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The Little Logic Book
Written by four members of the Calvin College philosophy department, The Little Logic Book is a valuable resource for teachers and undergraduate students of philosophy. In addition to providing clear introductions to the modes of reasoning students encounter in their philosophy course readings, it includes a nuanced description of common informal fallacies, a narrative overview of various philosophical accounts of scientific inference, and a concluding chapter on the ethics of argumentation. The book features engaging dialogues on social, philosophical and religious issues based on the styles of argument taken up in the chapters. In additions to core concepts, distinctions, explanations, rules of inference, methods of assessment, and examples, The Little Logic Book provides philosophical commentary that will stimulate discussion of the assumptions and implications of various kinds of human reasoning. Free downloadable exercises are available from the publisher.
220 pages, Paperback
First published September 16, 2013
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June 3, 2024
The four authors of The Little Logic Book are professors at Calvin College, and they published the work through their school’s publisher. The authors all teach and have published other works in the discipline of philosophy, and they decided to write an introductory and accessible work on logic from a Christian perspective (vii-viii). Hardy explains the unique scope of the book: “we also cover more topics than most introductory logic texts include. We have chapters on modal logic, counterfactuals, and probability theory. Such topics are usually reserved for intermediate and advanced logic courses” (x). Thus, the authors intend to guide the reader through introductory and concepts in logic as they compose a work that focuses on a multitude of logical issues. Readers will discover that each chapter fluctuates in difficulty of comprehension as one chapter focuses on a familiar and introductory issue in logic, and the following chapter is about an advance logical concept (see p. 78).
The Little Logic Book is about explanations of crucial logical concepts, so the authors are not focused on advancing an overall argument in each chapter of the book as they provide summaries to different topics. However, the reader may discern the authors’ thesis of the book in the preface the writers state the work’s threefold purpose: “first, affordability; second, some ethical reflection on the use of logic in argumentation; third, a balanced treatment of religious beliefs in the examples and exercises” (vii). This list is not an explicit thesis, but the authors contend that the discipline of logic should be accessible, ethical, and edifying for the Christian reader’s beliefs. The writers’ Christian convictions guide their view on logic as they believe in a close union between logical reasoning and Christian faith. The authors helpfully advance their argument for the discipline of logic as they structure the book around this threefold goal for a publication on logic. Their desire for faithful and virtuous logic shapes the explanations and examples of every chapter.
In chapters 1–3, the authors introduce the readers to the basic and complex logical notions of deductive arguments, truth tables, and quantification. The writers acclimate the readers to these topics with opening, illustrative, and ethically relevant argument between the characters of Rene, Andrea, and Melissa in each chapter (see ix). The authors develop the specific issue of propositional logic in these chapters as they focus on the “connectives” and “relations within simple propositions” (42). The chapters also contain visualizations of deductive arguments and truth tables which function as useful references for logical concepts that may confuse readers through simple and verbal descriptions.
Chapters 4–5 are about the elaborate topics of modal logic, then the authors transition to the more preliminary concept of inductive arguments in chapter 6. The authors arrange the book in such a manner that they do not progress from beginning issues to advanced notions. Rather, the chapters range in levels of academic difficulty concerning the discipline of logic. Chapter 4 is both a concise and systematic summary of modal logic as the authors’ primary concern is key terminology, visual forms, significance, and the uniqueness of modal logic (see 55). In chapter 5, the authors define the concept of counterfactuals: “Counterfactual reasoning typically deals with the implications of statements concerning states of affairs that, as far as we know, do not exist” (78). If chapter 4 is about the issue of truth (46), chapter 5 is about hypothetical reasoning. Furthermore, inductive arguments” are the “common” arguments about “a familiar pattern found in cases of some type, and projecting that pattern on a present case of that type” (88). Structure and validity are the crucial components of a deductive argument (5), but patterns and sound predictions are the components of an inductive argument.
