book review on philosophy and logic

Best Books on Logic

Sharpen your reasoning skills with the elite selection of books on logic, repeatedly featured for their exceptional ability to teach critical thinking and rational analysis..

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Last updated: February 27, 2024

The best books on Critical Thinking , recommended by Nigel Warburton

Calling bullshit: the art of skepticism in a data-driven world by carl bergstrom & jevin west, thinking, fast and slow by daniel kahneman, factfulness: ten reasons we're wrong about the world — and why things are better than you think by hans rosling, black box thinking: the surprising truth about success by matthew syed, the art of thinking clearly by rolf dobelli, critical thinking: your guide to effective argument, successful analysis and independent study by tom chatfield.

Do you know your straw man arguments from your weasel words? Nigel Warburton , Five Books philosophy editor and author of Thinking from A to Z,  selects some of the best books on critical thinking—and explains how they will help us make better-informed decisions and construct more valid arguments.

Do you know your straw man arguments from your weasel words? Nigel Warburton, Five Books philosophy editor and author of Thinking from A to Z,  selects some of the best books on critical thinking—and explains how they will help us make better-informed decisions and construct more valid arguments.

The best books on Logic , recommended by Tom Stoneham

Logic primer by colin allen & michael hand, logic by wilfrid hodges, paradoxes by r. m. sainsbury, tractatus logico-philosophicus by ludwig wittgenstein, philosophy of logic by willard van orman quine.

Logic is an excellent form of mind-training because it involves a very particular way of thinking and focus on truth. But how does it work and what are its limitations? Tom Stoneham , a professor of philosophy at the University of York, picks some great books for anyone who wants to learn more about logic.

Logic is an excellent form of mind-training because it involves a very particular way of thinking and focus on truth. But how does it work and what are its limitations? Tom Stoneham, a professor of philosophy at the University of York, picks some great books for anyone who wants to learn more about logic.

We ask experts to recommend the five best books in their subject and explain their selection in an interview.

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University of Notre Dame

Notre Dame Philosophical Reviews

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Philosophical Logic

John P. Burgess, Philosophical Logic , Princeton UP, 2009, 153pp., $19.95 (hbk), ISBN 9780691137896.

Reviewed by Alasdair Urquhart, University of Toronto

Burgess’s concise introduction to philosophical logic appears in the series Princeton Foundations of Contemporary Philosophy . In the preface, the author explains that he has aimed at providing a foundation for philosophical logic “sufficient to equip the reader to follow basic applications in analytic philosophy, and to tackle if desired more advanced works,” the background assumed being only that supplied by “any good introductory textbook” (p. vii). In spite of this, Burgess manages to include in his little monograph a surprisingly large quantity of technical material, even though much of it is only sketched.

The book is partly based on materials presented in the author’s seminar “Heresies in Logic”; it is primarily aimed at analytic philosophers who need some technical background in the parts of logic most heavily used in philosophical discussions. Although the first chapter offers a quick sketch of classical logic, the remaining chapters discuss nonclassical logics, namely, temporal logic, modal logic, conditional logic, relevantistic logic and intuitionistic logic. Although applications to artificial intelligence and computer science are mentioned, they are subordinated to philosophical motivations.

Chapter 1 gives a very brief review of the syntax and semantics of classical sentential and predicate logic. The basic results on completeness and decidability are mentioned, but not proved.

Chapter 2, the first really substantial chapter, is devoted to temporal logic in the style of Arthur Prior, where a future tense operator Fq and past tense operator Pq are added to classical sentential logic. After defining models for this language, Burgess introduces the minimal temporal logic L 0 (Prior’s name for this logic was K t , by analogy with the well known minimal modal logic K ); the rules and axioms of the minimal logic L 0 are developed briefly. The minimal temporal logic results when we place no conditions on the structure of time. The succeeding sections discuss the logics of time resulting when conditions are imposed that are assumed in classical and relativistic physics; for example, the conditions of transitivity and density validate certain formulas of temporal logic. Next is a brief discussion of Hamblin’s theorem that there are only fourteen “tenses” or temporal modalities if time is assumed to have the structure of the classical real line. The last section of this chapter discusses quantified temporal logic, and introduces the concept of rigid designator in the context of the logic of identity.

The third chapter is on the topic of modal logic. Although modal logic is probably of more interest to philosophers than temporal logic, Burgess chooses to discuss it later because of the greater intuitive clarity of the temporal modalities. He begins with semantical analysis based on Kripke models; he prefers the neutral terminology of “states” to the metaphysically loaded “possible worlds”. He follows this with a motivational discussion of different kinds of modality, such as dynamic, epistemic and deontic; logical and metaphysical necessity are distinguished, in the style of Kripke’s Naming and Necessity . A technical section follows, introducing the logics K , S4 , S4.2 , S4.3 and S5 , both from the semantic and syntactic point of view. A remarkable feature of this chapter is that it includes both completeness and decidability proofs. Completeness is proved using the standard canonical model method, while a proof of the finite model property for K is sketched. On the question of the correct modal logic for representing logical necessity, Burgess argues that S5 fits the bill. The chapter closes with a very brief discussion of quantified modal logic, as well as Quine’s critique.

There follows a chapter on the logic of indicative and counterfactual conditionals. After a short section on Gricean conversational implicature, Burgess discusses the probabilistic theory of indicative conditionals, including the Adams probabilistic criterion for asserting them. The main result here is David Lewis’s trivialization theorem, according to which there is no conditional connective for which a conditional probability can be identified with the probability of a conditional (given certain plausible assumptions). The succeeding section discusses what Burgess calls the “remoteness theory of indicative conditionals”, better known as the “Lewis-Stalnaker theory of conditionals”. Next comes a completeness proof for inferences from conditionals to conditionals (no embedded conditionals allowed); the validity notion is based on the Adams criterion. The remainder of the chapter is given over to mostly philosophical discussion about conventional implicature, and the difficulties involved in interpreting the relation of “remoteness from reality” used in the semantics of conditionals in terms of similarity in relevant respects.

The fifth chapter is on the topic of “relevantistic logic”, a terminology peculiar to this monograph. Burgess uses this idiosyncratic phrase because he wishes to include here not only relevance logics in the style of Anderson and Belnap, but also systems such as Parry’s analytic implication. Also included here is dialethism, the view that there are true contradictory statements — the commonly used term “dialetheism” is subjected to scathing criticism on philological grounds. This chapter stands out from the others by its polemical tone. In the other chapters, Burgess is generally content to enumerate the various systems, justifying the existence of alternative systems of modal logic (for example) by allowing that there can be alternative senses of necessity and possibility. Here, though, he mounts a direct attack on the motivation given to justify these systems of alternative logic. He argues that three basic principles (disjunction introduction, transitivity of entailment and disjunctive syllogism) are all indispensable in mathematical practice, and so the “relevantistic logicians” fail in their goal of giving a descriptive criticism of orthodox mathematical practice (p. 110). He does allow, though, that such logics can be of interest in practical applications; for example, Belnap’s suggested use of the four-valued logic underlying first-degree entailment in databases. On the purely technical side, the chapter includes a short development of the pure implicational part of the relevance logic R (Church’s weak theory of implication), and brief mention of other technical results in the area.

