meaning in logic and critical thinking

Introduction to Logic and Critical Thinking

(10 reviews)

Matthew Van Cleave, Lansing Community College

Copyright Year: 2016

Publisher: Matthew J. Van Cleave

Language: English

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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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Article • 8 min read

Critical Thinking

Developing the right mindset and skills.

By the Mind Tools Content Team

We make hundreds of decisions every day and, whether we realize it or not, we're all critical thinkers.

We use critical thinking each time we weigh up our options, prioritize our responsibilities, or think about the likely effects of our actions. It's a crucial skill that helps us to cut out misinformation and make wise decisions. The trouble is, we're not always very good at it!

In this article, we'll explore the key skills that you need to develop your critical thinking skills, and how to adopt a critical thinking mindset, so that you can make well-informed decisions.

What Is Critical Thinking?

Critical thinking is the discipline of rigorously and skillfully using information, experience, observation, and reasoning to guide your decisions, actions, and beliefs. You'll need to actively question every step of your thinking process to do it well.

Collecting, analyzing and evaluating information is an important skill in life, and a highly valued asset in the workplace. People who score highly in critical thinking assessments are also rated by their managers as having good problem-solving skills, creativity, strong decision-making skills, and good overall performance. [1]

Key Critical Thinking Skills

Critical thinkers possess a set of key characteristics which help them to question information and their own thinking. Focus on the following areas to develop your critical thinking skills:

Being willing and able to explore alternative approaches and experimental ideas is crucial. Can you think through "what if" scenarios, create plausible options, and test out your theories? If not, you'll tend to write off ideas and options too soon, so you may miss the best answer to your situation.

To nurture your curiosity, stay up to date with facts and trends. You'll overlook important information if you allow yourself to become "blinkered," so always be open to new information.

But don't stop there! Look for opposing views or evidence to challenge your information, and seek clarification when things are unclear. This will help you to reassess your beliefs and make a well-informed decision later. Read our article, Opening Closed Minds , for more ways to stay receptive.

Logical Thinking

You must be skilled at reasoning and extending logic to come up with plausible options or outcomes.

It's also important to emphasize logic over emotion. Emotion can be motivating but it can also lead you to take hasty and unwise action, so control your emotions and be cautious in your judgments. Know when a conclusion is "fact" and when it is not. "Could-be-true" conclusions are based on assumptions and must be tested further. Read our article, Logical Fallacies , for help with this.

Use creative problem solving to balance cold logic. By thinking outside of the box you can identify new possible outcomes by using pieces of information that you already have.

Self-Awareness

Many of the decisions we make in life are subtly informed by our values and beliefs. These influences are called cognitive biases and it can be difficult to identify them in ourselves because they're often subconscious.

Practicing self-awareness will allow you to reflect on the beliefs you have and the choices you make. You'll then be better equipped to challenge your own thinking and make improved, unbiased decisions.

One particularly useful tool for critical thinking is the Ladder of Inference . It allows you to test and validate your thinking process, rather than jumping to poorly supported conclusions.

Developing a Critical Thinking Mindset

Combine the above skills with the right mindset so that you can make better decisions and adopt more effective courses of action. You can develop your critical thinking mindset by following this process:

Gather Information

First, collect data, opinions and facts on the issue that you need to solve. Draw on what you already know, and turn to new sources of information to help inform your understanding. Consider what gaps there are in your knowledge and seek to fill them. And look for information that challenges your assumptions and beliefs.

Be sure to verify the authority and authenticity of your sources. Not everything you read is true! Use this checklist to ensure that your information is valid:

• Are your information sources trustworthy ? (For example, well-respected authors, trusted colleagues or peers, recognized industry publications, websites, blogs, etc.)
• Is the information you have gathered up to date ?
• Has the information received any direct criticism ?
• Does the information have any errors or inaccuracies ?
• Is there any evidence to support or corroborate the information you have gathered?
• Is the information you have gathered subjective or biased in any way? (For example, is it based on opinion, rather than fact? Is any of the information you have gathered designed to promote a particular service or organization?)

If any information appears to be irrelevant or invalid, don't include it in your decision making. But don't omit information just because you disagree with it, or your final decision will be flawed and bias.

Now observe the information you have gathered, and interpret it. What are the key findings and main takeaways? What does the evidence point to? Start to build one or two possible arguments based on what you have found.

You'll need to look for the details within the mass of information, so use your powers of observation to identify any patterns or similarities. You can then analyze and extend these trends to make sensible predictions about the future.

To help you to sift through the multiple ideas and theories, it can be useful to group and order items according to their characteristics. From here, you can compare and contrast the different items. And once you've determined how similar or different things are from one another, Paired Comparison Analysis can help you to analyze them.

The final step involves challenging the information and rationalizing its arguments.

Apply the laws of reason (induction, deduction, analogy) to judge an argument and determine its merits. To do this, it's essential that you can determine the significance and validity of an argument to put it in the correct perspective. Take a look at our article, Rational Thinking , for more information about how to do this.

Once you have considered all of the arguments and options rationally, you can finally make an informed decision.

Afterward, take time to reflect on what you have learned and what you found challenging. Step back from the detail of your decision or problem, and look at the bigger picture. Record what you've learned from your observations and experience.

Critical thinking involves rigorously and skilfully using information, experience, observation, and reasoning to guide your decisions, actions and beliefs. It's a useful skill in the workplace and in life.

You'll need to be curious and creative to explore alternative possibilities, but rational to apply logic, and self-aware to identify when your beliefs could affect your decisions or actions.

You can demonstrate a high level of critical thinking by validating your information, analyzing its meaning, and finally evaluating the argument.

Critical Thinking Infographic

See Critical Thinking represented in our infographic: An Elementary Guide to Critical Thinking .

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PHIL102: Introduction to Critical Thinking and Logic

Course introduction.

• Time: 40 hours
• College Credit Recommended ($25 Proctor Fee) -->
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The course touches upon a wide range of reasoning skills, from verbal argument analysis to formal logic, visual and statistical reasoning, scientific methodology, and creative thinking. Mastering these skills will help you become a more perceptive reader and listener, a more persuasive writer and presenter, and a more effective researcher and scientist.

The first unit introduces the terrain of critical thinking and covers the basics of meaning analysis, while the second unit provides a primer for analyzing arguments. All of the material in these first units will be built upon in subsequent units, which cover informal and formal logic, Venn diagrams, scientific reasoning, and strategic and creative thinking.

Course Syllabus

First, read the course syllabus. Then, enroll in the course by clicking "Enroll me". Click Unit 1 to read its introduction and learning outcomes. You will then see the learning materials and instructions on how to use them.

Unit 1: Introduction and Meaning Analysis

Critical thinking is a broad classification for a diverse array of reasoning techniques. In general, critical thinking works by breaking arguments and claims down to their basic underlying structure so we can see them clearly and determine whether they are rational. The idea is to help us do a better job of understanding and evaluating what we read, what we hear, and what we write and say.

In this unit, we will define the broad contours of critical thinking and learn why it is a valuable and useful object of study. We will also introduce the fundamentals of meaning analysis: the difference between literal meaning and implication, the principles of definition, how to identify when a disagreement is merely verbal, the distinction between necessary and sufficient conditions, and problems with the imprecision of ordinary language.

Completing this unit should take you approximately 5 hours.

Unit 2: Argument Analysis

Arguments are the fundamental components of all rational discourse: nearly everything we read and write, like scientific reports, newspaper columns, and personal letters, as well as most of our verbal conversations, contain arguments. Picking the arguments out from the rest of our often convoluted discourse can be difficult. Once we have identified an argument, we still need to determine whether or not it is sound. Luckily, arguments obey a set of formal rules that we can use to determine whether they are good or bad.

In this unit, you will learn how to identify arguments, what makes an argument sound as opposed to unsound or merely valid, the difference between deductive and inductive reasoning, and how to map arguments to reveal their structure.

Completing this unit should take you approximately 7 hours.

Unit 3: Basic Sentential Logic

This unit introduces a topic that many students find intimidating: formal logic. Although it sounds difficult and complicated, formal (or symbolic) logic is actually a fairly straightforward way of revealing the structure of reasoning. By translating arguments into symbols, you can more readily see what is right and wrong with them and learn how to formulate better arguments. Advanced courses in formal logic focus on using rules of inference to construct elaborate proofs. Using these techniques, you can solve many complicated problems simply by manipulating symbols on the page. In this course, however, you will only be looking at the most basic properties of a system of logic. In this unit, you will learn how to turn phrases in ordinary language into well-formed formulas, draw truth tables for formulas, and evaluate arguments using those truth tables.

Completing this unit should take you approximately 13 hours.

Unit 4: Venn Diagrams

In addition to using predicate logic, the limitations of sentential logic can also be overcome by using Venn diagrams to illustrate statements and arguments. Statements that include general words like "some" or "few" as well as absolute words like "every" and "all" – so-called categorical statements – lend themselves to being represented on paper as circles that may or may not overlap.

Venn diagrams are especially helpful when dealing with logical arguments called syllogisms. Syllogisms are a special type of three-step argument with two premises and a conclusion, which involve quantifying terms. In this unit, you will learn the basic principles of Venn diagrams, how to use them to represent statements, and how to use them to evaluate arguments.

Completing this unit should take you approximately 6 hours.

Unit 5: Fallacies

Now that you have studied the necessary structure of a good argument and can represent its structure visually, you might think it would be simple to pick out bad arguments. However, identifying bad arguments can be very tricky in practice. Very often, what at first appears to be ironclad reasoning turns out to contain one or more subtle errors.

Fortunately, there are many easily identifiable fallacies (mistakes of reasoning) that you can learn to recognize by their structure or content. In this unit, you will learn about the nature of fallacies, look at a couple of different ways of classifying them, and spend some time dealing with the most common fallacies in detail.

Completing this unit should take you approximately 3 hours.

Unit 6: Scientific Reasoning

Unlike the syllogistic arguments you explored in the last unit, which are a form of deductive argument, scientific reasoning is empirical. This means that it depends on observation and evidence, not logical principles. Although some principles of deductive reasoning do apply in science, such as the principle of contradiction, scientific arguments are often inductive. For this reason, science often deals with confirmation and disconfirmation.

Nonetheless, there are general guidelines about what constitutes good scientific reasoning, and scientists are trained to be critical of their inferences and those of others in the scientific community. In this unit, you will investigate some standard methods of scientific reasoning, some principles of confirmation and disconfirmation, and some techniques for identifying and reasoning about causation.

Completing this unit should take you approximately 4 hours.

Unit 7: Strategic Reasoning and Creativity

While most of this course has focused on the types of reasoning necessary to critique and evaluate existing knowledge or to extend our knowledge following correct procedures and rules, an enormous branch of our reasoning practice runs in the opposite direction. Strategic reasoning, problem-solving, and creative thinking all rely on an ineffable component of novelty supplied by the thinker.

Despite their seemingly mystical nature, problem-solving and creative thinking are best approached by following tried and tested procedures that prompt our cognitive faculties to produce new ideas and solutions by extending our existing knowledge. In this unit, you will investigate problem-solving techniques, representing complex problems visually, making decisions in risky and uncertain scenarios, and creative thinking in general.

Completing this unit should take you approximately 2 hours.

Study Guide

This study guide will help you get ready for the final exam. It discusses the key topics in each unit, walks through the learning outcomes, and lists important vocabulary terms. It is not meant to replace the course materials!

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Critical Thinking and Decision-Making  - What is Critical Thinking?

Critical thinking and decision-making  -, what is critical thinking, critical thinking and decision-making what is critical thinking.

Critical Thinking and Decision-Making: What is Critical Thinking?

Lesson 1: what is critical thinking, what is critical thinking.

Critical thinking is a term that gets thrown around a lot. You've probably heard it used often throughout the years whether it was in school, at work, or in everyday conversation. But when you stop to think about it, what exactly is critical thinking and how do you do it ?

Watch the video below to learn more about critical thinking.

Simply put, critical thinking is the act of deliberately analyzing information so that you can make better judgements and decisions . It involves using things like logic, reasoning, and creativity, to draw conclusions and generally understand things better.

This may sound like a pretty broad definition, and that's because critical thinking is a broad skill that can be applied to so many different situations. You can use it to prepare for a job interview, manage your time better, make decisions about purchasing things, and so much more.

The process

As humans, we are constantly thinking . It's something we can't turn off. But not all of it is critical thinking. No one thinks critically 100% of the time... that would be pretty exhausting! Instead, it's an intentional process , something that we consciously use when we're presented with difficult problems or important decisions.

Improving your critical thinking

In order to become a better critical thinker, it's important to ask questions when you're presented with a problem or decision, before jumping to any conclusions. You can start with simple ones like What do I currently know? and How do I know this? These can help to give you a better idea of what you're working with and, in some cases, simplify more complex issues.  

Real-world applications

Let's take a look at how we can use critical thinking to evaluate online information . Say a friend of yours posts a news article on social media and you're drawn to its headline. If you were to use your everyday automatic thinking, you might accept it as fact and move on. But if you were thinking critically, you would first analyze the available information and ask some questions :

• What's the source of this article?
• Is the headline potentially misleading?
• What are my friend's general beliefs?
• Do their beliefs inform why they might have shared this?

After analyzing all of this information, you can draw a conclusion about whether or not you think the article is trustworthy.

Critical thinking has a wide range of real-world applications . It can help you to make better decisions, become more hireable, and generally better understand the world around you.

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What Are Critical Thinking Skills and Why Are They Important?

Learn what critical thinking skills are, why they’re important, and how to develop and apply them in your workplace and everyday life.

We often use critical thinking skills without even realizing it. When you make a decision, such as which cereal to eat for breakfast, you're using critical thinking to determine the best option for you that day.

Critical thinking is like a muscle that can be exercised and built over time. It is a skill that can help propel your career to new heights. You'll be able to solve workplace issues, use trial and error to troubleshoot ideas, and more.

We'll take you through what it is and some examples so you can begin your journey in mastering this skill.

What is critical thinking?

Critical thinking is the ability to interpret, evaluate, and analyze facts and information that are available, to form a judgment or decide if something is right or wrong.

More than just being curious about the world around you, critical thinkers make connections between logical ideas to see the bigger picture. Building your critical thinking skills means being able to advocate your ideas and opinions, present them in a logical fashion, and make decisions for improvement.

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Why is critical thinking important?

Critical thinking is useful in many areas of your life, including your career. It makes you a well-rounded individual, one who has looked at all of their options and possible solutions before making a choice.

According to the University of the People in California, having critical thinking skills is important because they are [ 1 ]:

Crucial for the economy

Essential for improving language and presentation skills

Very helpful in promoting creativity

Important for self-reflection

The basis of science and democracy 

Critical thinking skills are used every day in a myriad of ways and can be applied to situations such as a CEO approaching a group project or a nurse deciding in which order to treat their patients.

Examples of common critical thinking skills

Critical thinking skills differ from individual to individual and are utilized in various ways. Examples of common critical thinking skills include:

Identification of biases: Identifying biases means knowing there are certain people or things that may have an unfair prejudice or influence on the situation at hand. Pointing out these biases helps to remove them from contention when it comes to solving the problem and allows you to see things from a different perspective.

Research: Researching details and facts allows you to be prepared when presenting your information to people. You’ll know exactly what you’re talking about due to the time you’ve spent with the subject material, and you’ll be well-spoken and know what questions to ask to gain more knowledge. When researching, always use credible sources and factual information.

Open-mindedness: Being open-minded when having a conversation or participating in a group activity is crucial to success. Dismissing someone else’s ideas before you’ve heard them will inhibit you from progressing to a solution, and will often create animosity. If you truly want to solve a problem, you need to be willing to hear everyone’s opinions and ideas if you want them to hear yours.

Analysis: Analyzing your research will lead to you having a better understanding of the things you’ve heard and read. As a true critical thinker, you’ll want to seek out the truth and get to the source of issues. It’s important to avoid taking things at face value and always dig deeper.

Problem-solving: Problem-solving is perhaps the most important skill that critical thinkers can possess. The ability to solve issues and bounce back from conflict is what helps you succeed, be a leader, and effect change. One way to properly solve problems is to first recognize there’s a problem that needs solving. By determining the issue at hand, you can then analyze it and come up with several potential solutions.

How to develop critical thinking skills

You can develop critical thinking skills every day if you approach problems in a logical manner. Here are a few ways you can start your path to improvement:

1. Ask questions.

Be inquisitive about everything. Maintain a neutral perspective and develop a natural curiosity, so you can ask questions that develop your understanding of the situation or task at hand. The more details, facts, and information you have, the better informed you are to make decisions.

2. Practice active listening.

Utilize active listening techniques, which are founded in empathy, to really listen to what the other person is saying. Critical thinking, in part, is the cognitive process of reading the situation: the words coming out of their mouth, their body language, their reactions to your own words. Then, you might paraphrase to clarify what they're saying, so both of you agree you're on the same page.

3. Develop your logic and reasoning.

This is perhaps a more abstract task that requires practice and long-term development. However, think of a schoolteacher assessing the classroom to determine how to energize the lesson. There's options such as playing a game, watching a video, or challenging the students with a reward system. Using logic, you might decide that the reward system will take up too much time and is not an immediate fix. A video is not exactly relevant at this time. So, the teacher decides to play a simple word association game.

Scenarios like this happen every day, so next time, you can be more aware of what will work and what won't. Over time, developing your logic and reasoning will strengthen your critical thinking skills.

Learn tips and tricks on how to become a better critical thinker and problem solver through online courses from notable educational institutions on Coursera. Start with Introduction to Logic and Critical Thinking from Duke University or Mindware: Critical Thinking for the Information Age from the University of Michigan.

Article sources

University of the People, “ Why is Critical Thinking Important?: A Survival Guide , https://www.uopeople.edu/blog/why-is-critical-thinking-important/.” Accessed May 18, 2023.

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This content has been made available for informational purposes only. Learners are advised to conduct additional research to ensure that courses and other credentials pursued meet their personal, professional, and financial goals.

Critical thinking definition

Critical thinking, as described by Oxford Languages, is the objective analysis and evaluation of an issue in order to form a judgement.

