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How Logic Works

How Logic Works
Author: Hans Halvorson
Publisher: Princeton University Press
Total Pages: 256
Release: 2024-08-06
Genre: Philosophy
ISBN: 0691211957

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A concise introduction to logic that teaches you not only how reasoning works, but why it works How Logic Works is an introductory logic textbook that is different by design. Rather than teaching elementary symbolic logic as an abstract or rote mathematical exercise divorced from ordinary thinking, Hans Halvorson presents it as the skill of clear and rigorous reasoning, which is essential in all fields and walks of life, from the sciences to the humanities—anywhere that making good arguments, and spotting bad ones, is critical to success. Instead of teaching how to apply algorithms using “truth trees,” as in the vast majority of logic textbooks, How Logic Works builds on and reinforces the innate human skills of making and evaluating arguments. It does this by introducing the methods of natural deduction, an approach that teaches students not only how to carry out a proof and solve a problem but also what the principles of valid reasoning are and how they can be applied to any subject. The book also allows students to transition smoothly to more advanced topics in logic by teaching them general techniques that apply to more complicated scenarios, such as how to formulate theories about specific subject matter. How Logic Works shows that formal logic—far from being only for mathematicians or a diversion from the really deep questions of philosophy and human life—is the best account we have of what it means to be rational. By teaching logic in a way that makes students aware of how they already use it, the book will help them to become even better thinkers. Offers a concise, readable, and user-friendly introduction to elementary symbolic logic that primarily uses natural deduction rather than algorithmic “truth trees” Draws on more than two decades’ experience teaching introductory logic to undergraduates Provides a stepping stone to more advanced topics


How Logic Works

How Logic Works
Author: Hans Halvorson
Publisher: Princeton University Press
Total Pages: 256
Release: 2020-09-01
Genre: Philosophy
ISBN: 0691208719

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A concise introduction to logic that teaches you not only how reasoning works, but why it works How Logic Works is an introductory logic textbook that is different by design. Rather than teaching elementary symbolic logic as an abstract or rote mathematical exercise divorced from ordinary thinking, Hans Halvorson presents it as the skill of clear and rigorous reasoning, which is essential in all fields and walks of life, from the sciences to the humanities—anywhere that making good arguments, and spotting bad ones, is critical to success. Instead of teaching how to apply algorithms using “truth trees,” as in the vast majority of logic textbooks, How Logic Works builds on and reinforces the innate human skills of making and evaluating arguments. It does this by introducing the methods of natural deduction, an approach that teaches students not only how to carry out a proof and solve a problem but also what the principles of valid reasoning are and how they can be applied to any subject. The book also allows students to transition smoothly to more advanced topics in logic by teaching them general techniques that apply to more complicated scenarios, such as how to formulate theories about specific subject matter. How Logic Works shows that formal logic—far from being only for mathematicians or a diversion from the really deep questions of philosophy and human life—is the best account we have of what it means to be rational. By teaching logic in a way that makes students aware of how they already use it, the book will help them to become even better thinkers. Offers a concise, readable, and user-friendly introduction to elementary symbolic logic that primarily uses natural deduction rather than algorithmic “truth trees” Draws on more than two decades’ experience teaching introductory logic to undergraduates Provides a stepping stone to more advanced topics


How Logic Works

How Logic Works
Author: Hans Halvorson
Publisher: Princeton University Press
Total Pages: 256
Release: 2020-09
Genre: Philosophy
ISBN: 0691182221

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"Logic instruction typically takes two forms. The first has the aim of teaching students to solve a certain sort of problem as efficiently as possible. This is the approach adopted by most logic textbooks and truth trees, the most popular method, gives students an algorithm for solving logic problems. The second has as its aim teaching students a certain style of thinking and, thus, concerns itself with how students solve problems. In How Logic Works, Hans Halvorson introduces students to the methods of natural deduction, a method which not only helps them solve problems, but helps them to understand the principles of valid reasoning for themselves. Halvorson uses formal logic to train students in the task of constructing paths between premises and conclusions. The student, then, will become an expert traveller in logical space, quickly recognizing the difference between a safe path (where truth is guaranteed to be preserved) and a hazardous path (where truth might be lost). This approach is premised on the fact that if a student learns natural deduction, she learns a skill that transfers to any domain where valid deductive reasoning is useful"--