The sixth and final chapter is on intuitionistic logic. Dummett, rather than Brouwer, is the main focus here — probably a wise choice, since contemporary analytic philosophers are more apt to find Dummett’s neo-Wittgensteinian motivation to their liking than Brouwer’s idealistic philosophy. After a short discussion on the notion of constructive proof, Burgess expounds the meaning of the logical operations in terms of their inferential role. A section on an axiomatic formulation of intuitionistic sentential logic follows, and then a description of the double-negation interpretation of classical theorems. Next is the Gödel interpretation of intuitionistic sentential logic in the modal system S4 , and the closely related topic of Kripke’s semantics for intuitionism. A completeness proof for the sentential part of intuitionism using the canonical model is sketched, followed by a discussion of intermediate logics and intuitionistic predicate logic. Kripke models are of course classical in nature; Burgess gives a short but sensitive discussion of the question of whether an intuitionistically acceptable completeness proof can be given — infinitely proceeding sequences in the Brouwerian sense are briefly introduced in this connection.

Burgess has managed to pack an amazing amount of good material into this short monograph, and it can be confidently recommended to any philosopher who wishes to go beyond an introductory logic course and venture into the wilds of philosophical logic. The technical details are of necessity sketchy, but the author provides the reader with helpful lists for further reading at the end of each chapter, as well as a good bibliography. This is an excellent little book, and deserves wide success.

Introduction to Logic and Critical Thinking

(10 reviews)

Matthew Van Cleave, Lansing Community College

Copyright Year: 2016

Publisher: Matthew J. Van Cleave

Language: English

Formats Available

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Reviewed by "yusef" Alexander Hayes, Professor, North Shore Community College on 6/9/21

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness. read more

Comprehensiveness rating: 5 see less

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness.

Content Accuracy rating: 5

The book is accurate.

Relevance/Longevity rating: 5

While many modern examples are used, and they are helpful, they are not necessarily needed. The usefulness of logical principles and skills have proved themselves, and this text presents them clearly with many examples.

Clarity rating: 5

It is obvious that the author cares about their subject, audience, and students. The text is comprehensible and interesting.

Consistency rating: 5

The format is easy to understand and is consistent in framing.

Modularity rating: 5

This text would be easy to adapt.

Organization/Structure/Flow rating: 5

The organization is excellent, my one suggestion would be a concluding chapter.

Interface rating: 5

I accessed the PDF version and it would be easy to work with.

Grammatical Errors rating: 5

The writing is excellent.

Cultural Relevance rating: 5

This is not an offensive text.

Reviewed by Susan Rottmann, Part-time Lecturer, University of Southern Maine on 3/2/21

I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it... read more

Comprehensiveness rating: 4 see less

I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it fits better for a general critical thinking course than for a true logic course. I'm not sure that I'd agree. I have been using Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," and I think that book is a better introduction to critical thinking for non-philosophy majors. However, the latter is not open source so I will figure out how to get by without it in the future. Overall, the book seems comprehensive if the subject is logic. The index is on the short-side, but fine. However, one issue for me is that there are no page numbers on the table of contents, which is pretty annoying if you want to locate particular sections.

Content Accuracy rating: 4

I didn't find any errors. In general the book uses great examples. However, they are very much based in the American context, not for an international student audience. Some effort to broaden the chosen examples would make the book more widely applicable.

Relevance/Longevity rating: 4

I think the book will remain relevant because of the nature of the material that it addresses, however there will be a need to modify the examples in future editions and as the social and political context changes.

Clarity rating: 3

The text is lucid, but I think it would be difficult for introductory-level students who are not philosophy majors. For example, in Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," the sub-headings are very accessible, such as "Experts cannot rescue us, despite what they say" or "wishful thinking: perhaps the biggest single speed bump on the road to critical thinking." By contrast, Van Cleave's "Introduction to Logic and Critical Thinking" has more subheadings like this: "Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form" or "Propositional logic and the four basic truth functional connectives." If students are prepared very well for the subject, it would work fine, but for students who are newly being introduced to critical thinking, it is rather technical.

It seems to be very consistent in terms of its terminology and framework.

Modularity rating: 4

The book is divided into 4 chapters, each having many sub-chapters. In that sense, it is readily divisible and modular. However, as noted above, there are no page numbers on the table of contents, which would make assigning certain parts rather frustrating. Also, I'm not sure why the book is only four chapter and has so many subheadings (for instance 17 in Chapter 2) and a length of 242 pages. Wouldn't it make more sense to break up the book into shorter chapters? I think this would make it easier to read and to assign in specific blocks to students.

Organization/Structure/Flow rating: 4

The organization of the book is fine overall, although I think adding page numbers to the table of contents and breaking it up into more separate chapters would help it to be more easily navigable.

Interface rating: 4

The book is very simply presented. In my opinion it is actually too simple. There are few boxes or diagrams that highlight and explain important points.

The text seems fine grammatically. I didn't notice any errors.

The book is written with an American audience in mind, but I did not notice culturally insensitive or offensive parts.

Overall, this book is not for my course, but I think it could work well in a philosophy course.

Reviewed by Daniel Lee, Assistant Professor of Economics and Leadership, Sweet Briar College on 11/11/19

This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument read more

Comprehensiveness rating: 3 see less

This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument

To the best of my ability, I regard this content as accurate, error-free, and unbiased

The book is broadly relevant and up-to-date, with a few stray temporal references (sydney olympics, particular presidencies). I don't view these time-dated examples as problematic as the logical underpinnings are still there and easily assessed

Clarity rating: 4

My only pushback on clarity is I didn't find the distinction between argument and explanation particularly helpful/useful/easy to follow. However, this experience may have been unique to my class.

To the best of my ability, I regard this content as internally consistent

I found this text quite modular, and was easily able to integrate other texts into my lessons and disregard certain chapters or sub-sections

The book had a logical and consistent structure, but to the extent that there are only 4 chapters, there isn't much scope for alternative approaches here

No problems with the book's interface

The text is grammatically sound

Cultural Relevance rating: 4

Perhaps the text could have been more universal in its approach. While I didn't find the book insensitive per-se, logic can be tricky here because the point is to evaluate meaningful (non-trivial) arguments, but any argument with that sense of gravity can also be traumatic to students (abortion, death penalty, etc)

No additional comments

Reviewed by Lisa N. Thomas-Smith, Graduate Part-time Instructor, CU Boulder on 7/1/19

The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text,... read more

The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text, and the index is very thorough.

The content is excellent. The text is thorough and accurate with no errors that I could discern. The terminology and exercises cover the material nicely and without bias.

The text should easily stand the test of time. The exercises are excellent and would be very helpful for students to internalize correct critical thinking practices. Because of the logical arrangement of the text and the many sub-sections, additional material should be very easy to add.

The text is extremely clearly and simply written. I anticipate that a diligent student could learn all of the material in the text with little additional instruction. The examples are relevant and easy to follow.

The text did not confuse terms or use inconsistent terminology, which is very important in a logic text. The discipline often uses multiple terms for the same concept, but this text avoids that trap nicely.

The text is fairly easily divisible. Since there are only four chapters, those chapters include large blocks of information. However, the chapters themselves are very well delineated and could be easily broken up so that parts could be left out or covered in a different order from the text.

The flow of the text is excellent. All of the information is handled solidly in an order that allows the student to build on the information previously covered.

The PDF Table of Contents does not include links or page numbers which would be very helpful for navigation. Other than that, the text was very easy to navigate. All the images, charts, and graphs were very clear

I found no grammatical errors in the text.

