is a little dense and may be skimmed. He does go into detail a bit much in some places and the non technical reader will be lost. But Shapiro usually does do a good job of summarizing complex thoughts.
This book whetted my appetite for more and I plan on continuing thinking about these things and hopefully take some classes in mathematical logic and philosophy.

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This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy.

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