Logic Works

Logic Works
Author: Lorne Falkenstein
Publisher: Routledge
Total Pages: 666
Release: 2021-11-30
Genre: Philosophy
ISBN: 1000451275

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Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. The book covers classical first-order logic and alternatives, including intuitionistic, free, and many-valued logic. It also considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, independent study as a course text, it covers more material than is typically covered in an introductory course. It also covers this material at greater length and in more depth with the purpose of making it accessible to those with no prior training in logic or formal systems. Online support material includes a detailed student solutions manual with a running commentary on all starred exercises, and a set of editable slide presentations for course lectures. Key Features Introduces an unusually broad range of topics, allowing instructors to craft courses to meet a range of various objectives Adopts a critical attitude to certain classical doctrines, exposing students to alternative ways to answer philosophical questions about logic Carefully considers the ways natural language both resists and lends itself to formalization Makes objectual semantics for quantified logic easy, with an incremental, rule-governed approach assisted by numerous simple exercises Makes important metatheoretical results accessible to introductory students through a discursive presentation of those results and by using simple case studies


The Art of Logic in an Illogical World

The Art of Logic in an Illogical World
Author: Eugenia Cheng
Publisher: Basic Books
Total Pages: 321
Release: 2018-09-11
Genre: Mathematics
ISBN: 154167250X

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How both logical and emotional reasoning can help us live better in our post-truth world In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic -- for example, emotion -- is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.


An Introduction to Mathematical Logic

An Introduction to Mathematical Logic
Author: Richard E. Hodel
Publisher: Courier Corporation
Total Pages: 514
Release: 2013-01-01
Genre: Mathematics
ISBN: 0486497852

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This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.


The Works in Logic by Bosniac Authors in Arabic

The Works in Logic by Bosniac Authors in Arabic
Author: Amir Ljubovic
Publisher: BRILL
Total Pages: 264
Release: 2008-11-30
Genre: Philosophy
ISBN: 9047441974

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This book provides a historical and comparative study of logic in Arabic in Bosnia and Herzegovina, from the first texts, 16th century, to the end of the 19th century, using authentic, completely unknown and unpublished manuscripts


The Craft of Thinking

The Craft of Thinking
Author: Anibal Bueno
Publisher:
Total Pages: 220
Release: 2021-07-13
Genre:
ISBN: 9781792408168

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Studies in Logic and Probability

Studies in Logic and Probability
Author: George Boole
Publisher: Courier Corporation
Total Pages: 514
Release: 2012-01-01
Genre: Mathematics
ISBN: 0486488268

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Authoritative account of the development of Boole's ideas in logic and probability theory ranges from The Mathematical Analysis of Logic to the end of his career. The Laws of Thought formed the most systematic statement of Boole's theories; this volume contains incomplete studies intended for a follow-up volume. 1952 edition.


Logic as a Liberal Art

Logic as a Liberal Art
Author: R. E. Houser
Publisher: Catholic University of America Press
Total Pages: 481
Release: 2019-12-10
Genre: Philosophy
ISBN: 0813232341

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In the twenty-first century there are two ways to study logic. The more recent approach is symbolic logic. The history of teaching logic since World War II, however, casts doubt on the idea that symbolic logic is best for a first logic course. Logic as a Liberal Art is designed as part of a minority approach, teaching logic in the "verbal" way, in the student's "natural" language, the approach invented by Aristotle. On utilitarian grounds alone, this "verbal" approach is superior for a first course in logic, for the whole range of students. For millennia, this "verbal" approach to logic was taught in conjunction with grammar and rhetoric, christened the trivium. The decline in teaching grammar and rhetoric in American secondary schools has led Dr. Rollen Edward Houser to develop this book. The first part treats grammar, rhetoric, and the essential nature of logic. Those teachers who look down upon rhetoric are free, of course, to skip those lessons. The treatment of logic itself follows Aristotle's division of the three acts of the mind (Prior Analytics 1.1). Formal logic is then taken up in Aristotle's order, with Parts on the logic of Terms, Propositions, and Arguments. The emphasis in Logic as a Liberal Art is on learning logic through doing problems. Consequently, there are more problems in each lesson than would be found, for example, in many textbooks. In addition, a special effort has been made to have easy, medium, and difficult problems in each Problem Set. In this way the problem sets are designed to offer a challenge to all students, from those most in need of a logic course to the very best students.