Cultural Relevance rating: 3

The text including examples and exercises did not seem to be offensive or insensitive in any specific way. However, the examples included references to black and white people, but few others. Also, the text is very American specific with many examples from and for an American audience. More diversity, especially in the examples, would be appropriate and appreciated.

Reviewed by Leslie Aarons, Associate Professor of Philosophy, CUNY LaGuardia Community College on 5/16/19

This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an... read more

This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an argument and an explanation; validity; soundness; and the distinctions between an inductive and a deductive argument in accessible terms in the first chapter. It also does a good job introducing and discussing informal fallacies (Chapter 4). The incorporation of opportunities to evaluate real-world arguments is also very effective. Chapter 2 also covers a number of formal methods of evaluating arguments, such as Venn Diagrams and Propositional logic and the four basic truth functional connectives, but to my mind, it is much more thorough in its treatment of Informal Logic and Critical Thinking skills, than it is of formal logic. I also appreciated that Van Cleave’s book includes exercises with answers and an index, but there is no glossary; which I personally do not find detracts from the book's comprehensiveness.

Overall, Van Cleave's book is error-free and unbiased. The language used is accessible and engaging. There were no glaring inaccuracies that I was able to detect.

Van Cleave's Textbook uses relevant, contemporary content that will stand the test of time, at least for the next few years. Although some examples use certain subjects like former President Obama, it does so in a useful manner that inspires the use of critical thinking skills. There are an abundance of examples that inspire students to look at issues from many different political viewpoints, challenging students to practice evaluating arguments, and identifying fallacies. Many of these exercises encourage students to critique issues, and recognize their own inherent reader-biases and challenge their own beliefs--hallmarks of critical thinking.

As mentioned previously, the author has an accessible style that makes the content relatively easy to read and engaging. He also does a suitable job explaining jargon/technical language that is introduced in the textbook.

Van Cleave uses terminology consistently and the chapters flow well. The textbook orients the reader by offering effective introductions to new material, step-by-step explanations of the material, as well as offering clear summaries of each lesson.

This textbook's modularity is really quite good. Its language and structure are not overly convoluted or too-lengthy, making it convenient for individual instructors to adapt the materials to suit their methodological preferences.

The topics in the textbook are presented in a logical and clear fashion. The structure of the chapters are such that it is not necessary to have to follow the chapters in their sequential order, and coverage of material can be adapted to individual instructor's preferences.

The textbook is free of any problematic interface issues. Topics, sections and specific content are accessible and easy to navigate. Overall it is user-friendly.

I did not find any significant grammatical issues with the textbook.

The textbook is not culturally insensitive, making use of a diversity of inclusive examples. Materials are especially effective for first-year critical thinking/logic students.

I intend to adopt Van Cleave's textbook for a Critical Thinking class I am teaching at the Community College level. I believe that it will help me facilitate student-learning, and will be a good resource to build additional classroom activities from the materials it provides.

Reviewed by Jennie Harrop, Chair, Department of Professional Studies, George Fox University on 3/27/18

While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters... read more

While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters that are dense with statistical analyses and critical vocabulary. These topics are likely better broached in manageable snippets rather than hefty single chapters.

The ideas addressed in Introduction to Logic and Critical Thinking are accurate but at times notably political. While politics are effectively used to exemplify key concepts, some students may be distracted by distinct political leanings.

The terms and definitions included are relevant, but the examples are specific to the current political, cultural, and social climates, which could make the materials seem dated in a few years without intentional and consistent updates.

While the reasoning is accurate, the author tends to complicate rather than simplify -- perhaps in an effort to cover a spectrum of related concepts. Beginning readers are likely to be overwhelmed and under-encouraged by his approach.

Consistency rating: 3

The four chapters are somewhat consistent in their play of definition, explanation, and example, but the structure of each chapter varies according to the concepts covered. In the third chapter, for example, key ideas are divided into sub-topics numbering from 3.1 to 3.10. In the fourth chapter, the sub-divisions are further divided into sub-sections numbered 4.1.1-4.1.5, 4.2.1-4.2.2, and 4.3.1 to 4.3.6. Readers who are working quickly to master new concepts may find themselves mired in similarly numbered subheadings, longing for a grounded concepts on which to hinge other key principles.

Modularity rating: 3

The book's four chapters make it mostly self-referential. The author would do well to beak this text down into additional subsections, easing readers' accessibility.

The content of the book flows logically and well, but the information needs to be better sub-divided within each larger chapter, easing the student experience.

The book's interface is effective, allowing readers to move from one section to the next with a single click. Additional sub-sections would ease this interplay even further.

Grammatical Errors rating: 4

Some minor errors throughout.

For the most part, the book is culturally neutral, avoiding direct cultural references in an effort to remain relevant.

Reviewed by Yoichi Ishida, Assistant Professor of Philosophy, Ohio University on 2/1/18

This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic,... read more

This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic, this textbook does not cover suppositional arguments, such as conditional proof and reductio ad absurdum. But other standard argument forms are covered. Chapter 3 covers inductive logic, and here this textbook introduces probability and its relationship with cognitive biases, which are rarely discussed in other textbooks. Chapter 4 introduces common informal fallacies. The answers to all the exercises are given at the end. However, the last set of exercises is in Chapter 3, Section 5. There are no exercises in the rest of the chapter. Chapter 4 has no exercises either. There is index, but no glossary.

The textbook is accurate.

The content of this textbook will not become obsolete soon.

The textbook is written clearly.

The textbook is internally consistent.

The textbook is fairly modular. For example, Chapter 3, together with a few sections from Chapter 1, can be used as a short introduction to inductive logic.

The textbook is well-organized.

There are no interface issues.

I did not find any grammatical errors.

This textbook is relevant to a first semester logic or critical thinking course.

Reviewed by Payal Doctor, Associate Professro, LaGuardia Community College on 2/1/18

This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner... read more

This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner book, but seems to be a good text for a course that needs a foundation for arguments. There are exercises on creating truth tables and proofs, so it could work as a logic primer in short sessions or with the addition of other course content.

The books is accurate in the information it presents. It does not contain errors and is unbiased. It covers the essential vocabulary clearly and givens ample examples and exercises to ensure the student understands the concepts

The content of the book is up to date and can be easily updated. Some examples are very current for analyzing the argument structure in a speech, but for this sort of text understandable examples are important and the author uses good examples.

The book is clear and easy to read. In particular, this is a good text for community college students who often have difficulty with reading comprehension. The language is straightforward and concepts are well explained.

The book is consistent in terminology, formatting, and examples. It flows well from one topic to the next, but it is also possible to jump around the text without loosing the voice of the text.

The books is broken down into sub units that make it easy to assign short blocks of content at a time. Later in the text, it does refer to a few concepts that appear early in that text, but these are all basic concepts that must be used to create a clear and understandable text. No sections are too long and each section stays on topic and relates the topic to those that have come before when necessary.

The flow of the text is logical and clear. It begins with the basic building blocks of arguments, and practice identifying more and more complex arguments is offered. Each chapter builds up from the previous chapter in introducing propositional logic, truth tables, and logical arguments. A select number of fallacies are presented at the end of the text, but these are related to topics that were presented before, so it makes sense to have these last.

The text is free if interface issues. I used the PDF and it worked fine on various devices without loosing formatting.