The authors continue to explain distinct logical problems and questions in chapters 7–9 through the exemplary ethical and religious contentions of Andrea, Melissa, and Rene. Chapter 7 is about the determination of causation by John Stuart Mill’s Method (99). Chapter 8 is more technical as the authors explore the use of probability in logical argumentation. While this chapter is the most mathematical section of the book, the authors highlight the relevance of probabilities in all disciplines and areas of argumentation (102–103). The authors dedicate chapter 9 to the use of Analogical arguments. Through their discussion on these types of arguments, the authors show how an understanding of probability and induction impact the utilization of analogical arguments (128). While the authors discuss a plethora of logical problems throughout the publication, they are careful to show how certain logical issues factor into other matters of logic. The authors define analogical argumentation: “we consider two sets of cases we take to be similar in relevant respects and argue that a characteristic known to belong to one will likely belong to the other” (133–134). The reader may observe the inductive aspects of patterns and projections in this definition of analogous argumentation as one notes pattern between two cases (see 128).
In chapters 10–13, the authors introduce the reader to the fascinating and sobering concept of informal fallacies, explanations and their distinction from logical argumentation (153), the impact of logic on the discipline of scientific inference (167), and a concluding chapter on ethics in logic which contributes to the unique goal of the book (see viii). In the conclusion of chapter 13, the authors make an argument that functions as a fitting and closing reflection to the book: “The world is full of complexity and mystery. We desire to be wise, but we are not omniscient. Voldemort-like arrogance and claims to mastery of complete and final truth don’t fit us very well. We know, and yet we know in part” (201). The authors take care to acknowledge the limits of logical reasoning and contend for epistemic humility in the task of argumentation. The final pages of the book contain a glossary of the key terms and concepts that the authors define in the book.
The Little Logic Book is a masterful text in the discipline of logic, but one may ask if there are any weaknesses in book about logical reasoning. Ultimately, there are no major weaknesses in the book, and there is no material in the book that diminishes the authors’ goals for the text. Yet, one minor weakness in the book is the authors’ use of visual formats for logical arguments. In a quick manner, the writers introduce the reader to many symbols for visual arguments in chapters 1, 2, and 4 of the work, but the use and combination of these symbols and visual arguments in the chapters on Modal Logic and Counterfactuals may be confusing for readers who learned about these symbols for the first time through reading the publication. The writers list a number of visual arguments with the newly introduced symbols in chapter 4 without any reminder or key for the meaning of each symbol (see, for example, 51). Thus, readers may find these visual arguments initially inaccessible, but this utilization of visual arguments is not a significant problem as readers may dispel their confusion through a review of previous chapters in the book.
Another minor weakness of the book is found in the authors’ discussion of counterfactuals. The writers acknowledge the “complications” and “difficulties” of their discussion on counterfactuals (78), but they could enhance their treatment of this subject with an extended explanation of how to consider and express a counterfactual due to the nonexistent nature of these scenarios (78). The writers dedicate space to valid and invalid counterfactuals (75–78), but novice readers may find the chapter incomplete and not know how to craft counterfactual arguments as readers do not know the source or limits of counterfactual ideas. However, due to the concise nature of the book, such an explanation may be beyond the scope of the chapter.
What are the strengths of The Little Logic Book? One strength of the book is the clarity of writing and style throughout the work. A work on the discipline of logic may be at risk of dense and extremely technical jargon that makes the book difficult to understand and follow. The book is for students and aspiring philosophers (see vii, 42), so the authors are careful not to assume the reader’s knowledge of any logical concept. Moreover, the end of each chapter contains a summary of the previous section of the book, and some chapters have brief introductions to the contents of the following chapter (see 42–43). These summaries allow the student to pause and reflect carefully on the essential materials of each chapter, and to understand why the authors move and choose to focus on the topics in the next chapters. In their discussion of affordability as a goal for their text on logic, the authors do not mention the need for a clear resource on the subject (vii), but the clarity of writing contributes to the authors’ goal as the book is accessible for all inquiring readers. They are correct in their assertion “that logic is not the exclusive property of professional logicians” (ix), so they do not write the book merely for professional logicians.