Active and skillful approach, evaluation, assessment, synthesis, and/or evaluation of information obtained from, or made by, observation, knowledge, reflection, acumen or conversation, as a guide to belief and action, requires the critical thinking process, which is why it's often used in education and academics.

Some even may view it as a backbone of modern thought.

However, it's a skill, and skills must be trained and encouraged to be used at its full potential.

People turn up to various approaches in improving their critical thinking, like:

• Developing technical and problem-solving skills
• Engaging in more active listening
• Actively questioning their assumptions and beliefs
• Seeking out more diversity of thought
• Opening up their curiosity in an intellectual way etc.

Is critical thinking useful in writing?

Critical thinking can help in planning your paper and making it more concise, but it's not obvious at first. We carefully pinpointed some the questions you should ask yourself when boosting critical thinking in writing:

• What information should be included?
• Which information resources should the author look to?
• What degree of technical knowledge should the report assume its audience has?
• What is the most effective way to show information?
• How should the report be organized?
• How should it be designed?
• What tone and level of language difficulty should the document have?

Usage of critical thinking comes down not only to the outline of your paper, it also begs the question: How can we use critical thinking solving problems in our writing's topic?

Let's say, you have a Powerpoint on how critical thinking can reduce poverty in the United States. You'll primarily have to define critical thinking for the viewers, as well as use a lot of critical thinking questions and synonyms to get them to be familiar with your methods and start the thinking process behind it.

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Module Four: Delivery of Demonstration Speeches

Critical thinking & reasoning: logic and the role of arguments.

Critical thinkers tend to exhibit certain traits that are common to them. These traits are summarized in Table 6.1: [1]

Recall that critical thinking is an active mode of thinking. Instead of just receiving messages and accepting them as is, we consider what they are saying. We ask if messages are well-supported. We determine if their logic is sound or slightly flawed. In other words, we act on the messages before we take action based on them. When we enact critical thinking on a message, we engage a variety of skills including: listening, analysis, evaluation, inference and interpretation or explanation, and self-regulation [2]

Next, we will examine each of these skills and their role in critical thinking in greater detail. As you read through the explanation of and examples for each skill, think about how it works in conjunction with the others. It’s important to note that while our discussion of the skills is presented in a linear manner, in practice our use of each skill is not so straightforward. We may exercise different skills simultaneously or jump forward and backward.

“ Martha Stewart ” by nrkbeta.  CC-BY-SA .

Without an open-minded mind, you can never be a great success. ~ Martha Stewart

In order to understand listening, we must first understand the difference between listening and hearing . At its most basic, hearing refers to the physiological process of receiving sounds, while listening refers to the  psychological process of interpreting or making sense of those sounds.

Every minute of every day we are surrounded by hundreds of different noises and sounds. If we were to try to make sense of each different sound we would probably spend our day just doing this. While we may hear all of the noises, we filter out many of them. They pass through our lives without further notice. Certain noises, however, jump to the forefront of our consciousness. As we listen to them, we make sense of these sounds. We do this every day without necessarily thinking about the process. Like many other bodily functions, it happens without our willing it to happen.

Critical thinking requires that we consciously listen to messages. We must focus on what is being said – and not said. We must strive not to be distracted by other outside noises or the internal noise of our own preconceived ideas. For the moment we only need to take in the message.

Listening becomes especially difficult when the message contains highly charged information. Think about what happens when you try to discuss a controversial issue such as abortion. As the other person speaks, you may have every good intention of listening to the entire argument.

However, when the person says something you feel strongly about you start formulating a counter-argument in your head. The end result is that both sides end up talking past each other without ever really listening to what the other says.

Once we have listened to a message, we can begin to analyze it. In practice we often begin analyzing messages while still listening to them. When we analyze something, we consider it in greater detail, separating out the main components of the message. In a sense, we are acting like a surgeon on the message, carving out all of the different elements and laying them out for further consideration and possible action.

Let’s return to Shonda’s persuasive speech to see analysis in action. As part of the needs section of her speech, Shonda makes the following remarks:

Americans today are some of the unhealthiest people on Earth. It seems like not a week goes by without some news story relating how we are the fattest country in the world. In addition to being overweight, we suffer from a number of other health problems. When I was conducting research for my speech, I read somewhere that heart attacks are the number one killer of men and the number two killer of women. Think about that. My uncle had a heart attack and had to be rushed to the hospital. They hooked him up to a bunch of different machines to keep him alive. We all thought he was going to die. He’s ok now, but he has to take a bunch of pills every day and eat a special diet. Plus he had to pay thousands of dollars in medical bills. Wouldn’t you like to know how to prevent this from happening to you?

If we were to analyze this part of Shonda’s speech (see Table 6.2), we could begin by looking at the claims she makes. We could then look at the evidence she presents in support of these claims. Having parsed out the various elements, we are then ready to evaluate them and by extension the message as a whole.

When we evaluate something we continue the process of analysis by assessing the various claims and arguments for validity. One way we evaluate a message is to ask questions about what is being said and who is saying it. The following is a list of typical questions we may ask, along with an evaluation of the ideas in Shonda’s speech.

Is the speaker credible?

Yes. While Shonda may not be an expert per se on the issue of health benefits related to wine, she has made herself a mini-expert through conducting research.

Does the statement ring true or false based on common sense?

It sounds kind of fishy. Four or more glasses of wine in one sitting doesn’t seem right. In fact, it seems like it might be bordering on binge drinking.

Does the logic employed hold up to scrutiny?

Based on the little bit of Shonda’s speech we see here, her logic does seem to be sound. As we will see later on, she actually commits a few fallacies.

What questions or objections are raised by the message?

In addition to the possibility of Shonda’s proposal being binge drinking, it also raises the possibility of creating alcoholism or causing other long term health problems.

How will further information affect the message?

More information will probably contradict her claims. In fact, most medical research in this area contradicts the claim that drinking 4 or more glasses of wine a day is a good thing.

Will further information strengthen or weaken the claims?

Most likely Shonda’s claims will be weakened.

What questions or objections are raised by the claims?

In addition to the objections we’ve already discussed, there is also the problem of the credibility of Shonda’s expert “doctor.”

A wise man proportions his belief to the evidence. ~ David Hume

Inference and Interpretation or Explanation

“Imply” or “Infer”?

For two relatively small words, imply and infer seem to generate an inordinately large amount of confusion. Understanding the difference between the two and knowing when to use the right one is not only a useful skill, but it also makes you sound a lot smarter!

Let’s begin with imply. Imply means to suggest or convey an idea. A speaker or a piece of writing implies things. For example, in Shonda’s speech, she implies it is better to drink more red wine. In other words, she never directly says that we need to drink more red wine, but she clearly hints at it when she suggests that drinking four or more glasses a day will provide us with health benefits.

Now let’s consider infer. Infer means that something in a speaker’s words or a piece of writing helps us to draw a conclusion outside of his/her words. We infer a conclusion. Returning to Shonda’s speech, we can infer she would want us to drink more red wine rather than less. She never comes right out and says this. However, by considering her overall message, we can draw this conclusion.

Another way to think of the difference between imply and infer is: A speaker (or writer for that matter) implies. The audience infers.

Therefore, it would be incorrect to say that Shonda infers we should drink more rather than less wine. She implies this. To help you differentiate between the two, remember that an inference is something that comes from outside the spoken or written text.

The next step in critically examining a message is to interpret or explain the conclusions that we draw from it. At this phase we consider the evidence and the claims together. In effect we are reassembling the components that we parsed out during analysis. We are continuing our evaluation by looking at the evidence, alternatives, and possible conclusions.

Before we draw any inferences or attempt any explanations, we should look at the evidence provided. When we consider evidence we must first determine what, if any, kind of support is provided. Of the evidence we then ask:

• Is the evidence sound?
• Does the evidence say what thespeaker says it does?
• Does contradictory evidenceexist?
• Is the evidence from a validcredible source?

Seatbelt by M.Minderhoud, CC-BY-SA .

Even though these are set up as yes or no questions, you’ll probably find in practice that your answers are a bit more complex. For example, let’s say you’re writing a speech on why we should wear our seatbelts at all times while driving. You’ve researched the topic and found solid, credible information setting forth the numerous reasons why wearing a seatbelt can help save your life and decrease the number of injuries experienced during a motor vehicle accident. Certainly, there exists contradictory evidence arguing seat belts can cause more injuries. For example, if you’re in an accident where your car is partially submerged in water, wearing a seatbelt may impede your ability to quickly exit the vehicle. Does the fact that this evidence exists negate your claims? Probably not, but you need to be thorough in evaluating and considering how you use your evidence.

A man who does not think for himself does not think at all. ~ Oscar Wilde

Self-Regulation

The final step in critically examining a message is actually a skill we should exercise throughout the entire process. With self-regulation, we consider our pre-existing thoughts on the subject and any biases we may have. We examine how what we think on an issue may have influenced the way we understand (or think we understand) the message and any conclusions we have drawn. Just as contradictory evidence doesn’t automatically negate our claims or invalidate our arguments, our biases don’t necessarily make our conclusions wrong. The goal of practicing self-regulation is not to disavow or deny our opinions. The goal is to create distance between our opinions and the messages we evaluate.

Man thinking on bus , by IG8. CC-BY .

The Value of Critical Thinking

In public speaking, the value of being a critical thinker cannot be overstressed. Critical thinking helps us to determine the truth or validity of arguments. However, it also helps us to formulate strong arguments for our speeches. Exercising critical thinking at all steps of the speech writing and delivering process can help us avoid situations like Shonda found herself in. Critical thinking is not a magical panacea that will make us super speakers. However, it is another tool that we can add to our speech toolbox.

As we will learn in the following pages, we construct arguments based on logic. Understanding the ways logic can be used and possibly misused is a vital skill. To help stress the importance of it, the Foundation for Critical Thinking has set forth universal standards of reasoning. These standards can be found in Table 6.3.

When the mind is thinking, it is talking to itself. ~ Plato

Logic and the Role of Arguments

“Sharia Law Billboard” by Matt57. Public domain.

We use logic every day. Even if we have never formally studied logical reasoning and fallacies, we can often tell when a person’s statement doesn’t sound right. Think about the claims we see in many advertisements today—Buy product X, and you will be beautiful/thin/happy or have the carefree life depicted in the advertisement. With very little critical thought, we know intuitively that simply buying a product will not magically change our lives. Even if we can’t identify the specific fallacy at work in the argument (non causa in this case), we know there is some flaw in the argument.

By studying logic and fallacies we can learn to formulate stronger and more cohesive arguments, avoiding problems like that mentioned above. The study of logic has a long history. We can trace the roots of modern logical study back to Aristotle in ancient Greece. Aristotle’s simple definition of logic as the means by which we come to know anything still provides a concise understanding of logic. [3] Of the classical pillars of a core liberal arts education of logic, grammar, and rhetoric, logic has developed as a fairly independent branch of philosophical studies. We use logic everyday when we construct statements, argue our point of view, and in myriad other ways. Understanding how logic is used will help us communicate more efficiently and effectively.

Defining Arguments

When we think and speak logically, we pull together statements that combine reasoning with evidence to support an assertion, arguments. A logical argument should not be confused with the type of argument you have with your sister or brother or any other person. When you argue with your sibling, you participate in a conflict in which you disagree about something. You may, however, use a logical argument in the midst of the argument with your sibling. Consider this example:

“Man and Woman Arguing” by mzacha. morgueFile .

Brother and sister, Sydney and Harrison are arguing about whose turn it is to clean their bathroom. Harrison tells Sydney she should do it because she is a girl and girls are better at cleaning. Sydney responds that being a girl has nothing to do with whose turn it is. She reminds Harrison that according to their work chart, they are responsible for cleaning the bathroom on alternate weeks. She tells him she cleaned the bathroom last week; therefore, it is his turn this week. Harrison, still unconvinced, refuses to take responsibility for the chore. Sydney then points to the work chart and shows him where it specifically says it is his turn this week. Defeated, Harrison digs out the cleaning supplies.

Throughout their bathroom argument, both Harrison and Sydney use logical arguments to advance their point. You may ask why Sydney is successful and Harrison is not. This is a good question. Let’s critically think about each of their arguments to see why one fails and one succeeds.

Let’s start with Harrison’s argument. We can summarize it into three points:

• Girls are better at cleaning bathrooms than boys.
• Sydney is a girl.
• Therefore, Sydney should clean the bathroom.

Harrison’s argument here is a form of deductive reasoning, specifically a syllogism. We will consider syllogisms in a few minutes. For our purposes here, let’s just focus on why Harrison’s argument fails to persuade Sydney. Assuming for the moment that we agree with Harrison’s first two premises, then it would seem that his argument makes sense. We know that Sydney is a girl, so the second premise is true. This leaves the first premise that girls are better at cleaning bathrooms than boys. This is the exact point where Harrison’s argument goes astray. The only way his entire argument will work is if we agree with the assumption girls are better at cleaning bathrooms than boys.

Let’s now look at Sydney’s argument and why it works. Her argument can be summarized as follows:

1. The bathroom responsibilities alternate weekly according to the work chart.

2. Sydney cleaned the bathroom last week.

3. The chart indicates it is Harrison’s turn to clean the bathroom this week.

4. Therefore, Harrison should clean the bathroom.

“Decorative toilet seat” by Bartux~commonswikiv. Public domain.

Sydney’s argument here is a form of inductive reasoning. We will look at inductive reasoning in depth below. For now, let’s look at why Sydney’s argument succeeds where Harrison’s fails. Unlike Harrison’s argument, which rests on assumption for its truth claims, Sydney’s argument rests on evidence. We can define evidence as anything used to support the validity of an assertion. Evidence includes: testimony, scientific findings, statistics, physical objects, and many others. Sydney uses two primary pieces of evidence: the work chart and her statement that she cleaned the bathroom last week. Because Harrison has no contradictory evidence, he can’t logically refute Sydney’s assertion and is therefore stuck with scrubbing the toilet.

Defining Deduction

Deductive reasoning refers to an argument in which the truth of its premises guarantees the truth of its conclusions. Think back to Harrison’s argument for Sydney cleaning the bathroom. In order for his final claim to be valid, we must accept the truth of his claims that girls are better at cleaning bathrooms than boys. The key focus in deductive arguments is that it must be impossible for the premises to be true and the conclusion to be false. The classic example is:

All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

We can look at each of these statements individually and see each is true in its own right. It is virtually impossible for the first two propositions to be true and the conclusion to be false. Any argument which fails to meet this standard commits a logical error or fallacy. Even if we might accept the arguments as good and the conclusion as possible, the argument fails as a form of deductive reasoning.

A few observations and much reasoning lead to error; many observations and a little reasoning to truth. ~ Alexis Carrel

Another way to think of deductive reasoning is to think of it as moving from a general premise to a specific premise. The basic line of reasoning looks like this:

“Deductive Reasoning” CC-BY-NC-ND .

This form of deductive reasoning is called a syllogism. A syllogism need not have only three components to its argument, but it must have at least three. We have Aristotle to thank for identifying the syllogism and making the study of logic much easier. The focus on syllogisms dominated the field of philosophy for thousands of years. In fact, it wasn’t until the early nineteenth century that we began to see the discussion of other types of logic and other forms of logical reasoning.

It is easy to fall prey to missteps in reasoning when we focus on syllogisms and deductive reasoning. Let’s return to Harrison’s argument and see what happens.

Logic: the art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. ~ Ambrose Bierce

“Applied Deductive Reasoning” CC-BY-NC-ND .

Considered in this manner, it should be clear how the strength of the conclusion depends upon us accepting as true the first two statements. This need for truth sets up deductive reasoning as a very rigid form of reasoning. If either one of the first two premises isn’t true, then the entire argument fails.

Let’s turn to recent world events for another example.

“US Invasion Deductive Reasoning Example” CC-BY-NC-ND .

In the debates over whether the United States should take military action in Iraq, this was the basic line of reasoning used to justify an invasion. This logic was sufficient for the United States to invade Iraq; however, as we have since learned, this line of reasoning also shows how quickly logic can go bad. We subsequently learned that the “experts” weren’t quite so confident, and their “evidence” wasn’t quite as concrete as originally represented.

Defining Induction

Inductive reasoning is often though of as the opposite of deductive reasoning; however, this approach is not wholly accurate. Inductive reasoning does move from the specific to the general. However, this fact alone does not make it the opposite of deductive reasoning. An argument which fails in its deductive reasoning may still stand inductively.

Unlike deductive reasoning, there is no standard format inductive arguments must take, making them more flexible. We can define an inductive argument as one in which the truth of its propositions lends support to the conclusion. The difference here in deduction is the truth of the propositions establishes with absolute certainty the truth of the conclusion. When we analyze an inductive argument, we do not focus on the truth of its premises. Instead we analyze inductive arguments for their strength or soundness.

“Inductive Reasoning Model” CC-BY-NC-ND .

Another significant difference between deduction and induction is inductive arguments do not have a standard format. Let’s return to Sydney’s argument to see how induction develops in action:

• Bathroom cleaning responsibilities alternate weekly according to the work chart.
• Sydney cleaned the bathroom last week.
• The chart indicates it is Harrison’s turn to clean the bathroom this week.
• Therefore, Harrison should clean the bathroom.

What Sydney does here is build to her conclusion that Harrison should clean the bathroom. She begins by stating the general house rule of alternate weeks for cleaning. She then adds in evidence before concluding her argument. While her argument is strong, we don’t know if it is true. There could be other factors Sydney has left out. Sydney may have agreed to take Harrison’s week of bathroom cleaning in exchange for him doing another one of her chores. Or there may be some extenuating circumstances preventing Harrison from bathroom cleaning this week.

You should carefully study the Art of Reasoning, as it is what most people are very deficient in, and I know few things more disagreeable than to argue, or even converse with a man who has no idea of inductive and deductive philosophy. ~ William John Wills

Let’s return to the world stage for another example. After the 9/11 attacks on the World Trade Center, we heard variations of the following arguments:

• The terrorists were Muslim (or Arab or Middle Eastern)
• The terrorists hated America.
• Therefore, all Muslims (or Arabs or Middle Easterners) hate America.

