How logic works : a user's guide

"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"-- Provided by publisher

A concise introduction to logic that teaches you notonly how reasoning works, but why it works How LogicWorks is an introductory logic textbook that is different bydesign. Rather than teaching elementary symbolic logic as anabstract or rote mathematical exercise divorced from ordinarythinking, Hans Halvorson presents it as the skill of clear andrigorous reasoning, which is essential in all fields and walks oflife, from the sciences to the humanities-anywhere that making goodarguments, and spotting bad ones, is critical to success. Insteadof teaching how to apply algorithms using "truth trees," as in thevast majority of logic textbooks, How Logic Works buildson and reinforces the innate human skills of making and evaluatingarguments. It does this by introducing the methods of naturaldeduction, an approach that teaches students not only how to carryout a proof and solve a problem but also what the principles ofvalid reasoning are and how they can be applied to any subject. Thebook also allows students to transition smoothly to more advancedtopics in logic by teaching them general techniques that apply tomore complicated scenarios, such as how to formulate theories aboutspecific subject matter. How Logic Works shows that formallogic-far from being only for mathematicians or a diversion fromthe really deep questions of philosophy and human life-is the bestaccount we have of what it means to be rational. By teaching logicin a way that makes students aware of how they already use it, thebook will help them to become even better thinkers.

• Offers a concise, readable, and user-friendly introduction toelementary symbolic logic that primarily uses natural deductionrather than algorithmic "truth trees"
• Draws on more than two decades' experience teachingintroductory logic to undergraduates
• Provides a stepping stone to more advanced topics

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 Cover 1 Contents 6 Preface 8 1. Logic for Humans 12 2. Deducing 19 3. Supposing 36 4. New Proofs from Old 62 5. Truth 75 6. Quantifying 95 7. Theories 127 8. Models 167 9. A Theory about Propositional Logic 187 10. A Theory about Predicate Logic 217 11. Beyond Logic 236 Resumé of Inference Rules 242 Useful Valid Argument Forms 244 Truth Tables 246 Validity Tests for Predicate Logic 248 Glossary 250 Acronyms 254 Index 256 Princeton,University,Press