1. The book contains no grammatical errors.

The text is culturally sensitive, but examples used are a bit odd and may be objectionable to some students. For instance, President Obama's speech on Syria is used to evaluate an extended argument. This is an excellent example and it is explained well, but some who disagree with Obama's policies may have trouble moving beyond their own politics. However, other examples look at issues from all political viewpoints and ask students to evaluate the argument, fallacy, etc. and work towards looking past their own beliefs. Overall this book does use a variety of examples that most students can understand and evaluate.

My favorite part of this book is that it seems to be written for community college students. My students have trouble understanding readings in the New York Times, so it is nice to see a logic and critical thinking text use real language that students can understand and follow without the constant need of a dictionary.

Reviewed by Rebecca Owen, Adjunct Professor, Writing, Chemeketa Community College on 6/20/17

This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current... read more

This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current events, funny scenarios, or other interesting ways to evaluate argument structure and validity. The third section, which deals with logical fallacies, is very clear and comprehensive. My only critique of the material included in the book is that the middle section may be a bit dense and math-oriented for learners who appreciate the more informal, informative style of the first and third section. Also, the book ends rather abruptly--it moves from a description of a logical fallacy to the answers for the exercises earlier in the text.

The content is very reader-friendly, and the author writes with authority and clarity throughout the text. There are a few surface-level typos (Starbuck's instead of Starbucks, etc.). None of these small errors detract from the quality of the content, though.

One thing I really liked about this text was the author's wide variety of examples. To demonstrate different facets of logic, he used examples from current media, movies, literature, and many other concepts that students would recognize from their daily lives. The exercises in this text also included these types of pop-culture references, and I think students will enjoy the familiarity--as well as being able to see the logical structures behind these types of references. I don't think the text will need to be updated to reflect new instances and occurrences; the author did a fine job at picking examples that are relatively timeless. As far as the subject matter itself, I don't think it will become obsolete any time soon.

The author writes in a very conversational, easy-to-read manner. The examples used are quite helpful. The third section on logical fallacies is quite easy to read, follow, and understand. A student in an argument writing class could benefit from this section of the book. The middle section is less clear, though. A student learning about the basics of logic might have a hard time digesting all of the information contained in chapter two. This material might be better in two separate chapters. I think the author loses the balance of a conversational, helpful tone and focuses too heavily on equations.

Consistency rating: 4

Terminology in this book is quite consistent--the key words are highlighted in bold. Chapters 1 and 3 follow a similar organizational pattern, but chapter 2 is where the material becomes more dense and equation-heavy. I also would have liked a closing passage--something to indicate to the reader that we've reached the end of the chapter as well as the book.

I liked the overall structure of this book. If I'm teaching an argumentative writing class, I could easily point the students to the chapters where they can identify and practice identifying fallacies, for instance. The opening chapter is clear in defining the necessary terms, and it gives the students an understanding of the toolbox available to them in assessing and evaluating arguments. Even though I found the middle section to be dense, smaller portions could be assigned.

The author does a fine job connecting each defined term to the next. He provides examples of how each defined term works in a sentence or in an argument, and then he provides practice activities for students to try. The answers for each question are listed in the final pages of the book. The middle section feels like the heaviest part of the whole book--it would take the longest time for a student to digest if assigned the whole chapter. Even though this middle section is a bit heavy, it does fit the overall structure and flow of the book. New material builds on previous chapters and sub-chapters. It ends abruptly--I didn't realize that it had ended, and all of a sudden I found myself in the answer section for those earlier exercises.

The simple layout is quite helpful! There is nothing distracting, image-wise, in this text. The table of contents is clearly arranged, and each topic is easy to find.

Tiny edits could be made (Starbuck's/Starbucks, for one). Otherwise, it is free of distracting grammatical errors.

This text is quite culturally relevant. For instance, there is one example that mentions the rumors of Barack Obama's birthplace as somewhere other than the United States. This example is used to explain how to analyze an argument for validity. The more "sensational" examples (like the Obama one above) are helpful in showing argument structure, and they can also help students see how rumors like this might gain traction--as well as help to show students how to debunk them with their newfound understanding of argument and logic.

The writing style is excellent for the subject matter, especially in the third section explaining logical fallacies. Thank you for the opportunity to read and review this text!

Reviewed by Laurel Panser, Instructor, Riverland Community College on 6/20/17

This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as... read more

This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as the 13th edition with the same title. Lori Watson is the second author on the 13th edition.

Competing with Hurley is difficult with respect to comprehensiveness. For example, Van Cleave’s book is comprehensive to the extent that it probably covers at least two-thirds or more of what is dealt with in most introductory, one-semester logic courses. Van Cleave’s chapter 1 provides an overview of argumentation including discerning non-arguments from arguments, premises versus conclusions, deductive from inductive arguments, validity, soundness and more. Much of Van Cleave’s chapter 1 parallel’s Hurley’s chapter 1. Hurley’s chapter 3 regarding informal fallacies is comprehensive while Van Cleave’s chapter 4 on this topic is less extensive. Categorical propositions are a topic in Van Cleave’s chapter 2; Hurley’s chapters 4 and 5 provide more instruction on this, however. Propositional logic is another topic in Van Cleave’s chapter 2; Hurley’s chapters 6 and 7 provide more information on this, though. Van Cleave did discuss messy issues of language meaning briefly in his chapter 1; that is the topic of Hurley’s chapter 2.

Van Cleave’s book includes exercises with answers and an index. A glossary was not included.

Reviews of open source textbooks typically include criteria besides comprehensiveness. These include comments on accuracy of the information, whether the book will become obsolete soon, jargon-free clarity to the extent that is possible, organization, navigation ease, freedom from grammar errors and cultural relevance; Van Cleave’s book is fine in all of these areas. Further criteria for open source books includes modularity and consistency of terminology. Modularity is defined as including blocks of learning material that are easy to assign to students. Hurley’s book has a greater degree of modularity than Van Cleave’s textbook. The prose Van Cleave used is consistent.

Van Cleave’s book will not become obsolete soon.

Van Cleave’s book has accessible prose.

Van Cleave used terminology consistently.

Van Cleave’s book has a reasonable degree of modularity.

Van Cleave’s book is organized. The structure and flow of his book is fine.

Problems with navigation are not present.

Grammar problems were not present.

Van Cleave’s book is culturally relevant.

Van Cleave’s book is appropriate for some first semester logic courses.