“1993 Word Trade Center bombing” by Bureau of ATF 1993 Explosives Incident Report. Public domain.

Clearly, we can see the problem in this line of reasoning. Beyond being a scary example of hyperbolic rhetoric, we can all probably think of at least one counter example to disprove the conclusion. However, individual passions and biases caused many otherwise rational people to say these things in the weeks following the attacks. This example also clearly illustrates how easy it is to get tripped up in your use of logic and the importance of practicing self-regulation.

• Adapted from Facione, P. A. (1990). Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction, The Delphi Report (Executive Summary) . Millbrae, CA: California Academic Press. ↵
• Adapted from Facione, P. A. (1990). ↵
• Aristotle. (1989). Prior Analytics (Trans. Robin Smith). Cambridge, MA: Hackett Publishing. ↵
• Image of man and woman arguing. Authored by : mzacha. Provided by : MorgueFile. Located at : http://mrg.bz/ynkIUa . License : All Rights Reserved . License Terms : Free to remix, commercial use, no attribution required. http://www.morguefile.com/license/morguefile
• Chapter 6 Logic and the Role of Arguments. Authored by : Terri Russ, J.D., Ph.D.. Provided by : Saint Mary's College, Notre Dame, IN. Located at : http://publicspeakingproject.org/psvirtualtext.html . Project : The Public Speaking Project. License : CC BY-NC-ND: Attribution-NonCommercial-NoDerivatives
• Martha Stewart nrkbeta. Authored by : nrkbeta. Located at : http://commons.wikimedia.org/wiki/File:Martha_Stewart_nrkbeta.jpg . License : CC BY-SA: Attribution-ShareAlike
• Seat belt BX. Authored by : M.Minderhoud. Located at : http://commons.wikimedia.org/wiki/File:Seat_belt_BX.jpg . License : CC BY-SA: Attribution-ShareAlike
• Man thinking in a bus. Authored by : IG8. Located at : https://www.flickr.com/photos/ig8/4295549232/ . License : CC BY: Attribution
• Sharia-Law-Billboard. Authored by : Matt57. Located at : http://commons.wikimedia.org/wiki/File:Sharia-law-Billboard.jpg . License : Public Domain: No Known Copyright
• Decorative toilet seat. Authored by : Bartux. Located at : http://commons.wikimedia.org/wiki/File:Decorative_toilet_seat.jpg%20 . License : Public Domain: No Known Copyright
• Image of 1993 World Trade Center bombing. Provided by : Bureau of ATF 1993 Explosives Incident Report. Located at : http://commons.wikimedia.org/wiki/File:WTC_1993_ATF_Commons.jpg . License : Public Domain: No Known Copyright

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19 Logic and Critical Thinking

Introduction [1].

This chapter is a primer on basic logical concepts that often appear in various critical thinking textbooks—concepts such as entailment, contraries, contradictories, necessary and sufficient conditions, etc. The chapter will not provide a historical genealogy of these concepts—in some sense critical thinking, argumentation theory, and formal logic all trace their roots back to at least Aristotle over two thousand years ago. As a result, for many of these concepts, determining whether the concept was a logic concept co-opted by critical thinking, or a critical thinking concept co-opted and changed by logic and then co-opted back again, is extremely difficult. Regardless, a brief orientation of the relationship of critical thinking and logic is in order.

Critical thinking, at least as it is most often justified, is a practical, skill-building exercise with the goal of improving our reasoning. This motivation, of understanding and improving our reasoning, has also been the motivation behind the development of logic over the past several thousand years. While we could study and understand each piece of reasoning individually, it is much more efficient to look for reasoning patterns that recur over and over again, to distinguish those patterns that are good from those that are bad, and so to find principles underpinning our reasoning that help us distinguish good reasoning from bad reasoning across the board. This push to generalize and theorize with the patterns of reasoning generated numerous formal logical systems, including the syllogistic and modal logics of Aristotle.

However, logic, especially formal logic, has not been constrained solely by the goal of understanding and improving our reasoning. Like abstract mathematics, the formal structures underpinning logical systems, are rich and complex enough to generate study all their own, with no concern for the original motivation that may have pushed us to study patterns of human reasoning. Regardless, many of logic’s concepts are still useful in organizing any study of reasoning.

In what follows I begin with a fairly substantial discussion of the core concept needed to understand the traditional logical concepts such as entailment or contradictory or necessary condition—the concept of a possibility. Once we have this notion in play, the definitions of the standard logical concepts, which I provide in Section 2, are quite straightforward. In the final section, I discuss the potential for misapplication of various concepts or distinctions.

1. Possibilities

1.1 possibility and reasoning.

The core concept of logic is the concept of a possibility (a case, a scenario, an option, a way things could be). While logicians and philosophers continue to work on illuminating the nature of possibilities, we can, even without a precise definition, still intuitively grasp the notion. You could stop reading right now or you could keep going. England didn’t win, but England could have won, if they had scored their penalty kick. That die, when rolled, will land on one of six possible sides. There are many things that might happen if the bill is passed into law. According to 18th century philosopher Gottfried Leibniz, God surveyed all the possible ways the universe might be and, being omnibenevolent, chose to create the best one (this one!?).

We appeal to possibilities all the time in our reasoning. Indeed, if there were but one way things could be and we knew completely what that way was like, then we would not need to reason at all—we would just know how things were going to unfold. But given that (i) we do not know completely how things are or how the future is going to unfold and (ii) we assume there are multiple possibilities for how the future might unfold, we need to reason about the ways things could be in order to learn how things are and how to best manage whatever the future brings. For example, the detective investigating a suspicious death gets a new piece of evidence—the deceased was killed by a rare poison. As a result, some scenarios are closed off as viable explanations of the death—e.g., the deceased was deliberately killed by someone who did not have access to the poison. Other scenarios, ones that may not have been in the detective’s awareness before the new piece of evidence was acquired, become relevant—e.g., that someone who knew or at least had access to the poison was responsible for the death. As a result, a new line of inquiry opens for the detective: find out who had access to the poison. Similarly, a doctor runs a series of tests to try to eliminate certain possible explanations for a given patient’s symptoms. Given certain results the possible explanations get narrowed down to one (and hopefully a treatment is available); given other results multiple possibilities remain and the doctor has to decide which tests may be required for progress to be made; unexpected results, while eliminating some possibilities may open up new possibilities that the doctor had not originally been considering. Finally, you are trying to decide when and in which order to run a list of errands. You take into account the likely lines at each location at different times of day, and the likely traffic at different times of day. After evaluating the possibilities, you choose the best option for you.

1.2 Types of possibil i ties

1.2 .1 physical & epistemic possibilities.

Given the ubiquity of possibilities in our reasoning, theorists often classify the possibilities. For example, physicists are interested in distinguishing the physical possibilities (the possibilities consistent with the laws of physics) from the physical impossibilities (the possibilities inconsistent with the laws of physics). Other general types of possibilities include epistemic possibilities—scenarios consistent with what we know; moral possibilities—those consistent with a given moral code; legal possibilities—situations consistent with what is permitted by a given legal code. We can even combine these types—epistemic physical possibilities are those that are consistent with the laws of physics as we currently know them. If what we know about the world changes at a fundamental level, what once was epistemically physically possible (measuring time independently of motion or gravity) may become epistemically physically impossible. Like for the detective and the doctor above, new, unexpected evidence may require an adjustment by the scientist in what possibilities are under consideration as viable explanations.

1.2 .2 Equally probable possibilities

Two other sorts of possibilities deserve mention. Probabilistic reasoning depends on possibilities of a very special sort—equally probable possibilities. To determine the probability that a fair coin will come up heads we assume that there are two equally likely possibilities, “heads’’ and “tails” (we usually ignore the extremely unlikely, though still physically possible situation in which the coin lands and stays on its edge). Failing to consider the relevant equally likely possibilities can make our probabilistic reasoning go awry. You will either win the lottery or you will not. There are two possibilities here, but treating them as equally likely is certainly an obvious mistake. Assuming the lottery is fair, the relevant equally likely possibilities are that each individual ticket (or set of numbers) will be the winner. If your ticket is one of many, then the probability you will win the lottery is much lower than the probability of your losing. Less obvious, but equally problematic is the following sort of case:

Three drawers contain the following mixture of coins—one contains two gold coins, one contains two silver coins, and one contains one gold coin and one silver coin. Without looking you pick a drawer, open it, and pick out a coin. When you open your eyes, you see the coin is gold. What is the probability that the other coin in that drawer is gold?

Many will reason as follows. The coin came from either the gold/gold drawer or the gold/silver drawer. Each drawer is equally likely and if it came from the gold/gold drawer the other coin is gold. But if it came from the gold/silver drawer the other coin is silver. Hence, the probability the other coin is gold is ½ or 50%. Unfortunately, the two possible drawers are not the relevant equally likely possibilities (no more than your winning or losing were the relevant equally likely possibilities in the lottery case). The relevant possibilities are opening a drawer and picking out a coin without looking. There are six different equally likely ways that could happen, one for each coin. Once you gain the new evidence that the coin you picked is gold when you open your eyes, you can eliminate three of the six possibilities, i.e. the ones in which you pick a silver coin. Of the three possibilities left two are such that the other coin is gold, i.e., the two possibilities in which you pick one of the two coins from the gold/gold drawer. Only in the gold/silver case is the other coin silver. Hence, the probability of the other coin being gold is 2/3. The moral here is that accurate probabilistic reasoning requires identifying and using the relevant equally likely possibilities from amongst all the sorts of possibilities that may present themselves—not always an easy task.

1.2 .3 Practical possibilities

Another significant type of possibility, especially in our everyday reasoning, is practical possibility—possibilities that are consistent with our means, desires, and will (or perhaps our epistemic practical possibilities—the possibilities that, given what we know or believe, are consistent with our means, desires, and will). When deciding how to get to an important meeting across town you are likely to not even consider the possibility that you flap your arms and fly, or the possibility that you use your personal matter/energy transport device, or even the possibility that you sprint all the way there. The first is physically impossible; the second, while perhaps physically possible, is beyond our current technological means; and the third, while certainly physically possible, is quite likely beyond your will and most certainly contrary to your strong desire to not arrive at the important meeting sweating profusely and gasping for breath. Instead you consider what your actual transportation options are (your own car, Uber, taxi, walk, subway, or some combination), how much time you have, how much money you are willing to spend, and then you try to find the optimal possibility (usually constrained by the desire to not spend too much time actually calculating the optimal possibility). Mundane decisions about which possibility to actualize like this happen all the time: what to eat this week, which movie to go see, what to do after dinner, when to get your hair cut, etc. Though mundane, they are still of interest to critical thinking or argumentation theorists since businesses and advertisers spend billions of dollars and devote millions of work-hours to trying to influence your desires and will in order to persuade you to choose their product.

Of more social significance are your individual choices that impact larger groups—in particular (if you live in a democracy) your voting choices, your decisions about how much effort you put into monitoring the outcome of your voting choices, and what the individuals or policies you voted for end up doing. In an optimal world, your political representatives would enact policies that benefit the most people in the most cost efficient, affordable, and just way. Of course, there may be little agreement about what is the most affordable, or just, or beneficial option, especially if what elected representatives take to be the best option is what will get them re-elected rather than what is actually good for their constituents. Regardless of the complexities and intricacies of public policy debate and decision-making, at the core is an attempt to find and agree upon a practical possibility, from amongst the myriad available, to actualize for our mutual benefit.

Given so many types of overlapping sets of possibilities, many of which differ for different individuals or groups of individuals—your set of practical possibilities does not likely match that of your neighbor even if the two sets overlap significantly; compare your set with someone of quite different socio-economic means and the sets overlap even less—and it is no surprise that numerous problems can arise when reasoning with and about possibilities. Individuals can consider too many possibilities, or more commonly, fail to consider all the relevant possibilities. For example, human beings are quite prone to confirmation bias—taking confirming instances as justifying an already-accepted theory or explanation rather than actively seeking out or testing for disconfirming instances. Detectives, or doctors, or researchers can become so fixated on the explanation they already believe to be correct that they are blind to the alternate explanations that are still consistent with the evidence available. In the case of probabilistic reasoning, we already saw cases of considering the wrong set of possibilities. Reasoners can also illegitimately shift the set of possibilities under consideration or shift the value assigned to various possibilities mid-reasoning. An egregious example can occur in public policy debates over the negative consequences of potential policies. When negative consequence X is a potential consequence of the opposition’s preferred policy it is judged to be likely enough to count as a reason against the policy, but when negative consequence X is a potential consequence of one’s own preferred policy, it is judged not to be likely enough to count as a reason against the policy. Identifying the correct set of possibilities and correct relative values of those possibilities is essential to reasoning correctly in numerous situations and yet identifying and ranking possibilities is often an extremely difficult task.

1.2 .4 Logical possibilities

One way to try to sidestep some of these problems is to determine what reasoning holds no matter what the possibilities in question are—to determine the patterns of reasoning that work in all the possibilities. After all, if a piece of reasoning works no matter what possibility you are considering, then you do not need to worry whether you are considering the right set of possibilities or not. Hence, one goal of formal logic is to be able to identify the structure that defines all the ways things could be, i.e., the logical possibilities.

The rough and ready notion of a “logical possibility” is a possibility that has no contradiction in it. Whilst it is not logically possible for an individual to both exist at a particular time and place and not exist at that time and place, which is contradictory, it is logically possible that the person exist in Montana in one instant, and then exist on one of the moons of Jupiter, say Io, in the next. There is no contradiction in the possibility that you exist in Montana in one instant and on Io in the next. But this possibility, while logically possible, is not physically possible. Given the distance from Montana to Io, we would need to violate the physical restriction on moving matter or energy (currently travelling below the speed of light) faster than the speed of light to get from Montana to Io from one instant to the next, so such travel is physically impossible.

Earlier I said that philosophers are still investigating and debating the nature of possibilities. But, whatever they are, there is one actualized one and lots of unactualized ones. In Leibniz’s argument that this world is the best of all possibilities, God examines all the possibilities and then actualizes the best one. Even if you doubt Leibniz’s argument, of all the myriad ways this universe could be, it is in fact one way, namely, the possibility that is actualized. The detective has numerous possibilities in mind about who is responsible for the deceased’s death; the detective hopes that by finding more evidence the possibilities can be reduced to one, the actual one. When you are deciding what to do tomorrow, you consider numerous possibilities and then engage in actions that make one (hopefully the one you wanted) actual.

But since there are lots of unactualized possibilities and only one actual possibility, how do we distinguish the unactualized possibilities from each other? Quite simply by what is true and false at each possibility. I flip a coin twice. There are four possible outcomes. Heads for the first flip and heads for the second; heads for the first and tails for the second; tails for the first, and heads for the second; and tails for both. Suppose the coin comes up tails on the first and heads on the second—that is the possibility that got actualized. How do we distinguish the three non-actualized possibilities? Well, in the first and second it is true that the coin first came up heads, but in fourth it is false that the coin first came up heads. But possibilities one and two differ in what is true and false of the second coin flip.

1.3 Declarative sentences and propositions

Given that we distinguish possibilities by what is true and false if they are actualized, one proposal for understanding possibilities is just as sets of declarative sentences. For example, the first coin flip possibility would be the set {“the first flip of the coin came up heads”, “the second flip of the coin came up heads”}. While initially appealing, the problem with this proposal is that sentences are not as well behaved as is needed to demarcate possibilities. Why?

Sometimes different sentences describe the same possibility or state of affairs. For example, “George is a bachelor” and “George is an unmarried male of marriageable age” describe the same state of affairs, but are different sentences since they are composed of different words. But since they are different sentences, sets that differ only in regards to which of these two sentences they contain are still different sets, and so different possibilities. Yet, we agreed the sentences were just two different ways of talking about the same possibility.

Alternatively, sometimes the same sentence can be used in different ways to describe different possibilities. For example, the sentence “The movie was a bomb” used in the United States likely describes a state of affairs in which the movie was bad, but the same sentence used in the United Kingdom likely describes a state of affairs in which the movie was good. But if one sentence can be used in different ways to describe different possibilities, then, once again, we cannot identify possibilities merely with sets of sentences.

To avoid the vagaries of sentences, logicians usually resort to propositions—what it is that declarative sentences express. “George is a bachelor” and “George is an unmarried male of marriageable age” express the same proposition about George’s marital status. “England won the World Cup in 1966” expresses a true proposition about the English national soccer team; “2+2 = 5” expresses a false proposition about the sum of 2 and 2. We use declarative sentences to express propositions directly, but other language use often involves them. For instance, when we ask, “did Hungary win the World Cup in 1938?” we wonder whether the proposition that Hungary won the 1938 World Cup is true or false. If we get the correct answer (they did not win—they lost to Italy 4-2 in the finals), then we stop wondering whether it is true or false and start believing it is false (and if the belief if strong enough and acquired in the correct way, we might even know that the proposition is false).

Instead of treating possibilities as sets of sentences, many logicians treat possibilities (or at least model possibilities) as sets of propositions. There are technical details that might require modifying even this proposal, but since the resolution of these details is unlikely to be relevant to the critical thinking project, we can take possibilities to be sets of propositions. The propositions that are members of a particular possibility are said to be true or obtain at that possibility. Propositions that are not members of a particular possibility are false at that possibility or do not obtain at that possibility. Armed with the concepts of (i) a possibility and (ii) propositions being true at or obtaining at possibilities, we can define many of the logical concepts that pervade logic and critical thinking textbooks. So even though some of the logical concepts that are forthcoming are, in some textbooks, defined in terms of sentences, the more common way is to define them in terms of propositions.

2. Logical concepts

2.1 types of propositions.