An additional strength of the book is the authors’ employment of logical exercises in certain chapters to aid students in acquisition of knowledge concerning a particular logical subject. For example, the chapter on Mill’s Methods contains an exercise that requires the student to compare the characters in the example and use the process of elimination to determine the cause of a problem (96–97). Additionally, in the chapter on Probabilities the authors list several questions involving probabilities and fallacies, then the next page contains the answer key to each question (113–114). Many academic books that introduce students to a discipline may contain exercises at the end of each chapter for the student to gain practical experience in the discipline or topic, and the consistent use and requirement of such exercises may become burdensome to certain readers. Nevertheless, the authors’ limited use of these exercises causes the exercises to feel like engaging and unique ways of learning the probabilities and Mill’s Methods for logical reasoning.
The tone of the book varies from academic summaries of logical and philosophical issues to informal illustrations about philosophers and the discipline of philosophy. The authors discuss the particulars of modal logic on one page, but also they are able to relate logical problems to culturally and personally relevant issues that students may appreciate (66). The clarity of certain chapters such as the discussion on Mill’s Methods will help the reader feel that she has a firm foundation for understanding this logical issue, and the brevity of the chapter may develop a desire to read mor extensive treatments of the logical issue. As an introductory work, the book should function as a gateway into more texts and studies on the discipline of logic. As a result of reading the book, students should be able to use basic skills in logical reasoning. As the authors point out, “Arguments are among the primary intellectual tools we use both in everyday life and in academic contexts” (2). Because of the inevitable use of argument in all areas of life, students should have a desire to sharpen this skill.
In conclusion, The Little Logic Book is a clear and concise book on the discipline of logic that will intrigue Christian readers and students. Yet, non-Christian readers may also find the book to be a helpful summary of key concepts in logical argumentation. The book is significant because of its accessibility for students who are inquiring about the subject of logic. The brevity and systematic nature of each chapter allows the book to function as a quick reference book for students who want revisit certain topics.
The Little Logic Book is about explanations of crucial logical concepts, so the authors are not focused on advancing an overall argument in each chapter of the book as they provide summaries to different topics. However, the reader may discern the authors’ thesis of the book in the preface the writers state the work’s threefold purpose: “first, affordability; second, some ethical reflection on the use of logic in argumentation; third, a balanced treatment of religious beliefs in the examples and exercises” (vii). This list is not an explicit thesis, but the authors contend that the discipline of logic should be accessible, ethical, and edifying for the Christian reader’s beliefs. The writers’ Christian convictions guide their view on logic as they believe in a close union between logical reasoning and Christian faith. The authors helpfully advance their argument for the discipline of logic as they structure the book around this threefold goal for a publication on logic. Their desire for faithful and virtuous logic shapes the explanations and examples of every chapter.
In chapters 1–3, the authors introduce the readers to the basic and complex logical notions of deductive arguments, truth tables, and quantification. The writers acclimate the readers to these topics with opening, illustrative, and ethically relevant argument between the characters of Rene, Andrea, and Melissa in each chapter (see ix). The authors develop the specific issue of propositional logic in these chapters as they focus on the “connectives” and “relations within simple propositions” (42). The chapters also contain visualizations of deductive arguments and truth tables which function as useful references for logical concepts that may confuse readers through simple and verbal descriptions.
Chapters 4–5 are about the elaborate topics of modal logic, then the authors transition to the more preliminary concept of inductive arguments in chapter 6. The authors arrange the book in such a manner that they do not progress from beginning issues to advanced notions. Rather, the chapters range in levels of academic difficulty concerning the discipline of logic. Chapter 4 is both a concise and systematic summary of modal logic as the authors’ primary concern is key terminology, visual forms, significance, and the uniqueness of modal logic (see 55). In chapter 5, the authors define the concept of counterfactuals: “Counterfactual reasoning typically deals with the implications of statements concerning states of affairs that, as far as we know, do not exist” (78). If chapter 4 is about the issue of truth (46), chapter 5 is about hypothetical reasoning. Furthermore, inductive arguments” are the “common” arguments about “a familiar pattern found in cases of some type, and projecting that pattern on a present case of that type” (88). Structure and validity are the crucial components of a deductive argument (5), but patterns and sound predictions are the components of an inductive argument.