Table of Contents

Chapter 1: Reconstructing and analyzing arguments

• 1.1 What is an argument?
• 1.2 Identifying arguments
• 1.3 Arguments vs. explanations
• 1.4 More complex argument structures
• 1.5 Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form
• 1.6 Validity
• 1.7 Soundness
• 1.8 Deductive vs. inductive arguments
• 1.9 Arguments with missing premises
• 1.10 Assuring, guarding, and discounting
• 1.11 Evaluative language
• 1.12 Evaluating a real-life argument

Chapter 2: Formal methods of evaluating arguments

• 2.1 What is a formal method of evaluation and why do we need them?
• 2.2 Propositional logic and the four basic truth functional connectives
• 2.3 Negation and disjunction
• 2.4 Using parentheses to translate complex sentences
• 2.5 “Not both” and “neither nor”
• 2.6 The truth table test of validity
• 2.7 Conditionals
• 2.8 “Unless”
• 2.9 Material equivalence
• 2.10 Tautologies, contradictions, and contingent statements
• 2.11 Proofs and the 8 valid forms of inference
• 2.12 How to construct proofs
• 2.13 Short review of propositional logic
• 2.14 Categorical logic
• 2.15 The Venn test of validity for immediate categorical inferences
• 2.16 Universal statements and existential commitment
• 2.17 Venn validity for categorical syllogisms

Chapter 3: Evaluating inductive arguments and probabilistic and statistical fallacies

• 3.1 Inductive arguments and statistical generalizations
• 3.2 Inference to the best explanation and the seven explanatory virtues
• 3.3 Analogical arguments
• 3.4 Causal arguments
• 3.5 Probability
• 3.6 The conjunction fallacy
• 3.7 The base rate fallacy
• 3.8 The small numbers fallacy
• 3.9 Regression to the mean fallacy
• 3.10 Gambler's fallacy

Chapter 4: Informal fallacies

• 4.1 Formal vs. informal fallacies
• 4.1.1 Composition fallacy
• 4.1.2 Division fallacy
• 4.1.3 Begging the question fallacy
• 4.1.4 False dichotomy
• 4.1.5 Equivocation
• 4.2 Slippery slope fallacies
• 4.2.1 Conceptual slippery slope
• 4.2.2 Causal slippery slope
• 4.3 Fallacies of relevance
• 4.3.1 Ad hominem
• 4.3.2 Straw man
• 4.3.3 Tu quoque
• 4.3.4 Genetic
• 4.3.5 Appeal to consequences
• 4.3.6 Appeal to authority

Answers to exercises Glossary/Index

Ancillary Material

About the book.

This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a “critical thinking textbook.”

About the Contributors

Matthew Van Cleave ,   PhD, Philosophy, University of Cincinnati, 2007.  VAP at Concordia College (Moorhead), 2008-2012.  Assistant Professor at Lansing Community College, 2012-2016. Professor at Lansing Community College, 2016-

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100 Best Logical Reasoning Books of All Time

We've researched and ranked the best logical reasoning books in the world, based on recommendations from world experts, sales data, and millions of reader ratings. Learn more

Thinking, Fast and Slow

Kahneman | 5.00

Barack Obama A few months ago, Mr. Obama read “Thinking, Fast and Slow,” by Daniel Kahneman, about how people make decisions — quick, instinctive thinking versus slower, contemplative deliberation. For Mr. Obama, a deliberator in an instinctive business, this may be as instructive as any political science text. (Source)

Bill Gates [On Bill Gates's reading list in 2012.] (Source)

Marc Andreessen Captivating dive into human decision making, marred by inclusion of several/many? psychology studies that fail to replicate. Will stand as a cautionary tale? (Source)

See more recommendations for this book...

Gödel, Escher, Bach

An Eternal Golden Braid

Douglas R. Hofstadter | 4.86

Steve Jurvetson [Steve Jurvetson recommended this book on the podcast "The Tim Ferriss Show".] (Source)

Seth Godin In the last week, I discovered that at least two of my smart friends hadn't read Godel, Escher, Bach. They have now. You should too. (Source)

Kevin Kelly Over the years, I kept finding myself returning to its insights, and each time I would arrive at them at a deeper level. (Source)

An Epic Search for Truth

Apostolos Doxiadis, Christos Papadimitriou | 4.75

Marcus du Sautoy This is quite a recent publication and I saw the first inklings of this graphic novel when I went to a meeting in Mykonos on maths and narrative and it really looked an incredibly exciting project. I enjoy the graphic novel as an art form and I’ve always enjoyed Tintin and this has a very Tintinesque line to it, the illustration. But it brings alive one of the great stories of 20th-century... (Source)

A Rulebook for Arguments

Anthony Weston | 4.72

Tractatus Logico-Philosophicus

Ludwig Wittgenstein and Bertrand Russell | 4.71

Reid Hoffman Reid recommends studying Ludwig Wittgenstein, about whom he's taught a course at Oxford. "One of the bedrocks of modern analytics philosophy is to think of [language] ... if you're trying to talk to someone else about some problem, and you're trying to make progress, how do you make language as positive an instrument as possible? What are the ways that language can work, and what are the way that... (Source)

Sonia Micu The book I read many times already is Wittgenstein’s Tractatus Logico-Philosophicus. Don’t say it’s pretentious. It is beautiful. Some even say it’s poetry. I am far from understanding his complicated genius, but I think I’ve learned how to read it and I think I’ll never stop going back to it. (Source)

Tom Stoneham Wittgenstein’s book is about how we understand the thinkable and the unthinkable, which is a traditional philosophical problem. (Source)

The Fallacy Detective

Thirty-Eight Lessons on How to Recognize Bad Reasoning

Nathaniel Bluedorn | 4.65

Being Logical

A Guide to Good Thinking

D.Q. McInerny | 4.63

Gödel's Proof

Ernest Nagel, James R. Newman, Douglas R. Hofstadter | 4.62

The Black Swan

The Impact of the Highly Improbable

Nassim Nicholas Taleb | 4.58

Jeff Bezos [From the book "The Everything Store: and the Age of Amazon"] “The scholar argues that people are wired to see patterns in chaos while remaining blind to unpredictable events, with massive consequences. Experimentation and empiricism trumps the easy and obvious narrative,” Stone writes. (Source)

James Altucher And throw in “The Black Swan” and “Fooled by Randomness”. “Fragile” means if you hit something might break. “Resilient” means if you hit something, it will stay the same. On my podcast Nassim discusses “Antifragility” – building a system, even on that works for you on a personal level, where you if you harm your self in some way it becomes stronger. That podcast changed my life He discusses... (Source)

Introduction to Logic

Irving Copi | 4.55

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Alice's Adventures in Wonderland & Through the Looking-Glass

Lewis Carroll | 4.49

Eric Weinstein [Eric Weinstein recommended this book on Twitter.] (Source)

Larry Doyle You’d have to be a zombie to miss the humour in it – it’s hilarious. Although the book is ancient, the humour feels modern (Source)

Jean Webb An imaginative, clever and fun fantasy story that satirises nineteenth century England at the same time as celebrating academic thinking. (Source)

An Illustrated Book of Bad Arguments

Ali Almossawi, Alejandro Giraldo | 4.48

A Very Short Introduction

Graham Priest | 4.44

Predictably Irrational

The Hidden Forces That Shape Our Decisions

Dan Ariely | 4.41

Max Levchin [Max Levchin recommended this book as an answer to "What business books would you advise young entrepreneurs read?"] (Source)

Nick Harkaway Predictably Irrational is an examination of the way in which we make decisions irrationally, and how that irrationality can be predicted. (Source)

Jonah Lehrer Dan Ariely is a very creative guy and was able to take this basic idea, that humans are irrational, and mine it in a million different directions. (Source)

From a Logical Point of View

Nine Logico-Philosophical Essays

Willard Van Orman Quine | 4.37

Robert Talisse Although Quine doesn’t often describe himself as a pragmatist, he is, in my view, a fully-fledged pragmatist and any attempt to call him a pragmatist in a deeply qualified sense is a mistake. The standard, popular story about the development and founding of pragmatism that gets told is that Dewey dies in 1952, and pragmatism comes to an end a little bit before his death. Pragmatism is America’s... (Source)

Philosophy of Logic

Willard Van Orman Quine | 4.34

Tom Stoneham Quine’s book is about when we construct a formal logic, when we create these formal languages, then we’re making philosophical decisions or choices about how we do it. The Philosophy of Logic is all about the philosophical arguments that underlie the decisions to do logic in one way or another. (Source)