I begin by discussing some common types of propositions that arise in our reasoning. The most basic is a simple proposition, propositions expressed by such declarative sentences as “George is a bachelor” or “the sky is blue” or “Romeo loves Juliet.” Simple propositions attribute something to some object(s) or thing(s). In the first case, of George, that he is a bachelor, and in the third case, of Romeo, that he loves another object, namely Juliet. N egations of simple propositions, propositions expressed by such declarative sentences as “George is not a bachelor” or “Hungary did not win the 1938 World Cup” say that the simple proposition does not obtain. Of course, we do not speak declaratively solely by affirming either simple propositions or the denial of simple propositions; we combine or modify our simple propositions such as in:

• “George is a bachelor, and so is Todd”;
• “Mary loves Antonio, but he does not love her back”;
• “George went to Sophie’s house or he went to the movies”;
• “If the butler did not do it, then the cook did”;
• “If I take the subway, I will be on time for my meeting”;
• “Every student in this class is eligible”;
• “Someone deliberately killed the deceased”;
• “In order to be on time for your meeting, you must take the subway”;
• “England did not win the game, but they might have if they had scored their penalty kick in the last minute.”

The first two sentences express conjunctions . For a conjunction to be true, both sub-parts of the conjunction have to be true. So for “George is a bachelor and so is Todd” to be true, both “George is a bachelor” and “Todd is a bachelor” must be true. [For ease of exposition I will often omit the phrase “the proposition expressed by” before mentioning sentences as I just did above.]

The sentence “George went to Sophie’s house or he went to the movies” expresses a disjunction. There are two sorts of disjunctions—inclusive and exclusive. For an inclusive disjunction to be true, at least one of the sub-parts must be true. For an exclusive di s junction to be true, exactly one of the sub-parts must be true. If our sentence about George expresses an exclusive disjunction, then for it to be true George needs to be in exactly one of two places—at Sophie’s house or at the movies. This is likely to be the usage of someone trying to tell us where George is at a particular moment. If, on the other hand, the sentence expresses an inclusive disjunction, then it will be true if George went to one of those locations and is still true if George went to both. This is likely to be the usage of someone just trying to lay out where George might have gone over a period of time. While some languages have different words for expressing inclusive and exclusive disjunctions. English relies on context or background knowledge, sometimes with limited success, to try to distinguish which type of disjunction is being expressed. Legal documents, in order to avoid the ambiguity of ‘or’ in English, often spell out exclusive disjunctions as “A or B and not both A and B” while representing inclusive disjunctions as “A and/or B”.

Sentences such as: “ If the butler did not do it, then the cook did” and “ If I take the subway, [ then ] I will be on time for my meeting,” express onditional propositions. Conditionals are frequently used in natural languages such as English, yet there is little agreement on how they are to be analyzed logically. (Some theorists even go so far as to deny that conditional sentences express propositions at all.) Usually the disagreement concerns determining exactly what it takes for conditionals to be true, but there is widespread agreement that declarative conditionals are false if the ‘if’­–part, the antecedent , is true, and the ‘then’–part, the consequent , is false. If it is true that I take the subway, and false that I will be on time for my meeting, then the conditional “If I take the subway, I will be on time for my meeting,” is false. As a consequence, logic has defined a minimal version of the conditional, called the material conditional . Material conditionals are false if the antecedent is true and the consequent is false, but true otherwise—in other words, material conditionals are the most permissive when considering what it takes for a conditional to be true. There has been much debate about whether indicative conditionals such as “If the butler did not do it, then the cook did” just express material conditionals or rather express something stronger. Despite the disagreement, the most common articulation of conditionals in introductory logic texts is in terms of material conditionals, and it is most often this sort of conditional that is coopted into critical thinking texts. One merely needs to keep in mind that the work on understanding conditionals is far from finished.

“ Every student in this class is eligible” expresses a universal proposition—a proposition that attributes something to every member of a specified group. For a universal proposition to be true there can be no instance of a member of the group not having the specified attribute. If “Every student in this class is eligible” is true, then there is no student in the class who is not eligible. Oftentimes the group is not fully identified in the sentence used to express the proposition. For example, saying “All the beer is in the fridge” or “All horses have heads” are unlikely to be taken as expressing that every single beer in the universe is in a particular fridge or that there is no single instance of a headless horse anywhere. Depending on the context of use, likely plausible interpretations of those sentences would be: “All the beer we brought home from the store (and which has not already been drunk) is in the fridge” and “Typical, normal live horses have heads.” But once the group is fully specified, for a universal proposition to be true, every member of the group must have the attributed property or properties.

Instead of saying that everything in a given group has a stated attribute, we often merely want to convey that at least one thing or some things in the group have a particular property as in “Someone deliberately killed the deceased.” Such propositions are existential propositions. They are true when at least one object in a specified group has a specified attribute. For example, “Some student is eligible” is true just so long as at least one student is indeed eligible.

So far, most of our examples of propositions can be true or false given a single possibility. Suppose we restrict ourselves to just the actual possibility—then it is either true that George is a bachelor at the actual possibility or it is not; if, at the actual possibility, there is no student in the class who is not eligible, then the universal “Every student in class is eligible” is true at the actual possibility and otherwise false. But some of our declarative sentences are not just about one possibility; rather, they depend on multiple possibilities. Sentences such as the last two on our list, which express modal propositions are examples. (They are called “modal” because expressions such as “must”, “can”, “might”, “would”, etc., were said to indicate the “mode” of the component proposition.)

Different modal expressions have different truth conditions. Consider, for example, the sentence—“In order to be on time for your meeting you must take the subway.” For it to be true, all the possible ways (probably some set of practical possibilities constrained by the background in which the sentence is uttered) in which you make the meeting on time include your taking the subway. In the case of England losing, but winning if they’d scored their penalty, the first part is a negation that is true just so long as England won is false. So the first part tells us what the actual possibility is like. But the second part tells us what the relevantly similar possibilities except for England scoring their penalty, are like—namely, that England won in at least one of those possibilities. Compare that with the stronger claim that England would have won if they had scored their penalty—that claim will be true just so long as England wins in all the relevantly similar possibilities. (Part of the debate about conditionals is whether even conditionals without explicit modal terms, such as ‘might’ or ‘would’ or ‘must’, etc. are really expressing propositions concerning multiple possibilities, and not just the actual one—again, a debate I will not be able to resolve here.)

This list is not at all meant to be exhaustive of the type of propositions we express via our declarative sentences. Rather, it is meant to give a flavor for the sorts of propositions dealt with in first and second logic courses, the sorts of propositions that logicians attempt to model and define clearly and precisely in their basic systems. Why are logicians interested in these sorts of propositions? Because they show up in many of the reasoning patterns that we use over and over. For example, if I tell you George is either at Sophie’s or at the movies, and you tell me he is not at movies, we both hopefully reason that we should check for George at Sophie’s house. Another example: If the IRS says that all taxpayers satisfying their three specified conditions can claim a particular deduction, and you determine that you satisfy those three conditions, you should reason that you can take that particular deduction. It is by recognizing these types of propositions, and the patterns that result in combining them, that formal logic, which focuses on the patterns, gets its impetus. But regardless of whether one is focusing on the goodness of patterns or more generally on the patterns and content of reasoning, both critical thinking theorists and logicians need to take special care in determining what proposition a given sentence in a particular context expresses, for without understanding the correct proposition we will not be considering and evaluating the correct possibilities.

Even though understanding and classifying what propositions various declarative sentences express is an ongoing project, there is another classification scheme that logicians often appeal to—necessary truths (also called tautologies), necessary falsehoods (also called contradictions), and contingent propositions. The definitions are as follows:

Necessary Truth : A proposition that is true in all possibilities.

Necessary Falsehood : A proposition that is false in all possibilities.

Contingent Proposition : A proposition that is true in some, but not all, possibilities.

Sentences such as: “Either Socrates corrupts the youth of Athens or he does not”, or “If it is raining, then it is raining” express necessary truths. For every possibility there is, either Socrates corrupts the youth of Athens in that possibility or he does not. Some have wondered if there any non-trivial tautologies, since the standard examples, such as the ones I just gave, seem to be pretty trivial, uninformative sentences. Many theoreticians hold that the truths of mathematics are all necessary truths and many of those truths are certainly non-trivial—they often take a lot of work for us to know that they are true. Others point out that even if many necessary truths seem trivial or uninformative, they are still very useful. Plato, for example, uses the Socrates sentence in part of his dialogue concerning whether Socrates should have been found guilty of a particular offense. Plato starts with the obvious truth that either Socrates corrupts the youth or he does not, but proceeds to argue that in either case, Socrates should not be found guilty.

Sentences such as “At a particular moment in time, Socrates is over six-feet tall and Socrates is not over six-feet tall” express necessary falsehoods. For any possibility, and any moment of time in that possibility, Socrates cannot be both over six-feet tall and not over six-feet tall. Necessary falsehoods, or contradictions as they are more commonly called, are useful as sign-posts of something having gone drastically wrong in our reasoning. If we can show that someone’s position contains or leads to a contradiction, then we show that they aren’t even talking about a genuine possibility at all, but rather an impossibility. Good reasoners generally want to avoid being committed to impossibilities, so they try to avoid being committed to contradictions in their reasoning.

Most of the propositions we deal with in our everyday reasoning are contingent ones. “The coin landed heads on the first flip” is true in some possibilities, but false in others. “George will arrive on time” is true in some, but false in others. Even complex propositions, such as “If I take the subway, I will make it to the meeting on time” are likely to be true in some possibilities (smooth running reliable subway system) and false in others (an unreliable or scanty subway system). The challenge for good reasoners, of course, is to try to figure out, on the basis of what we already know, and the acquisition of new evidence, which propositions are in fact true at the actual possibility and which are not true. The detective, the doctor, the scientist, the everyday reasoner, are all reasoning using various possibilities in order to try to determine which propositions are true or false at the actual possibility.

2.2 Relations amongst propositions

Given that reasoning is the moving from given propositions to other propositions, and logicians are trying to understand correct reasoning, many of the important concepts of logic concern not just types of propositions, but the relations amongst propositions, I finish this section with definitions, examples, and discussion of eight such relations.

Necessary condition

One proposition, A , is a necessary condition for another propos i tion , B, if there is no possibility in which B obtains and A does not.

If A is a necessary condition for B, then you cannot have B without A. For example, if it is true that meeting the eligibility requirements is a necessary condition for legitimately holding office, then there is no possibility in which one legitimately holds office and does not meet the eligibility requirements. But if it is false that meeting the eligibility requirements is a necessary condition for legitimately holding office, then there is at least one possibility in which one legitimately holds office and does not meet the eligibility requirements.

Sufficient condition

One proposition, A , is a sufficient condition for another propos i tion B, if there is no possibility in which A obtains and B does not.

If A is a sufficient condition for B, then A guarantees B. For example, if it is true that getting a perfect score on every assessment is sufficient for passing the course, then there is no possibility in which one gets a perfect score on every assessment and one does not pass the course. If it is false, then there is at least one possibility in which one gets a perfect score on every assessment and still does not pass the course.

In many elementary logic or critical thinking textbooks, necessary and sufficient conditions are treated as material conditionals. For example, “George attending class is sufficient for George passing the course” is treated as “If George attends class, then George passes the course.” But necessary and sufficient conditions cannot be material conditionals, since denying a sufficient or necessary condition is not the same as denying a material conditional. For example, saying “George attending class is not sufficient for George passing” is not the same as denying the material conditional “If George attends class, then George passes the course” is true. Denying the material conditional is just saying that it is actually the case that George attends class, but does not pass the course, i.e., that the antecedent is true and the consequent is false. But denying that George’s attending is sufficient for George’s passing is not saying that George attends and does not pass, but rather says that there is a possibility, not necessarily the actual one, in which George attends, but does not pass. In other words, necessary and sufficient conditions are describing what is true of a range of possibilities.

Equivalence

Two propositions are equivalent just so long as there is no poss i bility in which one is true and the other is false .

In other words, for each possibility, the two propositions are either both true or both false. For example, “All Euclidean triangles have three sides” and “All Euclidean triangles have three interior angles” are both true in all possibilities and false in none, so they are logically equivalent to each other. Similarly, “Either Peter failed to make the team or Abigail failed to make the team” is logically equivalent to “Abigail and Peter did not both make the team.” If the first proposition is true, then, on an inclusive disjunction reading, at least one of the two did not make the team, so it is true that they did not both make the team. If on the other hand the first proposition is false, then it is false Pater failed to make the team (and so made it) and it is false Abigail failed to make the team (and so also made it), in which case both made the team and the second proposition is also false. Since the propositions are true in the same possibilities and false in the same possibilities they are logically equivalent.

Equivalence of proposition is not to be confused with the equivalence of sentences. Two sentences are equivalent, such as “George is a bachelor” and “George is a unmarried male of marriageable age” just in case they express the same proposition. Two distinct propositions, on the other hand, are equivalent just in case they are true or false in exactly the same possibilities. Of course, without a clear notion of the identity conditions of propositions, it is often hard to determine whether we have two sentences expressing one proposition, or two sentences expressing two distinct propositions that are equivalent to each other. [Like possibilities, theorists are still debating how to understand propositions. For example, here I have defined possibilities as sets of propositions, but some theorists reverse the order of dependence and define propositions as sets of possibilities, i.e., the possibilities at which they are true. Either way, having defined one concept in the terms of the other, the theorist still owes us an account of the undefined concept—a task theorists continue to pursue.]

Consistency

Two propositions are consistent with each other just in case there is at least one possibility in which both are true.

For example, “Sphere A is completely red” is consistent with “Cube B is completely blue” just so long as there is a possibility in which both are true. But “Sphere A is completely red” is inconsistent with “Sphere A is partly blue” since there is no possibility in which both are true.

Two propositions are contrary to each other if there is no possibi l ity in which both are true.

Contrariness is a kind of inconsistency. As we just saw, “Sphere A is completely red” is inconsistent with “Sphere A is partly blue” because there is no possibility in which both are true, i.e., because they are contrary to each other. But even though both propositions cannot be true together, they both could be false together, such as in possibilities in which “Sphere A is completely green” is true. But there is an even stronger kind of inconsistency, than mere contrariness.

Contradictor y

Two propositions are contradictory to each other if there is no possibility in which both are true or both are false .

“Sphere A is completely red” is contradictory to “Sphere A is not completely red” since if one is true, the other is false and if one is false, the other is true. Similarly, if it is true that “Snow guarantees skiing” then it is false that “There is a possibility in which there is snow and no skiing” and vice versa.

One important reason to keep these two kinds of inconsistency separate is that reasoners sometimes treat inconsistency as if it were just the same as being contradictory—they reason that if two states of affairs are inconsistent, then if one is false, the other one must be true. But such reasoners miss or ignore the possibility that two inconsistent propositions might still both be false, and as we saw in the previous section, ignoring or missing relevant possibilities is prone to generate reasoning errors. Hence, knowing whether two propositions are consistent, or contrary, or contradictory gives us important information about which possibilities are still relevant to whatever inquiry or reasoning we are pursuing using those propositions.

Since logicians are motivated by the goal of distinguishing good reasoning from bad reasoning and at least one part of good reasoning is that what we reason from adequately supports what we reason to, logicians are very interested in relations of adequate support. One very special kind of adequate support is entailment.

Entailmen t

P roposition A entails proposition B just so long as there is no po s sibility in which A is true and B is false.

For example, “Sam’s car weighs over 1000kg” entails “Sam’s car weighs at least 500kg”—any possibility in which Sam’s car is over 1000kg it is clearly at least 500kg. “Sam’s car is a red hatchback” entails “Sam’s car is red” and “Sam possesses a car” and “Sam’s car is a hatchback”. Instead of talking about what a single proposition entails, logicians are often interested in what a group or set of propositions entails. [A set of propositions entails another proposition just so long as there is no possibility in which all members of the set are true and the other proposition is false.] For example, “George went to Sophie’s house or to the movies” and “George did not go to the movies” entail “George went to Sophie’s house.” On the other hand, “If Sally attends class, then she passes the course” and “Sally passes the course” does not entail “Sally attends class,” since there are possibilities in which Sally can study well enough on her own and there is no attendance requirement, such that while it is true that “If Sally attends, then she passes the course” and true that “she passes the course”, it is false that “she attends class”.

Logic, especially formal logic, is primarily interested in entailment and other consequence relations. But at the elementary levels of logic at least the concept of entailment is applied to a concept that is also of interest to critical thinking and argumentation theorists—the concept of an argument. In logic, arguments are often modeled as a set of a set of propositions (the premises) and another proposition (the conclusion). [But see Chapters 8 and 9 of this volume for a more detailed discussion of the concept of an argument.] Logicians define validity , a property of arguments, in terms of whether or not the entailment relation holds between the premises and the other proposition, the conclusion. If the premises entail the conclusion, then the argument is valid, i.e., there is no possibility in which the premises are true and the conclusion false, and otherwise the argument is invalid. [Validity here is not to be confused with the notion of ‘valid’ that is used in everyday speech to signify that something is “good” or “worthy of further consideration”, as in: “She made a valid point, when she said ….”. Nor is it to be confused with the notion of ‘valid’ that is used in survey research to signify the goodness or utility of a measuring instrument or the results of such an instrument—for that concept see Chapter 19 of this volume.]

In the previous section, I said that one of the motivations for studying logic was to try to find properties of good reasoning that would hold in all the possibilities. Entailment (and so validity) is one such property. If the arguments you make are valid, i.e. if your reasons entail your conclusion, then your reasoning, at least in terms of support, is good reasoning. Of course, other aspects of that reasoning might be problematic, but at least you know that your reasons, if true, guarantee your conclusion, no matter what set of possibilities is the relevant set.

But consider: Most of the coins on the table are heads-up and that quarter is a coin on the table, so it is heads up. “Most of the coins on the table are heads-up” and “That quarter is a coin on the table” do not entail that “That quarter is heads up” and yet in many situations we would likely say that the first two propositions give very strong reasons to believe the third. In other words while entailment is a sure sign of inferential goodness in reasoning, the lack of entailment does not necessarily mean there is a lack of inferential goodness. Sometimes we say our reasoning is good enough, even if our reasons do not entail what we infer from them. If, in the possibilities in which our reasons are true, enough of them also have what we infer to be true, then we can say that the inferential link is good because the reasons sufficiently support our conclusion. The general definition of sufficient support is as follows:

Sufficient Support

Propostion A (or a set of propositions) sufficiently supports a proposition B just so long as, in enough of the possibilities in which A (or the set of propositions) is true, B is also true.

