How Logic Works

A User's Guide

Hans Halvorson

• Publisher: Princeton University Press
• Year: 2020
• Print ISBN: 9780691211954, 9780691182223
• eBook ISBN: 9780691208718
• Topic: Philosophy
• Subtopic: Logic in Philosophy

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

Table of contents

• Cover
• Contents
• Preface
• 1. Logic for Humans
• 2. Deducing
• 3. Supposing
• 4. New Proofs from Old
• 5. Truth
• 6. Quantifying
• 7. Theories
• 8. Models
• 9. A Theory about Propositional Logic
• 10. A Theory about Predicate Logic
• 11. Beyond Logic
• Resumé of Inference Rules
• Useful Valid Argument Forms
• Truth Tables
• Validity Tests for Predicate Logic
• Glossary
• Acronyms
• Index