A Concise Introduction to Logic [with CD-ROM]

Patrick J. Hurley | 4.34

Computability and Logic

George S. Boolos | 4.33

Socratic Logic

Peter Kreeft | 4.33

Proofs and Refutations

The Logic of Mathematical Discovery

Imre Lakatos, John Worrall, Elie Zahar | 4.33

Alf Coles I first came across this book at university in a course on the philosophy of mathematics. Looking back, it was one of my first experiences of how maths could be different to how I was taught it. In the book, Lakatos takes a particular area of mathematics to do with shape and recreates an imaginary dialogue where he and the characters in the book go through this extraordinary process of developing... (Source)

Language, Truth, and Logic

Alfred J. Ayer | 4.33

To Mock a Mockingbird and Other Logic Puzzles

Raymond Smullyan | 4.31

Naming and Necessity

Saul A. Kripke | 4.31

The Demon-haunted World

Science As a Candle in the Dark

Carl Sagan | 4.31

James Randi First of all, Carl was my very good friend, and we had a lot of confidences over the years. He was the epitome of the scientific mind and the scientific thinker. In The Demon-Haunted World, one of his later books, he investigates pseudoscience, frauds and fakes, and the mistakes that scientists made over the years. It’s very comprehensive. He had a whole chapter devoted to “Carlos” – or Jose... (Source)

Philip Plait He holds your hand and shows you the wonders of science and the universe. The Demon-Haunted World is probably his best book. (Source)

Dallas Campbell @TheChilterns Even if you profoundly disagree with Clarke, it’s very detailed. The classic is of course ‘The Demon Haunted World’ by Carl Sagan. When I’m Prime Minister it will be compulsory reading at school! Best book on what science is/isn’t and why we think the way we do. 👍 (Source)

What Is the Name of This Book?

The Riddle of Dracula and Other Logical Puzzles

Raymond M. Smullyan | 4.30

Fooled by Randomness

The Hidden Role of Chance in Life and in the Markets

Nassim Nicholas Taleb | 4.29

Howard Marks Really about how much randomness there is in our world. (Source)

Anant Jain The five-book series, "Incerto", by Nassim Nicholas Taleb has had a profound impact on how I think about the world. There’s some overlap across the books — but you'll likely find the repetition helpful in retaining the content better. (Source)

An Introduction to Non-Classical Logic

From If to Is

Graham Priest | 4.29

and to the Methodology of Deductive Sciences

Alfred Tarski | 4.28

An Introduction to Elementary Logic

Wilfrid Hodges | 4.28

Tom Stoneham If you found algebra fun at school, you’re probably going to get on well with Logic Primer. (Source)

How to Solve It

A New Aspect of Mathematical Method

G. Polya, John H. Conway | 4.28

The Foundations of Arithmetic

A Logico-Mathematical Enquiry into the Concept of Number

Gottlob Frege, J. L. Austin | 4.27

With Good Reason

An Introduction to Informal Fallacies

S. Morris Engel | 4.26

The Trivium

The Liberal Arts of Logic, Grammar, and Rhetoric

Sister Miriam Joseph and Marguerite McGlin | 4.26

How to Prove It

A Structured Approach

Daniel J. Velleman | 4.25

Crimes Against Logic

Exposing the Bogus Arguments of Politicians, Priests, Journalists, and Other Serial Offenders

Jamie Whyte | 4.25

The Logic of Scientific Discovery

Karl R. Popper | 4.24

Nonsense: Red Herrings, Straw Men and Sacred Cows

How We Abuse Logic in Our Everyday Language

Robert J. Gula | 4.23

First-Order Logic

Raymond M. Smullyan | 4.23

How Not to Be Wrong

The Power of Mathematical Thinking

Jordan Ellenberg | 4.23

Bill Gates The writing is funny, smooth, and accessible -- not what you might expect from a book about math. What Ellenberg has written is ultimately a love letter to math. If the stories he tells add up to a larger lesson, it’s that 'to do mathematics is to be, at once, touched by fire and bound by reason' -- and that there are ways in which we’re all doing math, all the time. (Source)

Auston Bunsen I’ve got a few, one book that really impacted me early on as someone coming from a middle-class family was “Rich dad, Poor dad”. Since then I’ve read many books but one that really stands out is “How not to be wrong” by Jordan Ellenberg which really reignited my appetite & appreciation for math. (Source)

Nick Ganju Written for an audience of people who have historically been intimidated by math [...] and introduces things in a very simple way, and then works up to more complex concepts. (Source)

Antifragile

Things That Gain from Disorder

Nassim Nicholas Taleb | 4.22

James Altucher You ask about success. To be successful you have to avoid being “fragile” – the idea that if something hurts you, you let collapse completely. You also have to avoid simply being resilient. Bouncing back is not enough. Antifragile is when something tries to hurt you and you come back stronger. That is real life business. That is real life success. Nassim focuses on the economy. But when I read... (Source)

Marvin Liao eval(ez_write_tag([[250,250],'theceolibrary_com-leader-2','ezslot_7',164,'0','1'])); My list would be (besides the ones I mentioned in answer to the previous question) both business & Fiction/Sci-Fi and ones I personally found helpful to myself. The business books explain just exactly how business, work & investing are in reality & how to think properly & differentiate yourself. On... (Source)

Vlad Tenev The general concept is applicable to many fields beyond biology, for instance finance, economics and monetary policy. (Source)

المغالطات المنطقية

عادل مصطفى and Adil Mustafa | 4.22

Logically Fallacious

The Ultimate Collection of Over 300 Logical Fallacies - Academic Edition

Bo Bennett | 4.21

The Lady or the Tiger?

and Other Logic Puzzles

Raymond M. Smullyan | 4.20

The Loophole in LSAT Logical Reasoning

Ellen Cassidy | 4.20

Logic for Philosophy

Theodore Sider | 4.20

Critique of Pure Reason

Immanuel Kant, Paul Guyer, et al. | 4.20

Simon Blackburn An illuminating way to think of the Critique is as a kind of prolonged wrestling match with Hume. (Source)

Adrian Moore This is the greatest philosophical book of all time. This is Kant’s masterpiece. (Source)

Luciano Floridi I find reading Kant a bit like understanding cricket as a foreigner: hard to get at first, but once you get it, it’s very enjoyable. (Source)

Introduction to Metamathematics

S.C. Kleene | 4.19

The Skeptics' Guide to the Universe

How to Know What's Really Real in a World Increasingly Full of Fake

Steven Novella, Bob Novella - contributor, et al | 4.18

Asking the Right Questions

A Guide to Critical Thinking

M. Neil Browne, Stuart M. Keeley | 4.17

Philosophical Devices

Proofs, Probabilities, Possibilities, and Sets

David Papineau | 4.16

How to Win Every Argument

The Use and Abuse of Logic

Madsen Pirie | 4.16

The Art of Thinking Clearly

Better Thinking, Better Decision

dobelli rolf | 4.15

Robert Cialdini Dobelli examines our most common decision-making failings with engaging eloquence and describes how to counter them with instructive good sense. (Source)

Nigel Warburton This is an unpretentious book. Dobelli doesn’t claim to be an original thinker himself. He’s a summariser of other people’s thoughts. What he’s done is brought lots of different things together in one place. Each of the 99 entries is pretty short, and it’s the kind of book to dip into. (Source)

An Investigation of the Laws of Thought

George Boole | 4.15

Introducing Logic

A Graphic Guide

Dan Cryan | 4.13

Logic is the backbone of Western civilization, holding together its systems of philosophy, science and law. Yet despite logic's widely acknowledged importance, it remains an unbroken seal for many, due to its heavy use of jargon and mathematical symbolism.This book follows the historical development of logic, explains the symbols and methods involved and explores the philosophical issues surrounding the topic in an easy-to-follow and friendly manner. It will take you through the influence of logic on scientific method and the various sciences from physics to psychology, and will show you...