What counts as “enough” often varies from context to context. For example, in civil litigation, the conclusion of wrongdoing has to be supported by a preponderance of the evidence, i.e., the possibilities in which the defendant did what they are accused of, should be the case in more than 50% of the possibilities in which the provided evidence is true. But in criminal cases, the conclusion of wrongdoing should be supported beyond a reasonable doubt (which, at least if we take the vast majority of judges’ views on what that means, is above 80%). Statistical significance for supporting various hypotheses in the sciences is often set at 95% or higher. Determining what should count as “enough” in various contexts is often extremely challenging. At the very least, some of what counts as “enough” depends on the importance of the outcome. For example, since criminal sanctions are so much higher than civil sanctions, we demand more assurance that the evidence supports the conclusion of wrongdoing in the criminal case than in the civil case.

Logicians, I said, are primarily interested in consequence relations such as entailment. Different types of logic study these relations in different domains. For example, temporal or tense logics are interested in determining the consequence relations amongst uses of temporal phrases, such as, “in the future”, “in the past” and “now”. Modal logics study the consequence relations amongst propositions containing modal terms such as “must”, “can”, etc. But in addition to distinguishing types of logics by the types of propositions being modeled, logics are also categorized in terms of the type of consequence relation being studied. At the most general level, there are two types of logic—deductive and inductive. Deductive logic is concerned with entailment. Inductive logic is concerned with consequence relations weaker than entailment. Unsurprisingly, since there are many consequence relations weaker than entailment, inductive logic is a much less unified field of study than deductive logic. As we shall see in the next section, there are other uses of the terms ‘deductive’ and ‘inductive’, but these are generally misuses—the key difference between inductive and deductive logic is the type of consequence relation being studied.

I conclude this section with a final point about these eight definitions. They have all been given in terms of possibilities in general, i.e., logical possibilities. But for each definition, we could restrict the possibilities we are talking about and get restricted versions of these definitions. For example, physically necessary truths are those that hold in all the possibilities in which the physical laws hold. Morally necessary truths are those that are true in all the possibilities with the same moral code, etc. A set of propositions would physically entail another proposition if there is no physical possibility in which the propositions in the set are true and the other proposition is false. Two propositions are morally contradictory if there is no moral possibility in which both are true or both are false.

Even though explicit talk of these restricted kinds of logical concepts is rare, the theoretical apparatus is available and useful for trying to get clear on what various reasoners or arguers are in fact claiming. For example, in common discourse, when someone says that A entails B, I suspect they rarely mean that there is no possibility whatsoever in which A obtains and B does not; rather, for some contextually determined (though usually unspecified) group of possibilities there is no possibility in which A obtains and B does not. Similarly, for necessary and sufficient conditions; when someone says that snow is necessary for skiing, they probably do not mean that there is no possibility whatsoever in which there is skiing but no snow (there are in fact numerous possibilities—water skiing, roller skiing, sand skiing, skiing on artificial pellets, etc.), but rather that our typical conception of skiing requires snow. In the sciences, they are rarely concerned with logically necessary and sufficient conditions, but rather with causally necessary and sufficient conditions—conditions that require or guarantee something else in all the possibilities consistent with the causal laws. The moral for critical thinking is that even when one encounters terms such as ‘entails’ or ‘contradictory’ or ‘necessary condition’ they may not be being used in their strictly logical sense, but rather being used over a subset of relevant possibilities.

3. Logic and the activity of reasoning

3.1 logic and reasoning.

I conclude with some final comments about the application, and misapplication, of logical concepts in the study of reasoning. Logical systems are models. In particular, they are models of consequence relations between propositions. Some of the models are quite limited. For example, standard sentential or propositional logic systems ignore the internal structure of simple propositions and focus solely on connectives such as ‘and’, ‘or’ or ‘if,…then’. Others add elements to model ‘must’ and ‘can’ while still ignoring everything else, and so on. The hope is to ultimately get a model, or group of models, that illuminates the standards of good reasoning, at least with regards to inferential support. Like most models, logical models can be very helpful when properly applied within the domain they model. Trying to use the model outside the proper domain, however, can have drastic consequences. For example, claiming that the standard sentential logic system is a good model for explaining instances of good reasoning utilizing modal claims is clearly a mistake. (This is true not just for logical models. For example, using the “model” of the north star as a fixed point is extremely useful for general terrestrial navigation, but using the same model for routing certain sorts of messages, which requires quite precise location determination, gets poor results.) Similarly, since logic focuses on support relations and good reasoning usually involves not just adequate support, but good reasons as well, it is a mistake to think logic is the whole story of good reasoning. Indeed, logic has little to nothing to say about what makes reasons good reasons, but rather focuses on what can legitimately be inferred from whatever good reasons we find.

3.2 Arguments and explanations

Clearly the target domain we are trying to understand and improve—the activities of reasoning, arguing, justifying, persuading, etc., are much more complicated than any of the various logical systems that logicians produce to model certain aspects of those activities. And yet many theorists still try to find distinctions in the models that are really only distinctions in the activities and not really the concern of logic at all. For example, logicians and argumentation theorists have spent a lot of time trying to distinguish arguments from explanations. But suppose I lay out several reasons (including some reasons about what I think will happen in the next six months) why you should believe a particular company will fail in the next six months. Six months go by and the company fails and someone else asks “Why?” and I trot out my reasons again. Nothing has changed about the propositions involved, so, from the perspective of logic, there is one object, one set of propositions, here. Yet, how that object has been used has changed. Initially the reasons are used to argue that the company will fail. After the fact, the reasons are used to explain the company’s failure. We argue for propositions we are not sure of (or to convince others of propositions they are not sure of), but we explain propositions we are sure of, some of which may have been proved to us by argument, in order to understand why they are true. [Note that unlike my example, there are plenty of cases where the reasons one might give to argue for a proposition, which turns out to be true, need not be the reasons given when explaining why the proposition is true. For example, if something unexpected happens in the six months that contributes to the company’s failure that is likely to be a part of the act of explaining even though it was not part of the act of arguing.] The fact that there is a difference between acts of arguing and acts of explaining does not mean that, in the domain of logic, we should find separate kinds of things—arguments on the one hand and explanations on the other.

3.3 Inferring and implying

Going in the other direction, no one doubts that, considered in terms of propositions and support relations the inference from A to B and the implication of B by A are the same thing. But it is a mistake to think that the act of inferring is the same as the act of implying. You assert a group of facts (with the intention that I draw conclusions from those facts). I, being a good reasoner, draw those conclusions. You imply those conclusions and I infer those conclusions. Put another way, if I ask someone what they are inferring, I am asking about reasoning going on in their head, but if I ask someone what they are implying, I am asking about reasoning they hope to be going on in other people’s heads. Put yet another way, reasons do not infer conclusions, but rather imply them. People, when considering those reasons on their own, infer those conclusions, but do not imply them.

3.4 Deductive and inductive

Sometimes concepts are misapplied in both the model and the target domain. For example, some logic textbooks and critical thinking textbooks try to distinguish deductive arguments from inductive arguments, but from the perspective of logic there is nothing about the sets of propositions that compose arguments that make one kind of set deductive and another set inductive. For every group of reasons and a given conclusion we can ask whether the reasons entail the conclusion or not (the domain of deductive logic) or whether those very same reasons offer some support weaker than entailment or not (the domain of inductive logic.) Nor is it clear that we reason deductively or inductively—when we reason, we infer one or more propositions from others. Of that reasoning we did, we might wonder whether it is good or bad. The answer to that question will, in part, depend on what counts as good enough support in the situation in which I am using the reasoning. If the context requires entailment and the reasons do entail the conclusion, then the reasoning is adequate with regards to its support relation. If the reasons do not entail the conclusion, then it will fail to be adequate in such a situation. Similarly for a required support relation weaker than entailment—if reasons support the conclusion at or above the required level, then the support relation is adequate, whereas if it is below the required level the support relation is not adequate. The reasoning is one act of reasoning—whether the actual support relation of that reasoning is adequate or not depends on the situation. But none of this suddenly makes it the case that there are two distinct kinds of reasoning going on (even if there is a felt difference between realizing some reasons entail a conclusion versus realizing some premises only strongly support a conclusion.)

3.5 Linked vs. convergent arguments

One final example. The push for general principles often takes something that may track a real distinction or property in a certain specific set of cases and try to generalize it to all cases. For example, there is a strong intuition that reasons such as: “If you pass the test, then you will pass the course” and “You pass the test” work together to support the conclusion “you will pass the course” whereas reasons such as “You read all the supplemental material” and “You took good notes” and “You went to the tutor consistently” independently support the conclusion that “You are prepared for the test.” This intuition is strong enough, that numerous textbooks, especially those that use argument diagramming as a tool, try to distinguish arguments with linked premise structures from arguments with convergent premise structures. The problem here is two-fold. On the one hand, attempts to actually provide a rule for determining when a set (or subset) of reasons are linked or not have, to date, all failed, at least if we trust the intuitions that generated the drive to generalize the phenomena in the first place. On the other hand, the underlying judgments of whether premises are working together or are independent seem to vary from person to person and context to context enough to suspect that the distinction may not be tracking a real phenomenon that deserves to be represented or captured in our logical models.

4. Last word

Despite these injunctions to take care with the proper application of various concepts that have made their way into various textbooks, the core logical concepts of Section 2, such as sufficient support or co n sistency or necessary condition are useful in any study of reasoning. Even if good reasoners need to be careful and work diligently to determine which propositions are being expressed, and which possibilities are relevant, and what the needed standard of sufficient support is in a given situation, once these tasks are accomplished, we can evaluate our reasoning for inconsistencies and determine whether our reasons entail or at least adequately support our conclusions.

• © G.C. Goddu ↵

Studies in Critical Thinking Copyright © by G.C. Goddu is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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What Is Logic? What Is Critical Thinking?

Strategies and Skills for Critical Thinking, Using Logic

• Belief Systems
• Key Figures in Atheism
• M.A., Princeton University
• B.A., University of Pennsylvania

Logic is the science of how to evaluate arguments and reasoning. Critical thinking is a process of evaluation which uses logic to separate truth from falsehood, reasonable from unreasonable beliefs. If you want to better evaluate the various claims, ideas, and arguments you encounter, you need a better understanding of basic logic and the process of critical thinking.

These are not trivial pursuits. They are essential to making good decisions and forming sound beliefs about our world.

Who Cares About Logic?

Is learning about logic and how to properly construct arguments really important? Most people may not need such skills in their day-to-day lives, but the truth is that almost everyone will benefit from learning how to think more critically.

This does not only apply to our own beliefs, but also to all the ideas and claims that we regularly encounter. Without the right mental tools, we have little hope of reliably separating truth from falsehood.

Unskilled and Unaware

Everyone makes mistakes. Quite often, what is most important is the ability to first recognize our mistakes and then what we do about it.

Unfortunately, there are fields where the worse a person is, the less likely they are to even recognize that they have made mistakes, much less will be able to fix them. Indeed, they are actually likely to accuse those who know more of being the ones who are wrong.

Critical thinking and logic are one of these fields. Many people imagine that they are already quite good at it and thus don't believe that they need to learn more. This prevents them from ever improving.

What Is Logic?

People use words like "logic" and "logical" a lot, often without really understanding what they mean.

Strictly speaking, logic is the science or study of how to evaluate arguments and reasoning. It's not a matter of opinion, it's a science of how arguments must be formed in order to be reasonable or correct. Obviously, a better understanding is critical for helping us reason and think better. Without it, it's too easy for us to fall into error.

What Is Critical Thinking?

The term "critical thinking" is used often but it isn't always properly understood. Put simply, critical thinking means developing reliable, rational evaluations of an argument or idea.

Critical thinking is a means for separating truth from falsehood and reasonable from unreasonable beliefs. It frequently involves finding flaws in the arguments of others, but that's not all that it's about. It's not simply about criticizing ideas, it is about developing the ability to think about ideas with greater critical distance.

Agreement and Disagreement

Arguments are about disagreement - people aren't likely to argue over things they agree on. As obvious as that may be, it isn't always as obvious what, exactly, people disagree on. This is especially true for those who are caught up in the midst of a disagreement.

This is a problem because disagreements can't be resolved if those involved don't recognize what their disagreement is really about - or worse yet, actually disagree on what they disagree about. If those involved don't work that out, the only thing they'll accomplish by arguing is to create more animosity.

Propaganda and Persuasion

Propaganda is any organized, coordinated effort to convince masses of people to adopt some particular idea, belief, attitude, or viewpoint.

It's easiest to see government propaganda in the context of wartime. The label is also applicable to the efforts of corporations to buy their products, to apologists trying to get people to adopt their religion and many other situations. Understanding the nature of propaganda and how it works is critical to being able to think more critically about it.

• What Is Open Mindedness in Critical Thinking?
• The Importance of Logic and Philosophy
• What Is the Difference Between Denotation and Connotation?
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• Logic: What is a Non-Argument?
• Top Conversation Killers for Atheists
• What Is the Correspondence Theory of Truth?
• 7 Reasons People Believe in God
• Leonardo Da Vinci: Renaissance Humanist, Naturalist, Artist, Scientist
• Atheism and Skepticism in Ancient Greece
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• History of Humanism With Ancient Greek Philosophers
• Defining Science - How is Science Defined?

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Why is critical thinking important?

What do lawyers, accountants, teachers, and doctors all have in common?

What is critical thinking?

The Oxford English Dictionary defines critical thinking as “The objective, systematic, and rational analysis and evaluation of factual evidence in order to form a judgment on a subject, issue, etc.” Critical thinking involves the use of logic and reasoning to evaluate available facts and/or evidence to come to a conclusion about a certain subject or topic. We use critical thinking every day, from decision-making to problem-solving, in addition to thinking critically in an academic context!

Why is critical thinking important for academic success?

You may be asking “why is critical thinking important for students?” Critical thinking appears in a diverse set of disciplines and impacts students’ learning every day, regardless of major.

Critical thinking skills are often associated with the value of studying the humanities. In majors such as English, students will be presented with a certain text—whether it’s a novel, short story, essay, or even film—and will have to use textual evidence to make an argument and then defend their argument about what they’ve read. However, the importance of critical thinking does not only apply to the humanities. In the social sciences, an economics major , for example, will use what they’ve learned to figure out solutions to issues as varied as land and other natural resource use, to how much people should work, to how to develop human capital through education. Problem-solving and critical thinking go hand in hand. Biology is a popular major within LAS, and graduates of the biology program often pursue careers in the medical sciences. Doctors use critical thinking every day, tapping into the knowledge they acquired from studying the biological sciences to diagnose and treat different diseases and ailments.

Students in the College of LAS take many courses that require critical thinking before they graduate. You may be asked in an Economics class to use statistical data analysis to evaluate the impact on home improvement spending when the Fed increases interest rates (read more about real-world experience with Datathon ). If you’ve ever been asked “How often do you think about the Roman Empire?”, you may find yourself thinking about the Roman Empire more than you thought—maybe in an English course, where you’ll use text from Shakespeare’s Antony and Cleopatra to make an argument about Roman imperial desire.  No matter what the context is, critical thinking will be involved in your academic life and can take form in many different ways.

The benefits of critical thinking in everyday life

Building better communication.

One of the most important life skills that students learn as early as elementary school is how to give a presentation. Many classes require students to give presentations, because being well-spoken is a key skill in effective communication. This is where critical thinking benefits come into play: using the skills you’ve learned, you’ll be able to gather the information needed for your presentation, narrow down what information is most relevant, and communicate it in an engaging way. 

Typically, the first step in creating a presentation is choosing a topic. For example, your professor might assign a presentation on the Gilded Age and provide a list of figures from the 1870s—1890s to choose from. You’ll use your critical thinking skills to narrow down your choices. You may ask yourself:

• What figure am I most familiar with?
• Who am I most interested in? 
• Will I have to do additional research? 

After choosing your topic, your professor will usually ask a guiding question to help you form a thesis: an argument that is backed up with evidence. Critical thinking benefits this process by allowing you to focus on the information that is most relevant in support of your argument. By focusing on the strongest evidence, you will communicate your thesis clearly.

Finally, once you’ve finished gathering information, you will begin putting your presentation together. Creating a presentation requires a balance of text and visuals. Graphs and tables are popular visuals in STEM-based projects, but digital images and graphics are effective as well. Critical thinking benefits this process because the right images and visuals create a more dynamic experience for the audience, giving them the opportunity to engage with the material.

Presentation skills go beyond the classroom. Students at the University of Illinois will often participate in summer internships to get professional experience before graduation. Many summer interns are required to present about their experience and what they learned at the end of the internship. Jobs frequently also require employees to create presentations of some kind—whether it’s an advertising pitch to win an account from a potential client, or quarterly reporting, giving a presentation is a life skill that directly relates to critical thinking. 

Fostering independence and confidence

An important life skill many people start learning as college students and then finessing once they enter the “adult world” is how to budget. There will be many different expenses to keep track of, including rent, bills, car payments, and groceries, just to name a few! After developing your critical thinking skills, you’ll put them to use to consider your salary and budget your expenses accordingly. Here’s an example:

• You earn a salary of $75,000 a year. Assume all amounts are before taxes.
• 1,800 x 12 = 21,600
• 75,000 – 21,600 = 53,400
• This leaves you with $53,400
• 320 x 12 = 3,840 a year
• 53,400-3,840= 49,560
• 726 x 12 = 8,712
• 49,560 – 8,712= 40,848
• You’re left with $40,848 for miscellaneous expenses. You use your critical thinking skills to decide what to do with your $40,848. You think ahead towards your retirement and decide to put $500 a month into a Roth IRA, leaving $34,848. Since you love coffee, you try to figure out if you can afford a daily coffee run. On average, a cup of coffee will cost you $7. 7 x 365 = $2,555 a year for coffee. 34,848 – 2,555 = 32,293
• You have $32,293 left. You will use your critical thinking skills to figure out how much you would want to put into savings, how much you want to save to treat yourself from time to time, and how much you want to put aside for emergency funds. With the benefits of critical thinking, you will be well-equipped to budget your lifestyle once you enter the working world.

Enhancing decision-making skills

Choosing the right university for you.