The authors continue to explain distinct logical problems and questions in chapters 7–9 through the exemplary ethical and religious contentions of Andrea, Melissa, and Rene. Chapter 7 is about the determination of causation by John Stuart Mill’s Method (99). Chapter 8 is more technical as the authors explore the use of probability in logical argumentation. While this chapter is the most mathematical section of the book, the authors highlight the relevance of probabilities in all disciplines and areas of argumentation (102–103). The authors dedicate chapter 9 to the use of Analogical arguments. Through their discussion on these types of arguments, the authors show how an understanding of probability and induction impact the utilization of analogical arguments (128). While the authors discuss a plethora of logical problems throughout the publication, they are careful to show how certain logical issues factor into other matters of logic. The authors define analogical argumentation: “we consider two sets of cases we take to be similar in relevant respects and argue that a characteristic known to belong to one will likely belong to the other” (133–134). The reader may observe the inductive aspects of patterns and projections in this definition of analogous argumentation as one notes pattern between two cases (see 128).
In chapters 10–13, the authors introduce the reader to the fascinating and sobering concept of informal fallacies, explanations and their distinction from logical argumentation (153), the impact of logic on the discipline of scientific inference (167), and a concluding chapter on ethics in logic which contributes to the unique goal of the book (see viii). In the conclusion of chapter 13, the authors make an argument that functions as a fitting and closing reflection to the book: “The world is full of complexity and mystery. We desire to be wise, but we are not omniscient. Voldemort-like arrogance and claims to mastery of complete and final truth don’t fit us very well. We know, and yet we know in part” (201). The authors take care to acknowledge the limits of logical reasoning and contend for epistemic humility in the task of argumentation. The final pages of the book contain a glossary of the key terms and concepts that the authors define in the book.
The Little Logic Book is a masterful text in the discipline of logic, but one may ask if there are any weaknesses in book about logical reasoning. Ultimately, there are no major weaknesses in the book, and there is no material in the book that diminishes the authors’ goals for the text. Yet, one minor weakness in the book is the authors’ use of visual formats for logical arguments. In a quick manner, the writers introduce the reader to many symbols for visual arguments in chapters 1, 2, and 4 of the work, but the use and combination of these symbols and visual arguments in the chapters on Modal Logic and Counterfactuals may be confusing for readers who learned about these symbols for the first time through reading the publication. The writers list a number of visual arguments with the newly introduced symbols in chapter 4 without any reminder or key for the meaning of each symbol (see, for example, 51). Thus, readers may find these visual arguments initially inaccessible, but this utilization of visual arguments is not a significant problem as readers may dispel their confusion through a review of previous chapters in the book.
Another minor weakness of the book is found in the authors’ discussion of counterfactuals. The writers acknowledge the “complications” and “difficulties” of their discussion on counterfactuals (78), but they could enhance their treatment of this subject with an extended explanation of how to consider and express a counterfactual due to the nonexistent nature of these scenarios (78). The writers dedicate space to valid and invalid counterfactuals (75–78), but novice readers may find the chapter incomplete and not know how to craft counterfactual arguments as readers do not know the source or limits of counterfactual ideas. However, due to the concise nature of the book, such an explanation may be beyond the scope of the chapter.
What are the strengths of The Little Logic Book? One strength of the book is the clarity of writing and style throughout the work. A work on the discipline of logic may be at risk of dense and extremely technical jargon that makes the book difficult to understand and follow. The book is for students and aspiring philosophers (see vii, 42), so the authors are careful not to assume the reader’s knowledge of any logical concept. Moreover, the end of each chapter contains a summary of the previous section of the book, and some chapters have brief introductions to the contents of the following chapter (see 42–43). These summaries allow the student to pause and reflect carefully on the essential materials of each chapter, and to understand why the authors move and choose to focus on the topics in the next chapters. In their discussion of affordability as a goal for their text on logic, the authors do not mention the need for a clear resource on the subject (vii), but the clarity of writing contributes to the authors’ goal as the book is accessible for all inquiring readers. They are correct in their assertion “that logic is not the exclusive property of professional logicians” (ix), so they do not write the book merely for professional logicians.