Logic is the backbone of Western civilization, holding together its systems of philosophy, science and law. Yet despite logic's widely acknowledged importance, it remains an unbroken seal for many, due to its heavy use of jargon and mathematical symbolism.This book follows the historical development of logic, explains the symbols and methods involved and explores the philosophical issues surrounding the topic in an easy-to-follow and friendly manner. It will take you through the influence of logic on scientific method and the various sciences from physics to psychology, and will show you why computers and digital technology are just another case of logic in action.

The Art of Reasoning

An Introduction to Logic and Critical Thinking

David Kelley | 4.13

Methods of Logic

Willard Van Orman Quine | 4.13

Philosophical Investigations

Ludwig Wittgenstein, G. E. M. Anscombe, et al. | 4.12

Introduction to Mathematical Philosophy

Bertrand Russell | 4.12

Thinking Toolbox

Nathaniel Bluedorn, Hans Bluedorn, Richard LaPierre | 4.12

-When it is dumb to argue

-Using the scientific method

-Five rules of brainstorming

-Who has a reason to lie?

-How to analyze opposing viewpoints

-How to analyze evidence and sources

-How to list reasons why you believe something

-And much more

We wrote this book for children and adults who want to...

We wrote this book for children and adults who want to learn logic and critical thinking skills.

The Thinking Toolbox follows the same style as The Fallacy Detective with lessons and exercises and an answer key in the back.

-Fun to use not dry like a math textbook

-Can be used after The Fallacy Detective

-Introductory teaches skills you can use right away

-Self-teaching format

-For ages twelve and older

-Over 60 cartoon illustrations by Richard LaPierre Book Details:

A God-Centered Approach to the Foundation of Western Thought

Vern S. Poythress | 4.11

The Logical Structure of the World and Pseudoproblems in Philosophy

Rudolf Carnap, Rolf A. George | 4.10

Logic Made Easy

How to Know When Language Deceives You

Deborah J. Bennett | 4.10

The Categorial Analysis of Logic

Robert Goldblatt | 4.09

The Frege Reader

Gottlob Frege, Michael Beaney | 4.09

Alice in Wonderland

Lewis Carroll, Rene Cloke | 4.09

Foti Panagio As for a non-business book, it’s got to be Alice in Wonderland by C. S. Lewis. It’s an unrivalled work of imagination and shows what it looks like to “think outside the box”. Sometimes I like to flick through a copy and look at the illustrations if I’m stuck on a problem and need some inspiration. (Source)

Attacking Faulty Reasoning

A Practical Guide to Fallacy-Free Arguments

T. Edward Damer | 4.09

Meaning and Necessity

A Study in Semantics and Modal Logic

Rudolf Carnap | 4.08

The Laws of Truth

Nicholas J.J. Smith | 4.08

The Powerscore 2020 Digital LSAT Logical Reasoning Bible

2020 Digital LSAT Edition

David M. Killoran | 4.07

On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Dover Books on Mathematics)

Kurt Gödel | 4.07

Informal Logic

A Handbook for Critical Argument

Douglas N. Walton | 4.07

Logic, Semantics, Metamathematics

Alfred Tarski | 4.07

The Right Use of Reason in the Inquiry After Truth

Isaac Watts | 4.06

R. M. Sainsbury | 4.06

Tom Stoneham I love this book. Whole university courses are taught around this book. It’s an absolute classic. (Source)

Sophie's World

Jostein Gaarder, Paulette Moller | 4.06

Algorithms to Live By

The Computer Science of Human Decisions

Brian Christian and Tom Griffiths | 4.06

Doug McMillon Here are some of my favorite reads from 2017. Lots of friends and colleagues send me book suggestions and it's impossible to squeeze them all in. I continue to be super curious about how digital and tech are enabling people to transform our lives but I try to read a good mix of books that apply to a variety of areas and stretch my thinking more broadly. (Source)

Sriram Krishnan @rabois @nealkhosla Yes! Love that book (Source)

Chris Oliver This is a great book talking about how you can use computer science to help you make decisions in life. How do you know when to make a decision on the perfect house? Car? etc? It helps you apply algorithms to making those decisions optimally without getting lost. (Source)

From Frege to Gödel

A Source Book in Mathematical Logic, 1879-1931

Jean van Heijenoort | 4.05

Come, Let Us Reason

An Introduction to Logical Thinking

Dr. Norman L. Geisler, Ron M. Brooks | 4.05

An Introduction to Formal Logic

Peter Smith | 4.05

The LSAT Trainer

A Remarkable Self-Study Guide For The Self-Driven Student

Mike Kim | 4.05

Incompleteness

The Proof and Paradox of Kurt Gödel (Great Discoveries)

Rebecca Goldstein | 4.05

Labyrinths of Reason

Paradox, Puzzles and the Frailty of Knowledge

William Poundstone | 4.05

Philosophy of Logics

Susan Haack | 4.04

The Logic of Sense

Gilles Deleuze, Constantin V. Boundas, Mark Lester, Charles Stivale | 4.04

Understanding Arguments

An Introduction to Informal Logic

Walter Sinnott-Armstrong, Robert J. Fogelin | 4.04

Logical Labyrinths

Raymond Smullyan | 4.04

You Are Not So Smart

Why You Have Too Many Friends on Facebook, Why Your Memory Is Mostly Fiction, and 46 Other Ways You're Deluding Yourself

David McRaney | 4.03

Jessica Flitter Honestly, almost every major topic that we cover in an introductory social psychology chapter is covered in the book. It makes psychology real: this isn’t something that theoretically exists in the classroom. It exists every single day. That’s why I love this book. (Source)

Rationality

From AI to Zombies

Eliezer Yudkowsk | 4.03

Mathematical Logic

Stephen Cole Kleene | 4.03

More Precisely

The Math You Need to Do Philosophy

Eric Steinhart | 4.03

Harry Gensler | 4.02

Modal Logic for Open Minds (Center for the Study of Language and Information - Lecture Notes)

Johan van Benthem | 4.02

Lewis Carroll's Symbolic Logic

Lewis Carroll, Charles Lutwidge Dodgson, III William Warren Bartley | 4.02

The Powerscore 2020 LSAT Logic Games Bible

David M. Killoran | 4.02

A Mathematical Introduction to Logic

Herbert B. Enderton | 4.02

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Logic and Philosophy: A Modern Introduction Thirteenth Edition

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• ISBN-10 1624669352
• ISBN-13 978-1624669354
• Edition Thirteenth
• Publisher Hackett Publishing Company, Inc.
• Publication date February 24, 2021
• Language English
• Dimensions 6.5 x 1 x 9.5 inches
• Print length 464 pages
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• Publisher ‏ : ‎ Hackett Publishing Company, Inc.; Thirteenth edition (February 24, 2021)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 464 pages
• ISBN-10 ‏ : ‎ 1624669352
• ISBN-13 ‏ : ‎ 978-1624669354
• Item Weight ‏ : ‎ 1.6 pounds
• Dimensions ‏ : ‎ 6.5 x 1 x 9.5 inches
• #65 in Logic (Books)
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By Jim Holt

• Sept. 25, 2009

Well, this is unexpected — a comic book about the quest for logical certainty in mathematics. The story spans the decades from the late 19th century to World War II, a period when the nature of mathematical truth was being furiously debated. The stellar cast, headed up by Bertrand Russell, includes the greatest philosophers, logicians and mathematicians of the era, along with sundry wives and mistresses, plus a couple of homicidal maniacs, an apocryphal barber and Adolf Hitler.