One of the biggest decisions you’ll make in your life is what college or university to go to. There are many factors to consider when making this decision, and critical thinking importance will come into play when determining these factors.

Many high school seniors apply to colleges with the hope of being accepted into a certain program, whether it’s biology, psychology, political science, English, or something else entirely. Some students apply with certain schools in mind due to overall rankings. Students also consider the campus a school is set in. While some universities such as the University of Illinois are nestled within college towns, New York University is right in Manhattan, in a big city setting. Some students dream of going to large universities, and other students prefer smaller schools. The diversity of a university’s student body is also a key consideration. For many 17- and 18-year-olds, college is a time to meet peers from diverse racial and socio-economic backgrounds and learn about life experiences different than one’s own.

With all these factors in mind, you’ll use critical thinking to decide which are most important to you—and which school is the right fit for you.

Develop your critical thinking skills at the University of Illinois

At the University of Illinois, not only will you learn how to think critically, but you will put critical thinking into practice. In the College of LAS, you can choose from 70+ majors where you will learn the importance and benefits of critical thinking skills. The College of Liberal Arts & Sciences at U of I offers a wide range of undergraduate and graduate programs in life, physical, and mathematical sciences; humanities; and social and behavioral sciences. No matter which program you choose, you will develop critical thinking skills as you go through your courses in the major of your choice. And in those courses, the first question your professors may ask you is, “What is the goal of critical thinking?” You will be able to respond with confidence that the goal of critical thinking is to help shape people into more informed, more thoughtful members of society.

With such a vast representation of disciplines, an education in the College of LAS will prepare you for a career where you will apply critical thinking skills to real life, both in and outside of the classroom, from your undergraduate experience to your professional career. If you’re interested in becoming a part of a diverse set of students and developing skills for lifelong success, apply to LAS today!

Read more first-hand stories from our amazing students at the LAS Insider blog .

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1.6: Basic Logical Concepts

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Consistency

Two (or more) statements are inconsistent with each other when it is logically impossible for all of them to be true at the same time. For example: The earth is flat, and The earth is spherical are inconsistent statements since nothing can be both flat and spherical. On the other hand, if you have any two statements that are both true, they are certainly consistent.

A sentence X entails Y if Y follows logically from X. In other words, if X is true then Y must also be true, e.g. 30 people have died in the riots entails more than 20 people died in the riots,but not vice-versa.

If X entails Y and we find out that Y is false, then we should conclude that X is also false. But of course, if X entails Y and we find out that X is false, it does not follow that Y is also false.

If X entails Y but Y does not entail X, then we say that X is a stronger claim than Y (or Y is weaker than X). For example, all birds can fly is stronger than most birds can fly, which is still stronger than some birds can fly.

A stronger claim is of course more likely to be wrong. To use a typical example, suppose we want to praise a person X but are not sure whether X is the best or not, we might use the weaker claim “X is one of the best” rather than the stronger “X is the best”. So we need not be accused of speaking falsely even if it turns out that X is not the best.

Logical Equivalence

If two statements entail each other then they are logically equivalent. For example, everyone is ill is equivalent to nobody is not ill, and cheap things are no good is actually equivalent to good things are not cheap. If two statements are logically equivalent, then necessarily they must always have the same truth value.

In ordinary usage, the word “argument” is often used to refer to a heated dispute between two or more parties. But in logic and critical thinking, the term has a different meaning. Here,an argument is taken to be a list of statements, one of which is the conclusion and the others are the premises (assumptions) of the argument. To give an argument is to provide a set of premises as reasons for accepting the conclusion. The ability to construct, identify and evaluate arguments is a crucial part of critical thinking. We all have lots of opinions on lots of things,but most people are not good at giving arguments in support of their opinions.

Here is an example of a short argument made up of three statements. The first two statements are the premises, and the last one is the conclusion:

• Every star produces radiation.
• The Sun is a star.
• Therefore, the Sun produces radiation.

Arguments in real life often are not presented in such a neat manner, with the premises and conclusions clearly laid out. So how do we identify them? There are no easy mechanical rules,and we usually have to rely on the context in order to determine which are the premises and the conclusions. But sometimes the job can be made easier by the presence of certain premise or conclusion indicators. For example, if a person makes a statement, and then adds “this is because ...”, then it is quite likely that the first statement is presented as a conclusion, supported by the statements that come afterwards. Words like “after all”, “suppose” and “since” are also often used to precede premises. Conclusions, on the other hand, are often preceded by words like “therefore”, “so”, “it follows that”.

The secret to good reading and writing skill is to develop the ability to construct and summarize arguments, and to present arguments clearly and systematically. The same goes for giving good presentations.

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Critical Thinking

Critical thinking is a widely accepted educational goal. Its definition is contested, but the competing definitions can be understood as differing conceptions of the same basic concept: careful thinking directed to a goal. Conceptions differ with respect to the scope of such thinking, the type of goal, the criteria and norms for thinking carefully, and the thinking components on which they focus. Its adoption as an educational goal has been recommended on the basis of respect for students’ autonomy and preparing students for success in life and for democratic citizenship. “Critical thinkers” have the dispositions and abilities that lead them to think critically when appropriate. The abilities can be identified directly; the dispositions indirectly, by considering what factors contribute to or impede exercise of the abilities. Standardized tests have been developed to assess the degree to which a person possesses such dispositions and abilities. Educational intervention has been shown experimentally to improve them, particularly when it includes dialogue, anchored instruction, and mentoring. Controversies have arisen over the generalizability of critical thinking across domains, over alleged bias in critical thinking theories and instruction, and over the relationship of critical thinking to other types of thinking.

2.1 Dewey’s Three Main Examples

2.2 dewey’s other examples, 2.3 further examples, 2.4 non-examples, 3. the definition of critical thinking, 4. its value, 5. the process of thinking critically, 6. components of the process, 7. contributory dispositions and abilities, 8.1 initiating dispositions, 8.2 internal dispositions, 9. critical thinking abilities, 10. required knowledge, 11. educational methods, 12.1 the generalizability of critical thinking, 12.2 bias in critical thinking theory and pedagogy, 12.3 relationship of critical thinking to other types of thinking, other internet resources, related entries.

Use of the term ‘critical thinking’ to describe an educational goal goes back to the American philosopher John Dewey (1910), who more commonly called it ‘reflective thinking’. He defined it as

active, persistent and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it, and the further conclusions to which it tends. (Dewey 1910: 6; 1933: 9)

and identified a habit of such consideration with a scientific attitude of mind. His lengthy quotations of Francis Bacon, John Locke, and John Stuart Mill indicate that he was not the first person to propose development of a scientific attitude of mind as an educational goal.

In the 1930s, many of the schools that participated in the Eight-Year Study of the Progressive Education Association (Aikin 1942) adopted critical thinking as an educational goal, for whose achievement the study’s Evaluation Staff developed tests (Smith, Tyler, & Evaluation Staff 1942). Glaser (1941) showed experimentally that it was possible to improve the critical thinking of high school students. Bloom’s influential taxonomy of cognitive educational objectives (Bloom et al. 1956) incorporated critical thinking abilities. Ennis (1962) proposed 12 aspects of critical thinking as a basis for research on the teaching and evaluation of critical thinking ability.

Since 1980, an annual international conference in California on critical thinking and educational reform has attracted tens of thousands of educators from all levels of education and from many parts of the world. Also since 1980, the state university system in California has required all undergraduate students to take a critical thinking course. Since 1983, the Association for Informal Logic and Critical Thinking has sponsored sessions in conjunction with the divisional meetings of the American Philosophical Association (APA). In 1987, the APA’s Committee on Pre-College Philosophy commissioned a consensus statement on critical thinking for purposes of educational assessment and instruction (Facione 1990a). Researchers have developed standardized tests of critical thinking abilities and dispositions; for details, see the Supplement on Assessment . Educational jurisdictions around the world now include critical thinking in guidelines for curriculum and assessment. Political and business leaders endorse its importance.

For details on this history, see the Supplement on History .

2. Examples and Non-Examples

Before considering the definition of critical thinking, it will be helpful to have in mind some examples of critical thinking, as well as some examples of kinds of thinking that would apparently not count as critical thinking.

Dewey (1910: 68–71; 1933: 91–94) takes as paradigms of reflective thinking three class papers of students in which they describe their thinking. The examples range from the everyday to the scientific.

Transit : “The other day, when I was down town on 16th Street, a clock caught my eye. I saw that the hands pointed to 12:20. This suggested that I had an engagement at 124th Street, at one o'clock. I reasoned that as it had taken me an hour to come down on a surface car, I should probably be twenty minutes late if I returned the same way. I might save twenty minutes by a subway express. But was there a station near? If not, I might lose more than twenty minutes in looking for one. Then I thought of the elevated, and I saw there was such a line within two blocks. But where was the station? If it were several blocks above or below the street I was on, I should lose time instead of gaining it. My mind went back to the subway express as quicker than the elevated; furthermore, I remembered that it went nearer than the elevated to the part of 124th Street I wished to reach, so that time would be saved at the end of the journey. I concluded in favor of the subway, and reached my destination by one o’clock.” (Dewey 1910: 68-69; 1933: 91-92)

Ferryboat : “Projecting nearly horizontally from the upper deck of the ferryboat on which I daily cross the river is a long white pole, having a gilded ball at its tip. It suggested a flagpole when I first saw it; its color, shape, and gilded ball agreed with this idea, and these reasons seemed to justify me in this belief. But soon difficulties presented themselves. The pole was nearly horizontal, an unusual position for a flagpole; in the next place, there was no pulley, ring, or cord by which to attach a flag; finally, there were elsewhere on the boat two vertical staffs from which flags were occasionally flown. It seemed probable that the pole was not there for flag-flying.

“I then tried to imagine all possible purposes of the pole, and to consider for which of these it was best suited: (a) Possibly it was an ornament. But as all the ferryboats and even the tugboats carried poles, this hypothesis was rejected. (b) Possibly it was the terminal of a wireless telegraph. But the same considerations made this improbable. Besides, the more natural place for such a terminal would be the highest part of the boat, on top of the pilot house. (c) Its purpose might be to point out the direction in which the boat is moving.

“In support of this conclusion, I discovered that the pole was lower than the pilot house, so that the steersman could easily see it. Moreover, the tip was enough higher than the base, so that, from the pilot's position, it must appear to project far out in front of the boat. Morevoer, the pilot being near the front of the boat, he would need some such guide as to its direction. Tugboats would also need poles for such a purpose. This hypothesis was so much more probable than the others that I accepted it. I formed the conclusion that the pole was set up for the purpose of showing the pilot the direction in which the boat pointed, to enable him to steer correctly.” (Dewey 1910: 69-70; 1933: 92-93)

Bubbles : “In washing tumblers in hot soapsuds and placing them mouth downward on a plate, bubbles appeared on the outside of the mouth of the tumblers and then went inside. Why? The presence of bubbles suggests air, which I note must come from inside the tumbler. I see that the soapy water on the plate prevents escape of the air save as it may be caught in bubbles. But why should air leave the tumbler? There was no substance entering to force it out. It must have expanded. It expands by increase of heat, or by decrease of pressure, or both. Could the air have become heated after the tumbler was taken from the hot suds? Clearly not the air that was already entangled in the water. If heated air was the cause, cold air must have entered in transferring the tumblers from the suds to the plate. I test to see if this supposition is true by taking several more tumblers out. Some I shake so as to make sure of entrapping cold air in them. Some I take out holding mouth downward in order to prevent cold air from entering. Bubbles appear on the outside of every one of the former and on none of the latter. I must be right in my inference. Air from the outside must have been expanded by the heat of the tumbler, which explains the appearance of the bubbles on the outside. But why do they then go inside? Cold contracts. The tumbler cooled and also the air inside it. Tension was removed, and hence bubbles appeared inside. To be sure of this, I test by placing a cup of ice on the tumbler while the bubbles are still forming outside. They soon reverse” (Dewey 1910: 70–71; 1933: 93–94).

Dewey (1910, 1933) sprinkles his book with other examples of critical thinking. We will refer to the following.

Weather : A man on a walk notices that it has suddenly become cool, thinks that it is probably going to rain, looks up and sees a dark cloud obscuring the sun, and quickens his steps (1910: 6–10; 1933: 9–13).

Disorder : A man finds his rooms on his return to them in disorder with his belongings thrown about, thinks at first of burglary as an explanation, then thinks of mischievous children as being an alternative explanation, then looks to see whether valuables are missing, and discovers that they are (1910: 82–83; 1933: 166–168).

Typhoid : A physician diagnosing a patient whose conspicuous symptoms suggest typhoid avoids drawing a conclusion until more data are gathered by questioning the patient and by making tests (1910: 85–86; 1933: 170).

Blur : A moving blur catches our eye in the distance, we ask ourselves whether it is a cloud of whirling dust or a tree moving its branches or a man signaling to us, we think of other traits that should be found on each of those possibilities, and we look and see if those traits are found (1910: 102, 108; 1933: 121, 133).

Suction pump : In thinking about the suction pump, the scientist first notes that it will draw water only to a maximum height of 33 feet at sea level and to a lesser maximum height at higher elevations, selects for attention the differing atmospheric pressure at these elevations, sets up experiments in which the air is removed from a vessel containing water (when suction no longer works) and in which the weight of air at various levels is calculated, compares the results of reasoning about the height to which a given weight of air will allow a suction pump to raise water with the observed maximum height at different elevations, and finally assimilates the suction pump to such apparently different phenomena as the siphon and the rising of a balloon (1910: 150–153; 1933: 195–198).

Diamond : A passenger in a car driving in a diamond lane reserved for vehicles with at least one passenger notices that the diamond marks on the pavement are far apart in some places and close together in others. Why? The driver suggests that the reason may be that the diamond marks are not needed where there is a solid double line separating the diamond line from the adjoining lane, but are needed when there is a dotted single line permitting crossing into the diamond lane. Further observation confirms that the diamonds are close together when a dotted line separates the diamond lane from its neighbour, but otherwise far apart.

Rash : A woman suddenly develops a very itchy red rash on her throat and upper chest. She recently noticed a mark on the back of her right hand, but was not sure whether the mark was a rash or a scrape. She lies down in bed and thinks about what might be causing the rash and what to do about it. About two weeks before, she began taking blood pressure medication that contained a sulfa drug, and the pharmacist had warned her, in view of a previous allergic reaction to a medication containing a sulfa drug, to be on the alert for an allergic reaction; however, she had been taking the medication for two weeks with no such effect. The day before, she began using a new cream on her neck and upper chest; against the new cream as the cause was mark on the back of her hand, which had not been exposed to the cream. She began taking probiotics about a month before. She also recently started new eye drops, but she supposed that manufacturers of eye drops would be careful not to include allergy-causing components in the medication. The rash might be a heat rash, since she recently was sweating profusely from her upper body. Since she is about to go away on a short vacation, where she would not have access to her usual physician, she decides to keep taking the probiotics and using the new eye drops but to discontinue the blood pressure medication and to switch back to the old cream for her neck and upper chest. She forms a plan to consult her regular physician on her return about the blood pressure medication.

Candidate : Although Dewey included no examples of thinking directed at appraising the arguments of others, such thinking has come to be considered a kind of critical thinking. We find an example of such thinking in the performance task on the Collegiate Learning Assessment (CLA+), which its sponsoring organization describes as

a performance-based assessment that provides a measure of an institution’s contribution to the development of critical-thinking and written communication skills of its students. (Council for Aid to Education 2017)

A sample task posted on its website requires the test-taker to write a report for public distribution evaluating a fictional candidate’s policy proposals and their supporting arguments, using supplied background documents, with a recommendation on whether to endorse the candidate.

Immediate acceptance of an idea that suggests itself as a solution to a problem (e.g., a possible explanation of an event or phenomenon, an action that seems likely to produce a desired result) is “uncritical thinking, the minimum of reflection” (Dewey 1910: 13). On-going suspension of judgment in the light of doubt about a possible solution is not critical thinking (Dewey 1910: 108). Critique driven by a dogmatically held political or religious ideology is not critical thinking; thus Paulo Freire (1968 [1970]) is using the term (e.g., at 1970: 71, 81, 100, 146) in a more politically freighted sense that includes not only reflection but also revolutionary action against oppression. Derivation of a conclusion from given data using an algorithm is not critical thinking.

What is critical thinking? There are many definitions. Ennis (2016) lists 14 philosophically oriented scholarly definitions and three dictionary definitions. Following Rawls (1971), who distinguished his conception of justice from a utilitarian conception but regarded them as rival conceptions of the same concept, Ennis maintains that the 17 definitions are different conceptions of the same concept. Rawls articulated the shared concept of justice as

a characteristic set of principles for assigning basic rights and duties and for determining… the proper distribution of the benefits and burdens of social cooperation. (Rawls 1971: 5)

Bailin et al. (1999b) claim that, if one considers what sorts of thinking an educator would take not to be critical thinking and what sorts to be critical thinking, one can conclude that educators typically understand critical thinking to have at least three features.

• It is done for the purpose of making up one’s mind about what to believe or do.
• The person engaging in the thinking is trying to fulfill standards of adequacy and accuracy appropriate to the thinking.
• The thinking fulfills the relevant standards to some threshold level.

One could sum up the core concept that involves these three features by saying that critical thinking is careful goal-directed thinking. This core concept seems to apply to all the examples of critical thinking described in the previous section. As for the non-examples, their exclusion depends on construing careful thinking as excluding jumping immediately to conclusions, suspending judgment no matter how strong the evidence, reasoning from an unquestioned ideological or religious perspective, and routinely using an algorithm to answer a question.

