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How Logic Works: A User's Guide
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.
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.
256 pages, Paperback
Published August 6, 2024
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About the author
Hans Halvorson
7 books15 followersThe Stuart Professor of Philosophy at Princeton University, Dr. Halvorson's research interests include category theory, logic, philosophy of science, philosophy of physics, and the interplay of science and religion.
In 2001, he received a PhD in Philosophy from the University of Pittsburgh, where he also earned an MA in Mathematics (1998) and an MA in Philosophy (1997). He graduated from Calvin College in 1995 with a BA in Philosophy.
Academic appointments:
2016- Stuart Professor of Philosophy, Princeton
2010-16 full professor: Princeton philosophy
2012 associated faculty: Princeton mathematics
2005-10 associate professor: Princeton philosophy
2001-05 assistant professor: Princeton philosophy
In 2001, he received a PhD in Philosophy from the University of Pittsburgh, where he also earned an MA in Mathematics (1998) and an MA in Philosophy (1997). He graduated from Calvin College in 1995 with a BA in Philosophy.
Academic appointments:
2016- Stuart Professor of Philosophy, Princeton
2010-16 full professor: Princeton philosophy
2012 associated faculty: Princeton mathematics
2005-10 associate professor: Princeton philosophy
2001-05 assistant professor: Princeton philosophy
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Displaying 1 - 2 of 2 reviews
May 31, 2025
PROS: Couple of the advantages of this book in the sea of introductory textbooks about propositional logic is its compactness and use of Lemmon-style natural deduction. It's a bit harder than Fitch or tree method but it really compels you to think about how inferences are made, which makes it very easy to understand other styles of proofs. I should also mention that some concepts are thoroughly investigated and expressed in a very comprehensive way.
CONS: I felt like sometimes there's a lack of examples before exercises. I understand one learns logic through exercise and thinking for themselves but considering this is an entry-level book, I think more worked examples for some chapters would've been very helpful, especially when dealing with Quantification and relationship of existential and universal claims.This book also lacks overall philosophical context for some concepts, especially in the chapters following QL. I suppose this book isn't really designed for self-study but still...
Overall, going through this book alongside the famous one by Peter Smith allowed me to greatly better my understanding of Propositional logic. I would highly recommend "How Logic Works" to anyone interested in the subject matter, however I'd strongly advise supplementing it with other material(s).
CONS: I felt like sometimes there's a lack of examples before exercises. I understand one learns logic through exercise and thinking for themselves but considering this is an entry-level book, I think more worked examples for some chapters would've been very helpful, especially when dealing with Quantification and relationship of existential and universal claims.This book also lacks overall philosophical context for some concepts, especially in the chapters following QL. I suppose this book isn't really designed for self-study but still...
Overall, going through this book alongside the famous one by Peter Smith allowed me to greatly better my understanding of Propositional logic. I would highly recommend "How Logic Works" to anyone interested in the subject matter, however I'd strongly advise supplementing it with other material(s).
October 15, 2025
Very good, explanation wise; especially in the early chapters.
Maybe too little on metalogic, and should have something more substantial on modality.
Maybe too little on metalogic, and should have something more substantial on modality.
Displaying 1 - 2 of 2 reviews