Improbable material for comic-book treatment? Not really. The principals in this intellectual drama are superheroes of a sort. They go up against a powerful nemesis, who might be called Dark Antinomy. Each is haunted by an inner demon, the Specter of Madness. Their quest has a tragic arc, not unlike that of Superman or Donald Duck.

So, at least, the creators of “Logicomix” would have us believe. First published last year in Greece (where it became a surprise best seller), the comic book — er, graphic novel? — is the brainchild of Apostolos Doxiadis, previously the author of a not-bad mathematical fiction called “Uncle Petros and Goldbach’s Conjecture.” For expert assistance on logic, Doxiadis called on his friend Christos Papadimitriou, a professor of computer science at Berkeley and the author of a novel about Alan Turing. The art was done by Alecos Papadatos (drawings) and Annie Di Donna (color).

All four collaborators pop up in interludes throughout the book. (Doxiadis, evidently a handsome fellow, is drawn to look rather like Robert Goulet.) We see them chatting in the artists’ studio or strolling around contemporary Athens, accompanied by an adorable dog called Manga (Greek slang for “cool dude,” not a reference to Japanese comics). They argue about the developing ­logic-and-­madness theme and fret over whether there’s too much or too little technical stuff for the average reader. It’s almost as if they want to pre-empt the stern judgment of the reviewer. Fat chance.

The story proper opens on Sept. 4, 1939, three days after the Nazi invasion of Poland. Bertrand Russell is giving a public lecture at an American university on the role of logic in human affairs. Angry isolationists in the audience challenge Russell to explain how logic could justify participating in a world war. Ah, he responds, but what is logic?

In a series of flashbacks, Russell recounts his epic struggle with that question. We see him first as a little boy, in the 1870s, being brought up by his grandparents after the mysterious — to him, at least — disappearance of his mother and father. (Before succumbing to disease, Russell’s parents lived in a scandalous ménage-a-trois with a rather sinister amateur scientist.) Russell’s grandfather, Lord John Russell, a Whig aristocrat and reformer, had twice been prime minister, but it was his dour and pious grandmother who dominated his childhood. Not only did he suffer from crushing loneliness, but it was borne in upon him that his Uncle Willy had to be shut away as a violent lunatic. (His Aunt Agatha was none too sane either.) This was the beginning of his lifelong terror of hereditary madness, and the impetus for many a nightmare, which the cartoonists depict with lurid relish.

The adolescent Russell sought refuge in the abstractions of mathematics. (In his autobiography, he claimed it was his love of mathematics that saved him from suicide.) His vision of an enchanted logical world was jarred, however, when he reached Cambridge and found that mathematics as practiced there was little more than a bag of calculating tricks, sloppily based on physical intuition rather than rigorous proof. If certain knowledge was to be achieved, he grew convinced, the house of mathematics had to be rebuilt from scratch on firm logical foundations.

Russell’s quest for certainty coincided with a busy erotic career. We see him courting Alys, the pretty American Quaker girl who would become the first of his four wives. (The cartoonists inexplicably neglect to depict what Russell later described as “the happiest morning of my life,” when Alys allowed him to kiss her breasts). The young couple set off on a tour of the Continent, where Russell seeks out Gottlob Frege, the greatest logician since Aristotle, and Georg Cantor, the creator of the mathematical theory of infinity. Both men, to Russell’s consternation, prove to be slightly daft. In Paris, at the 1900 International Congress of Mathematicians, he witnesses a titanic clash between Henri Poincaré and David Hilbert, the two greatest mathematicians of the day, over the importance of intuition versus proof. Returning to England, Russell spends the next decade laboring with Alfred North Whitehead to complete the epic “Principia Mathematica” — all the while doing his best to seduce Whitehead’s comely wife, Evelyn. Their (stillborn) masterpiece runs many thousands of pages, a mere 362 of which are required to prove the interesting proposition “1 + 1 = 2.”

All of this is presented with real graphic verve. (Even though I’m a text guy, I couldn’t keep my eyes off the witty drawings.) To ginger up the story, the authors often deviate from the actual facts. As they admit in an afterword, Russell never met Frege or Cantor in the flesh. Nor, I am fairly certain, did he ever say to Whitehead, “I’m tired, man.” (You expect Whitehead to reply, “Me too, bro!”) We are assured, however, that no liberties have been taken with “the great adventure of ideas.” And for the most part the ideas are conveyed accurately, and with delightful simplicity. If you don’t know much about infinity, for instance, you are invited to check in to “Hilbert’s Hotel” — which, with its infinite number of rooms, can miraculously accommodate additional guests even when it’s completely full.

There is one serious misstep, though. It has to do with the notorious paradox that Russell discovered in the spring of 1901: the paradox of the set of all sets that don’t contain themselves as members. (Think of the barber of Seville, who shaves all men, and only those men, who do not shave themselves. Does this barber shave himself or not? Either possibility yields a contradiction.) The authors have fun unpacking Russell’s paradox, but they exaggerate its fallout. The paradox did ultimately doom Russell’s (and Frege’s) project of reducing mathematics to pure logic. However — and this is something that Russell himself failed to realize, along with the authors — it left mathematics pretty much undisturbed. When Cantor heard of Russell’s paradox, he did not react like a madman, the way ­“Logicomix” caricatures him. He calmly observed that it did not apply to his own theory of sets, which evolved into the present-day foundation of mathematics.

It is true that Cantor did suffer fits of madness (the magus of infinity died in a mental asylum), as did many other figures in this story. Frege, the consummate logician, ended up a foaming anti-Semite. Kurt Gödel, who proved that no logical system could capture all of mathematics, starved himself to death out of a paranoid fear that people were poisoning his food. Russell maintained his own grip on sanity, but his fear of hereditary madness was borne out when his elder son became schizophrenic and his granddaughter, also schizophrenic, committed suicide by setting herself afire. Russell’s philosophical confidence, however, was shattered by his onetime pupil Ludwig Wittgenstein, who made him realize that he had never really understood what logic was.

Is it madness to be driven by a passion for something as inhuman as abstract certainty? This is a question the four creators of “Logicomix” ponder as, in a beguiling coda, they make their way through nighttime Athens to an open-air performance of the “Oresteia.” Oddly enough, Aeschylus’ trilogy furnishes the concluding wisdom, which, at the risk of triteness, I’ll condense into a mathematical inequality:

Life > logic.

Written by Apostolos Doxiadis and Christos H. Papadimitriou

Illustrated by Alecos Papadatos and Annie Di Donna

347 pp. Bloomsbury. $22.95

Jim Holt is the author of “Stop Me if You’ve Heard This: A History and Philosophy of Jokes.” He is at work on a book about the puzzle of existence.

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