If the core of critical thinking is careful goal-directed thinking, conceptions of it can vary according to its presumed scope, its presumed goal, one’s criteria and threshold for being careful, and the thinking component on which one focuses As to its scope, some conceptions (e.g., Dewey 1910, 1933) restrict it to constructive thinking on the basis of one’s own observations and experiments, others (e.g., Ennis 1962; Fisher & Scriven 1997; Johnson 1992) to appraisal of the products of such thinking. Ennis (1991) and Bailin et al. (1999b) take it to cover both construction and appraisal. As to its goal, some conceptions restrict it to forming a judgment (Dewey 1910, 1933; Lipman 1987; Facione 1990a). Others allow for actions as well as beliefs as the end point of a process of critical thinking (Ennis 1991; Bailin et al. 1999b). As to the criteria and threshold for being careful, definitions vary in the term used to indicate that critical thinking satisfies certain norms: “intellectually disciplined” (Scriven & Paul 1987), “reasonable” (Ennis 1991), “skillful” (Lipman 1987), “skilled” (Fisher & Scriven 1997), “careful” (Bailin & Battersby 2009). Some definitions specify these norms, referring variously to “consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusions to which it tends” (Dewey 1910, 1933); “the methods of logical inquiry and reasoning” (Glaser 1941); “conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication” (Scriven & Paul 1987); the requirement that “it is sensitive to context, relies on criteria, and is self-correcting” (Lipman 1987); “evidential, conceptual, methodological, criteriological, or contextual considerations” (Facione 1990a); and “plus-minus considerations of the product in terms of appropriate standards (or criteria)” (Johnson 1992). Stanovich and Stanovich (2010) propose to ground the concept of critical thinking in the concept of rationality, which they understand as combining epistemic rationality (fitting one’s beliefs to the world) and instrumental rationality (optimizing goal fulfillment); a critical thinker, in their view, is someone with “a propensity to override suboptimal responses from the autonomous mind” (2010: 227). These variant specifications of norms for critical thinking are not necessarily incompatible with one another, and in any case presuppose the core notion of thinking carefully. As to the thinking component singled out, some definitions focus on suspension of judgment during the thinking (Dewey 1910; McPeck 1981), others on inquiry while judgment is suspended (Bailin & Battersby 2009), others on the resulting judgment (Facione 1990a), and still others on the subsequent emotive response (Siegel 1988).

In educational contexts, a definition of critical thinking is a “programmatic definition” (Scheffler 1960: 19). It expresses a practical program for achieving an educational goal. For this purpose, a one-sentence formulaic definition is much less useful than articulation of a critical thinking process, with criteria and standards for the kinds of thinking that the process may involve. The real educational goal is recognition, adoption and implementation by students of those criteria and standards. That adoption and implementation in turn consists in acquiring the knowledge, abilities and dispositions of a critical thinker.

Conceptions of critical thinking generally do not include moral integrity as part of the concept. Dewey, for example, took critical thinking to be the ultimate intellectual goal of education, but distinguished it from the development of social cooperation among school children, which he took to be the central moral goal. Ennis (1996, 2011) added to his previous list of critical thinking dispositions a group of dispositions to care about the dignity and worth of every person, which he described as a “correlative” (1996) disposition without which critical thinking would be less valuable and perhaps harmful. An educational program that aimed at developing critical thinking but not the correlative disposition to care about the dignity and worth of every person, he asserted, “would be deficient and perhaps dangerous” (Ennis 1996: 172).

Dewey thought that education for reflective thinking would be of value to both the individual and society; recognition in educational practice of the kinship to the scientific attitude of children’s native curiosity, fertile imagination and love of experimental inquiry “would make for individual happiness and the reduction of social waste” (Dewey 1910: iii). Schools participating in the Eight-Year Study took development of the habit of reflective thinking and skill in solving problems as a means to leading young people to understand, appreciate and live the democratic way of life characteristic of the United States (Aikin 1942: 17–18, 81). Harvey Siegel (1988: 55–61) has offered four considerations in support of adopting critical thinking as an educational ideal. (1) Respect for persons requires that schools and teachers honour students’ demands for reasons and explanations, deal with students honestly, and recognize the need to confront students’ independent judgment; these requirements concern the manner in which teachers treat students. (2) Education has the task of preparing children to be successful adults, a task that requires development of their self-sufficiency. (3) Education should initiate children into the rational traditions in such fields as history, science and mathematics. (4) Education should prepare children to become democratic citizens, which requires reasoned procedures and critical talents and attitudes. To supplement these considerations, Siegel (1988: 62–90) responds to two objections: the ideology objection that adoption of any educational ideal requires a prior ideological commitment and the indoctrination objection that cultivation of critical thinking cannot escape being a form of indoctrination.

Despite the diversity of our 11 examples, one can recognize a common pattern. Dewey analyzed it as consisting of five phases:

• suggestions , in which the mind leaps forward to a possible solution;
• an intellectualization of the difficulty or perplexity into a problem to be solved, a question for which the answer must be sought;
• the use of one suggestion after another as a leading idea, or hypothesis , to initiate and guide observation and other operations in collection of factual material;
• the mental elaboration of the idea or supposition as an idea or supposition ( reasoning , in the sense on which reasoning is a part, not the whole, of inference); and
• testing the hypothesis by overt or imaginative action. (Dewey 1933: 106–107; italics in original)

The process of reflective thinking consisting of these phases would be preceded by a perplexed, troubled or confused situation and followed by a cleared-up, unified, resolved situation (Dewey 1933: 106). The term ‘phases’ replaced the term ‘steps’ (Dewey 1910: 72), thus removing the earlier suggestion of an invariant sequence. Variants of the above analysis appeared in (Dewey 1916: 177) and (Dewey 1938: 101–119).

The variant formulations indicate the difficulty of giving a single logical analysis of such a varied process. The process of critical thinking may have a spiral pattern, with the problem being redefined in the light of obstacles to solving it as originally formulated. For example, the person in Transit might have concluded that getting to the appointment at the scheduled time was impossible and have reformulated the problem as that of rescheduling the appointment for a mutually convenient time. Further, defining a problem does not always follow after or lead immediately to an idea of a suggested solution. Nor should it do so, as Dewey himself recognized in describing the physician in Typhoid as avoiding any strong preference for this or that conclusion before getting further information (Dewey 1910: 85; 1933: 170). People with a hypothesis in mind, even one to which they have a very weak commitment, have a so-called “confirmation bias” (Nickerson 1998): they are likely to pay attention to evidence that confirms the hypothesis and to ignore evidence that counts against it or for some competing hypothesis. Detectives, intelligence agencies, and investigators of airplane accidents are well advised to gather relevant evidence systematically and to postpone even tentative adoption of an explanatory hypothesis until the collected evidence rules out with the appropriate degree of certainty all but one explanation. Dewey’s analysis of the critical thinking process can be faulted as well for requiring acceptance or rejection of a possible solution to a defined problem, with no allowance for deciding in the light of the available evidence to suspend judgment. Further, given the great variety of kinds of problems for which reflection is appropriate, there is likely to be variation in its component events. Perhaps the best way to conceptualize the critical thinking process is as a checklist whose component events can occur in a variety of orders, selectively, and more than once. These component events might include (1) noticing a difficulty, (2) defining the problem, (3) dividing the problem into manageable sub-problems, (4) formulating a variety of possible solutions to the problem or sub-problem, (5) determining what evidence is relevant to deciding among possible solutions to the problem or sub-problem, (6) devising a plan of systematic observation or experiment that will uncover the relevant evidence, (7) carrying out the plan of systematic observation or experimentation, (8) noting the results of the systematic observation or experiment, (9) gathering relevant testimony and information from others, (10) judging the credibility of testimony and information gathered from others, (11) drawing conclusions from gathered evidence and accepted testimony, and (12) accepting a solution that the evidence adequately supports (cf. Hitchcock 2017: 485).

Checklist conceptions of the process of critical thinking are open to the objection that they are too mechanical and procedural to fit the multi-dimensional and emotionally charged issues for which critical thinking is urgently needed (Paul 1984). For such issues, a more dialectical process is advocated, in which competing relevant world views are identified, their implications explored, and some sort of creative synthesis attempted.

If one considers the critical thinking process illustrated by the 11 examples, one can identify distinct kinds of mental acts and mental states that form part of it. To distinguish, label and briefly characterize these components is a useful preliminary to identifying abilities, skills, dispositions, attitudes, habits and the like that contribute causally to thinking critically. Identifying such abilities and habits is in turn a useful preliminary to setting educational goals. Setting the goals is in its turn a useful preliminary to designing strategies for helping learners to achieve the goals and to designing ways of measuring the extent to which learners have done so. Such measures provide both feedback to learners on their achievement and a basis for experimental research on the effectiveness of various strategies for educating people to think critically. Let us begin, then, by distinguishing the kinds of mental acts and mental events that can occur in a critical thinking process.

• Observing : One notices something in one’s immediate environment (sudden cooling of temperature in Weather , bubbles forming outside a glass and then going inside in Bubbles , a moving blur in the distance in Blur , a rash in Rash ). Or one notes the results of an experiment or systematic observation (valuables missing in Disorder , no suction without air pressure in Suction pump )
• Feeling : One feels puzzled or uncertain about something (how to get to an appointment on time in Transit , why the diamonds vary in frequency in Diamond ). One wants to resolve this perplexity. One feels satisfaction once one has worked out an answer (to take the subway express in Transit , diamonds closer when needed as a warning in Diamond ).
• Wondering : One formulates a question to be addressed (why bubbles form outside a tumbler taken from hot water in Bubbles , how suction pumps work in Suction pump , what caused the rash in Rash ).
• Imagining : One thinks of possible answers (bus or subway or elevated in Transit , flagpole or ornament or wireless communication aid or direction indicator in Ferryboat , allergic reaction or heat rash in Rash ).
• Inferring : One works out what would be the case if a possible answer were assumed (valuables missing if there has been a burglary in Disorder , earlier start to the rash if it is an allergic reaction to a sulfa drug in Rash ). Or one draws a conclusion once sufficient relevant evidence is gathered (take the subway in Transit , burglary in Disorder , discontinue blood pressure medication and new cream in Rash ).
• Knowledge : One uses stored knowledge of the subject-matter to generate possible answers or to infer what would be expected on the assumption of a particular answer (knowledge of a city’s public transit system in Transit , of the requirements for a flagpole in Ferryboat , of Boyle’s law in Bubbles , of allergic reactions in Rash ).
• Experimenting : One designs and carries out an experiment or a systematic observation to find out whether the results deduced from a possible answer will occur (looking at the location of the flagpole in relation to the pilot’s position in Ferryboat , putting an ice cube on top of a tumbler taken from hot water in Bubbles , measuring the height to which a suction pump will draw water at different elevations in Suction pump , noticing the frequency of diamonds when movement to or from a diamond lane is allowed in Diamond ).
• Consulting : One finds a source of information, gets the information from the source, and makes a judgment on whether to accept it. None of our 11 examples include searching for sources of information. In this respect they are unrepresentative, since most people nowadays have almost instant access to information relevant to answering any question, including many of those illustrated by the examples. However, Candidate includes the activities of extracting information from sources and evaluating its credibility.
• Identifying and analyzing arguments : One notices an argument and works out its structure and content as a preliminary to evaluating its strength. This activity is central to Candidate . It is an important part of a critical thinking process in which one surveys arguments for various positions on an issue.
• Judging : One makes a judgment on the basis of accumulated evidence and reasoning, such as the judgment in Ferryboat that the purpose of the pole is to provide direction to the pilot.
• Deciding : One makes a decision on what to do or on what policy to adopt, as in the decision in Transit to take the subway.

By definition, a person who does something voluntarily is both willing and able to do that thing at that time. Both the willingness and the ability contribute causally to the person’s action, in the sense that the voluntary action would not occur if either (or both) of these were lacking. For example, suppose that one is standing with one’s arms at one’s sides and one voluntarily lifts one’s right arm to an extended horizontal position. One would not do so if one were unable to lift one’s arm, if for example one’s right side was paralyzed as the result of a stroke. Nor would one do so if one were unwilling to lift one’s arm, if for example one were participating in a street demonstration at which a white supremacist was urging the crowd to lift their right arm in a Nazi salute and one were unwilling to express support in this way for the racist Nazi ideology. The same analysis applies to a voluntary mental process of thinking critically. It requires both willingness and ability to think critically, including willingness and ability to perform each of the mental acts that compose the process and to coordinate those acts in a sequence that is directed at resolving the initiating perplexity.

Consider willingness first. We can identify causal contributors to willingness to think critically by considering factors that would cause a person who was able to think critically about an issue nevertheless not to do so (Hamby 2014). For each factor, the opposite condition thus contributes causally to willingness to think critically on a particular occasion. For example, people who habitually jump to conclusions without considering alternatives will not think critically about issues that arise, even if they have the required abilities. The contrary condition of willingness to suspend judgment is thus a causal contributor to thinking critically.

Now consider ability. In contrast to the ability to move one’s arm, which can be completely absent because a stroke has left the arm paralyzed, the ability to think critically is a developed ability, whose absence is not a complete absence of ability to think but absence of ability to think well. We can identify the ability to think well directly, in terms of the norms and standards for good thinking. In general, to be able do well the thinking activities that can be components of a critical thinking process, one needs to know the concepts and principles that characterize their good performance, to recognize in particular cases that the concepts and principles apply, and to apply them. The knowledge, recognition and application may be procedural rather than declarative. It may be domain-specific rather than widely applicable, and in either case may need subject-matter knowledge, sometimes of a deep kind.

Reflections of the sort illustrated by the previous two paragraphs have led scholars to identify the knowledge, abilities and dispositions of a “critical thinker”, i.e., someone who thinks critically whenever it is appropriate to do so. We turn now to these three types of causal contributors to thinking critically. We start with dispositions, since arguably these are the most powerful contributors to being a critical thinker, can be fostered at an early stage of a child’s development, and are susceptible to general improvement (Glaser 1941: 175)

8. Critical Thinking Dispositions

Educational researchers use the term ‘dispositions’ broadly for the habits of mind and attitudes that contribute causally to being a critical thinker. Some writers (e.g., Paul & Elder 2006; Hamby 2014; Bailin & Battersby 2016) propose to use the term ‘virtues’ for this dimension of a critical thinker. The virtues in question, although they are virtues of character, concern the person’s ways of thinking rather than the person’s ways of behaving towards others. They are not moral virtues but intellectual virtues, of the sort articulated by Zagzebski (1996) and discussed by Turri, Alfano, and Greco (2017).

On a realistic conception, thinking dispositions or intellectual virtues are real properties of thinkers. They are general tendencies, propensities, or inclinations to think in particular ways in particular circumstances, and can be genuinely explanatory (Siegel 1999). Sceptics argue that there is no evidence for a specific mental basis for the habits of mind that contribute to thinking critically, and that it is pedagogically misleading to posit such a basis (Bailin et al. 1999a). Whatever their status, critical thinking dispositions need motivation for their initial formation in a child—motivation that may be external or internal. As children develop, the force of habit will gradually become important in sustaining the disposition (Nieto & Valenzuela 2012). Mere force of habit, however, is unlikely to sustain critical thinking dispositions. Critical thinkers must value and enjoy using their knowledge and abilities to think things through for themselves. They must be committed to, and lovers of, inquiry.

A person may have a critical thinking disposition with respect to only some kinds of issues. For example, one could be open-minded about scientific issues but not about religious issues. Similarly, one could be confident in one’s ability to reason about the theological implications of the existence of evil in the world but not in one’s ability to reason about the best design for a guided ballistic missile.

Critical thinking dispositions can usefully be divided into initiating dispositions (those that contribute causally to starting to think critically about an issue) and internal dispositions (those that contribute causally to doing a good job of thinking critically once one has started) (Facione 1990a: 25). The two categories are not mutually exclusive. For example, open-mindedness, in the sense of willingness to consider alternative points of view to one’s own, is both an initiating and an internal disposition.

Using the strategy of considering factors that would block people with the ability to think critically from doing so, we can identify as initiating dispositions for thinking critically attentiveness, a habit of inquiry, self-confidence, courage, open-mindedness, willingness to suspend judgment, trust in reason, wanting evidence for one’s beliefs, and seeking the truth. We consider briefly what each of these dispositions amounts to, in each case citing sources that acknowledge them.

• Attentiveness : One will not think critically if one fails to recognize an issue that needs to be thought through. For example, the pedestrian in Weather would not have looked up if he had not noticed that the air was suddenly cooler. To be a critical thinker, then, one needs to be habitually attentive to one’s surroundings, noticing not only what one senses but also sources of perplexity in messages received and in one’s own beliefs and attitudes (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
• Habit of inquiry : Inquiry is effortful, and one needs an internal push to engage in it. For example, the student in Bubbles could easily have stopped at idle wondering about the cause of the bubbles rather than reasoning to a hypothesis, then designing and executing an experiment to test it. Thus willingness to think critically needs mental energy and initiative. What can supply that energy? Love of inquiry, or perhaps just a habit of inquiry. Hamby (2015) has argued that willingness to inquire is the central critical thinking virtue, one that encompasses all the others. It is recognized as a critical thinking disposition by Dewey (1910: 29; 1933: 35), Glaser (1941: 5), Ennis (1987: 12; 1991: 8), Facione (1990a: 25), Bailin et al. (1999b: 294), Halpern (1998: 452), and Facione, Facione, & Giancarlo (2001).
• Self-confidence : Lack of confidence in one’s abilities can block critical thinking. For example, if the woman in Rash lacked confidence in her ability to figure things out for herself, she might just have assumed that the rash on her chest was the allergic reaction to her medication against which the pharmacist had warned her. Thus willingness to think critically requires confidence in one’s ability to inquire (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
• Courage : Fear of thinking for oneself can stop one from doing it. Thus willingness to think critically requires intellectual courage (Paul & Elder 2006: 16).
• Open-mindedness : A dogmatic attitude will impede thinking critically. For example, a person who adheres rigidly to a “pro-choice” position on the issue of the legal status of induced abortion is likely to be unwilling to consider seriously the issue of when in its development an unborn child acquires a moral right to life. Thus willingness to think critically requires open-mindedness, in the sense of a willingness to examine questions to which one already accepts an answer but which further evidence or reasoning might cause one to answer differently (Dewey 1933; Facione 1990a; Ennis 1991; Bailin et al. 1999b; Halpern 1998, Facione, Facione, & Giancarlo 2001). Paul (1981) emphasizes open-mindedness about alternative world-views, and recommends a dialectical approach to integrating such views as central to what he calls “strong sense” critical thinking.
• Willingness to suspend judgment : Premature closure on an initial solution will block critical thinking. Thus willingness to think critically requires a willingness to suspend judgment while alternatives are explored (Facione 1990a; Ennis 1991; Halpern 1998).
• Trust in reason : Since distrust in the processes of reasoned inquiry will dissuade one from engaging in it, trust in them is an initiating critical thinking disposition (Facione 1990a, 25; Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001; Paul & Elder 2006). In reaction to an allegedly exclusive emphasis on reason in critical thinking theory and pedagogy, Thayer-Bacon (2000) argues that intuition, imagination, and emotion have important roles to play in an adequate conception of critical thinking that she calls “constructive thinking”. From her point of view, critical thinking requires trust not only in reason but also in intuition, imagination, and emotion.
• Seeking the truth : If one does not care about the truth but is content to stick with one’s initial bias on an issue, then one will not think critically about it. Seeking the truth is thus an initiating critical thinking disposition (Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001). A disposition to seek the truth is implicit in more specific critical thinking dispositions, such as trying to be well-informed, considering seriously points of view other than one’s own, looking for alternatives, suspending judgment when the evidence is insufficient, and adopting a position when the evidence supporting it is sufficient.