An additional strength of the book is the authors’ employment of logical exercises in certain chapters to aid students in acquisition of knowledge concerning a particular logical subject. For example, the chapter on Mill’s Methods contains an exercise that requires the student to compare the characters in the example and use the process of elimination to determine the cause of a problem (96–97). Additionally, in the chapter on Probabilities the authors list several questions involving probabilities and fallacies, then the next page contains the answer key to each question (113–114). Many academic books that introduce students to a discipline may contain exercises at the end of each chapter for the student to gain practical experience in the discipline or topic, and the consistent use and requirement of such exercises may become burdensome to certain readers. Nevertheless, the authors’ limited use of these exercises causes the exercises to feel like engaging and unique ways of learning the probabilities and Mill’s Methods for logical reasoning.
The tone of the book varies from academic summaries of logical and philosophical issues to informal illustrations about philosophers and the discipline of philosophy. The authors discuss the particulars of modal logic on one page, but also they are able to relate logical problems to culturally and personally relevant issues that students may appreciate (66). The clarity of certain chapters such as the discussion on Mill’s Methods will help the reader feel that she has a firm foundation for understanding this logical issue, and the brevity of the chapter may develop a desire to read mor extensive treatments of the logical issue. As an introductory work, the book should function as a gateway into more texts and studies on the discipline of logic. As a result of reading the book, students should be able to use basic skills in logical reasoning. As the authors point out, “Arguments are among the primary intellectual tools we use both in everyday life and in academic contexts” (2). Because of the inevitable use of argument in all areas of life, students should have a desire to sharpen this skill.
In conclusion, The Little Logic Book is a clear and concise book on the discipline of logic that will intrigue Christian readers and students. Yet, non-Christian readers may also find the book to be a helpful summary of key concepts in logical argumentation. The book is significant because of its accessibility for students who are inquiring about the subject of logic. The brevity and systematic nature of each chapter allows the book to function as a quick reference book for students who want revisit certain topics.
February 1, 2019
I'm rating this book for what it is and not what it isn't. This is not a "big logic book," a textbook to be used over a semester. The authors note that at the beginning. The book lacks exercises, though they are available online should anyone be interested in testing their knowledge. What this book is is a relatively short introduction to logic. It provides brief, clear introductions to deductive arguments, truth tables, modal logic, counterfactuals, inductive arguments, probability, analogical arguments, informal logical fallacies, and more. It's written clearly and is about 200 pages long.
The book is pitched toward undergraduate students. The chapters begin with fictional conversations between a cast of undergraduate characters. This is meant to make the book more interesting and easier to digest. I could have skipped this. This feature reminds me of Bartholomew and Goheen's Christian Philosophy--the same kind of technique is used. That being said, the introductions were relatively short and didn't detract from the content.
This is a recommended resource for those beginning a study of logic. Frankly, we all need to be more logical.
The book is pitched toward undergraduate students. The chapters begin with fictional conversations between a cast of undergraduate characters. This is meant to make the book more interesting and easier to digest. I could have skipped this. This feature reminds me of Bartholomew and Goheen's Christian Philosophy--the same kind of technique is used. That being said, the introductions were relatively short and didn't detract from the content.
This is a recommended resource for those beginning a study of logic. Frankly, we all need to be more logical.
February 12, 2026
Maybe it was because I had to read the book faster than I should have because the Amazon delivery was late, but I was lost until maybe the fourth chapter. It felt like I was dropped into the middle of the content in the field of philosophical study, and having had no prior understanding, I was definitely lost for a little while. Very theoretical for someone new to the topic. Perhaps if I was more aware, I would enjoy it more. I found the samples helpful. I wish the introductory illustrations at the beginning of each chapter would have been carried throughout it's chapter.
April 18, 2020
Excellent book on logic. Small and short but incredibly informative. I would say intermediate level. The reader with some understanding of logic will benefit most.
October 26, 2020
Good intro.
December 18, 2020
Helpful, just very dry to read
February 3, 2026
Helpful and informative, just dry. Most like a text book than anything else.
February 9, 2026
Extremely dry with a whole bunch of jargon and unneeded use of equations to describe logic.
Displaying 1 - 9 of 9 reviews