Some of the initiating dispositions, such as open-mindedness and willingness to suspend judgment, are also internal critical thinking dispositions, in the sense of mental habits or attitudes that contribute causally to doing a good job of critical thinking once one starts the process. But there are many other internal critical thinking dispositions. Some of them are parasitic on one’s conception of good thinking. For example, it is constitutive of good thinking about an issue to formulate the issue clearly and to maintain focus on it. For this purpose, one needs not only the corresponding ability but also the corresponding disposition. Ennis (1991: 8) describes it as the disposition “to determine and maintain focus on the conclusion or question”, Facione (1990a: 25) as “clarity in stating the question or concern”. Other internal dispositions are motivators to continue or adjust the critical thinking process, such as willingness to persist in a complex task and willingness to abandon nonproductive strategies in an attempt to self-correct (Halpern 1998: 452). For a list of identified internal critical thinking dispositions, see the Supplement on Internal Critical Thinking Dispositions .

Some theorists postulate skills, i.e., acquired abilities, as operative in critical thinking. It is not obvious, however, that a good mental act is the exercise of a generic acquired skill. Inferring an expected time of arrival, as in Transit , has some generic components but also uses non-generic subject-matter knowledge. Bailin et al. (1999a) argue against viewing critical thinking skills as generic and discrete, on the ground that skilled performance at a critical thinking task cannot be separated from knowledge of concepts and from domain-specific principles of good thinking. Talk of skills, they concede, is unproblematic if it means merely that a person with critical thinking skills is capable of intelligent performance.

Despite such scepticism, theorists of critical thinking have listed as general contributors to critical thinking what they variously call abilities (Glaser 1941; Ennis 1962, 1991), skills (Facione 1990a; Halpern 1998) or competencies (Fisher & Scriven 1997). Amalgamating these lists would produce a confusing and chaotic cornucopia of more than 50 possible educational objectives, with only partial overlap among them. It makes sense instead to try to understand the reasons for the multiplicity and diversity, and to make a selection according to one’s own reasons for singling out abilities to be developed in a critical thinking curriculum. Two reasons for diversity among lists of critical thinking abilities are the underlying conception of critical thinking and the envisaged educational level. Appraisal-only conceptions, for example, involve a different suite of abilities than constructive-only conceptions. Some lists, such as those in (Glaser 1941), are put forward as educational objectives for secondary school students, whereas others are proposed as objectives for college students (e.g., Facione 1990a).

The abilities described in the remaining paragraphs of this section emerge from reflection on the general abilities needed to do well the thinking activities identified in section 6 as components of the critical thinking process described in section 5 . The derivation of each collection of abilities is accompanied by citation of sources that list such abilities and of standardized tests that claim to test them.

Observational abilities : Careful and accurate observation sometimes requires specialist expertise and practice, as in the case of observing birds and observing accident scenes. However, there are general abilities of noticing what one’s senses are picking up from one’s environment and of being able to articulate clearly and accurately to oneself and others what one has observed. It helps in exercising them to be able to recognize and take into account factors that make one’s observation less trustworthy, such as prior framing of the situation, inadequate time, deficient senses, poor observation conditions, and the like. It helps as well to be skilled at taking steps to make one’s observation more trustworthy, such as moving closer to get a better look, measuring something three times and taking the average, and checking what one thinks one is observing with someone else who is in a good position to observe it. It also helps to be skilled at recognizing respects in which one’s report of one’s observation involves inference rather than direct observation, so that one can then consider whether the inference is justified. These abilities come into play as well when one thinks about whether and with what degree of confidence to accept an observation report, for example in the study of history or in a criminal investigation or in assessing news reports. Observational abilities show up in some lists of critical thinking abilities (Ennis 1962: 90; Facione 1990a: 16; Ennis 1991: 9). There are items testing a person’s ability to judge the credibility of observation reports in the Cornell Critical Thinking Tests, Levels X and Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). Norris and King (1983, 1985, 1990a, 1990b) is a test of ability to appraise observation reports.

Emotional abilities : The emotions that drive a critical thinking process are perplexity or puzzlement, a wish to resolve it, and satisfaction at achieving the desired resolution. Children experience these emotions at an early age, without being trained to do so. Education that takes critical thinking as a goal needs only to channel these emotions and to make sure not to stifle them. Collaborative critical thinking benefits from ability to recognize one’s own and others’ emotional commitments and reactions.

Questioning abilities : A critical thinking process needs transformation of an inchoate sense of perplexity into a clear question. Formulating a question well requires not building in questionable assumptions, not prejudging the issue, and using language that in context is unambiguous and precise enough (Ennis 1962: 97; 1991: 9).

Imaginative abilities : Thinking directed at finding the correct causal explanation of a general phenomenon or particular event requires an ability to imagine possible explanations. Thinking about what policy or plan of action to adopt requires generation of options and consideration of possible consequences of each option. Domain knowledge is required for such creative activity, but a general ability to imagine alternatives is helpful and can be nurtured so as to become easier, quicker, more extensive, and deeper (Dewey 1910: 34–39; 1933: 40–47). Facione (1990a) and Halpern (1998) include the ability to imagine alternatives as a critical thinking ability.

Inferential abilities : The ability to draw conclusions from given information, and to recognize with what degree of certainty one’s own or others’ conclusions follow, is universally recognized as a general critical thinking ability. All 11 examples in section 2 of this article include inferences, some from hypotheses or options (as in Transit , Ferryboat and Disorder ), others from something observed (as in Weather and Rash ). None of these inferences is formally valid. Rather, they are licensed by general, sometimes qualified substantive rules of inference (Toulmin 1958) that rest on domain knowledge—that a bus trip takes about the same time in each direction, that the terminal of a wireless telegraph would be located on the highest possible place, that sudden cooling is often followed by rain, that an allergic reaction to a sulfa drug generally shows up soon after one starts taking it. It is a matter of controversy to what extent the specialized ability to deduce conclusions from premisses using formal rules of inference is needed for critical thinking. Dewey (1933) locates logical forms in setting out the products of reflection rather than in the process of reflection. Ennis (1981a), on the other hand, maintains that a liberally-educated person should have the following abilities: to translate natural-language statements into statements using the standard logical operators, to use appropriately the language of necessary and sufficient conditions, to deal with argument forms and arguments containing symbols, to determine whether in virtue of an argument’s form its conclusion follows necessarily from its premisses, to reason with logically complex propositions, and to apply the rules and procedures of deductive logic. Inferential abilities are recognized as critical thinking abilities by Glaser (1941: 6), Facione (1990a: 9), Ennis (1991: 9), Fisher & Scriven (1997: 99, 111), and Halpern (1998: 452). Items testing inferential abilities constitute two of the five subtests of the Watson Glaser Critical Thinking Appraisal (Watson & Glaser 1980a, 1980b, 1994), two of the four sections in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), three of the seven sections in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), 11 of the 34 items on Forms A and B of the California Critical Thinking Skills Test (Facione 1990b, 1992), and a high but variable proportion of the 25 selected-response questions in the Collegiate Learning Assessment (Council for Aid to Education 2017).

Experimenting abilities : Knowing how to design and execute an experiment is important not just in scientific research but also in everyday life, as in Rash . Dewey devoted a whole chapter of his How We Think (1910: 145–156; 1933: 190–202) to the superiority of experimentation over observation in advancing knowledge. Experimenting abilities come into play at one remove in appraising reports of scientific studies. Skill in designing and executing experiments includes the acknowledged abilities to appraise evidence (Glaser 1941: 6), to carry out experiments and to apply appropriate statistical inference techniques (Facione 1990a: 9), to judge inductions to an explanatory hypothesis (Ennis 1991: 9), and to recognize the need for an adequately large sample size (Halpern 1998). The Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) includes four items (out of 52) on experimental design. The Collegiate Learning Assessment (Council for Aid to Education 2017) makes room for appraisal of study design in both its performance task and its selected-response questions.

Consulting abilities : Skill at consulting sources of information comes into play when one seeks information to help resolve a problem, as in Candidate . Ability to find and appraise information includes ability to gather and marshal pertinent information (Glaser 1941: 6), to judge whether a statement made by an alleged authority is acceptable (Ennis 1962: 84), to plan a search for desired information (Facione 1990a: 9), and to judge the credibility of a source (Ennis 1991: 9). Ability to judge the credibility of statements is tested by 24 items (out of 76) in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) and by four items (out of 52) in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). The College Learning Assessment’s performance task requires evaluation of whether information in documents is credible or unreliable (Council for Aid to Education 2017).

Argument analysis abilities : The ability to identify and analyze arguments contributes to the process of surveying arguments on an issue in order to form one’s own reasoned judgment, as in Candidate . The ability to detect and analyze arguments is recognized as a critical thinking skill by Facione (1990a: 7–8), Ennis (1991: 9) and Halpern (1998). Five items (out of 34) on the California Critical Thinking Skills Test (Facione 1990b, 1992) test skill at argument analysis. The College Learning Assessment (Council for Aid to Education 2017) incorporates argument analysis in its selected-response tests of critical reading and evaluation and of critiquing an argument.

Judging skills and deciding skills : Skill at judging and deciding is skill at recognizing what judgment or decision the available evidence and argument supports, and with what degree of confidence. It is thus a component of the inferential skills already discussed.

Lists and tests of critical thinking abilities often include two more abilities: identifying assumptions and constructing and evaluating definitions.

In addition to dispositions and abilities, critical thinking needs knowledge: of critical thinking concepts, of critical thinking principles, and of the subject-matter of the thinking.

We can derive a short list of concepts whose understanding contributes to critical thinking from the critical thinking abilities described in the preceding section. Observational abilities require an understanding of the difference between observation and inference. Questioning abilities require an understanding of the concepts of ambiguity and vagueness. Inferential abilities require an understanding of the difference between conclusive and defeasible inference (traditionally, between deduction and induction), as well as of the difference between necessary and sufficient conditions. Experimenting abilities require an understanding of the concepts of hypothesis, null hypothesis, assumption and prediction, as well as of the concept of statistical significance and of its difference from importance. They also require an understanding of the difference between an experiment and an observational study, and in particular of the difference between a randomized controlled trial, a prospective correlational study and a retrospective (case-control) study. Argument analysis abilities require an understanding of the concepts of argument, premiss, assumption, conclusion and counter-consideration. Additional critical thinking concepts are proposed by Bailin et al. (1999b: 293), Fisher & Scriven (1997: 105–106), and Black (2012).

According to Glaser (1941: 25), ability to think critically requires knowledge of the methods of logical inquiry and reasoning. If we review the list of abilities in the preceding section, however, we can see that some of them can be acquired and exercised merely through practice, possibly guided in an educational setting, followed by feedback. Searching intelligently for a causal explanation of some phenomenon or event requires that one consider a full range of possible causal contributors, but it seems more important that one implements this principle in one’s practice than that one is able to articulate it. What is important is “operational knowledge” of the standards and principles of good thinking (Bailin et al. 1999b: 291–293). But the development of such critical thinking abilities as designing an experiment or constructing an operational definition can benefit from learning their underlying theory. Further, explicit knowledge of quirks of human thinking seems useful as a cautionary guide. Human memory is not just fallible about details, as people learn from their own experiences of misremembering, but is so malleable that a detailed, clear and vivid recollection of an event can be a total fabrication (Loftus 2017). People seek or interpret evidence in ways that are partial to their existing beliefs and expectations, often unconscious of their “confirmation bias” (Nickerson 1998). Not only are people subject to this and other cognitive biases (Kahneman 2011), of which they are typically unaware, but it may be counter-productive for one to make oneself aware of them and try consciously to counteract them or to counteract social biases such as racial or sexual stereotypes (Kenyon & Beaulac 2014). It is helpful to be aware of these facts and of the superior effectiveness of blocking the operation of biases—for example, by making an immediate record of one’s observations, refraining from forming a preliminary explanatory hypothesis, blind refereeing, double-blind randomized trials, and blind grading of students’ work.

Critical thinking about an issue requires substantive knowledge of the domain to which the issue belongs. Critical thinking abilities are not a magic elixir that can be applied to any issue whatever by somebody who has no knowledge of the facts relevant to exploring that issue. For example, the student in Bubbles needed to know that gases do not penetrate solid objects like a glass, that air expands when heated, that the volume of an enclosed gas varies directly with its temperature and inversely with its pressure, and that hot objects will spontaneously cool down to the ambient temperature of their surroundings unless kept hot by insulation or a source of heat. Critical thinkers thus need a rich fund of subject-matter knowledge relevant to the variety of situations they encounter. This fact is recognized in the inclusion among critical thinking dispositions of a concern to become and remain generally well informed.

Experimental educational interventions, with control groups, have shown that education can improve critical thinking skills and dispositions, as measured by standardized tests. For information about these tests, see the Supplement on Assessment .

What educational methods are most effective at developing the dispositions, abilities and knowledge of a critical thinker? Abrami et al. (2015) found that in the experimental and quasi-experimental studies that they analyzed dialogue, anchored instruction, and mentoring each increased the effectiveness of the educational intervention, and that they were most effective when combined. They also found that in these studies a combination of separate instruction in critical thinking with subject-matter instruction in which students are encouraged to think critically was more effective than either by itself. However, the difference was not statistically significant; that is, it might have arisen by chance.

Most of these studies lack the longitudinal follow-up required to determine whether the observed differential improvements in critical thinking abilities or dispositions continue over time, for example until high school or college graduation. For details on studies of methods of developing critical thinking skills and dispositions, see the Supplement on Educational Methods .

12. Controversies

Scholars have denied the generalizability of critical thinking abilities across subject domains, have alleged bias in critical thinking theory and pedagogy, and have investigated the relationship of critical thinking to other kinds of thinking.

McPeck (1981) attacked the thinking skills movement of the 1970s, including the critical thinking movement. He argued that there are no general thinking skills, since thinking is always thinking about some subject-matter. It is futile, he claimed, for schools and colleges to teach thinking as if it were a separate subject. Rather, teachers should lead their pupils to become autonomous thinkers by teaching school subjects in a way that brings out their cognitive structure and that encourages and rewards discussion and argument. As some of his critics (e.g., Paul 1985; Siegel 1985) pointed out, McPeck’s central argument needs elaboration, since it has obvious counter-examples in writing and speaking, for which (up to a certain level of complexity) there are teachable general abilities even though they are always about some subject-matter. To make his argument convincing, McPeck needs to explain how thinking differs from writing and speaking in a way that does not permit useful abstraction of its components from the subject-matters with which it deals. He has not done so. Nevertheless, his position that the dispositions and abilities of a critical thinker are best developed in the context of subject-matter instruction is shared by many theorists of critical thinking, including Dewey (1910, 1933), Glaser (1941), Passmore (1980), Weinstein (1990), and Bailin et al. (1999b).

McPeck’s challenge prompted reflection on the extent to which critical thinking is subject-specific. McPeck argued for a strong subject-specificity thesis, according to which it is a conceptual truth that all critical thinking abilities are specific to a subject. (He did not however extend his subject-specificity thesis to critical thinking dispositions. In particular, he took the disposition to suspend judgment in situations of cognitive dissonance to be a general disposition.) Conceptual subject-specificity is subject to obvious counter-examples, such as the general ability to recognize confusion of necessary and sufficient conditions. A more modest thesis, also endorsed by McPeck, is epistemological subject-specificity, according to which the norms of good thinking vary from one field to another. Epistemological subject-specificity clearly holds to a certain extent; for example, the principles in accordance with which one solves a differential equation are quite different from the principles in accordance with which one determines whether a painting is a genuine Picasso. But the thesis suffers, as Ennis (1989) points out, from vagueness of the concept of a field or subject and from the obvious existence of inter-field principles, however broadly the concept of a field is construed. For example, the principles of hypothetico-deductive reasoning hold for all the varied fields in which such reasoning occurs. A third kind of subject-specificity is empirical subject-specificity, according to which as a matter of empirically observable fact a person with the abilities and dispositions of a critical thinker in one area of investigation will not necessarily have them in another area of investigation.

The thesis of empirical subject-specificity raises the general problem of transfer. If critical thinking abilities and dispositions have to be developed independently in each school subject, how are they of any use in dealing with the problems of everyday life and the political and social issues of contemporary society, most of which do not fit into the framework of a traditional school subject? Proponents of empirical subject-specificity tend to argue that transfer is more likely to occur if there is critical thinking instruction in a variety of domains, with explicit attention to dispositions and abilities that cut across domains. But evidence for this claim is scanty. There is a need for well-designed empirical studies that investigate the conditions that make transfer more likely.

It is common ground in debates about the generality or subject-specificity of critical thinking dispositions and abilities that critical thinking about any topic requires background knowledge about the topic. For example, the most sophisticated understanding of the principles of hypothetico-deductive reasoning is of no help unless accompanied by some knowledge of what might be plausible explanations of some phenomenon under investigation.

Critics have objected to bias in the theory, pedagogy and practice of critical thinking. Commentators (e.g., Alston 1995; Ennis 1998) have noted that anyone who takes a position has a bias in the neutral sense of being inclined in one direction rather than others. The critics, however, are objecting to bias in the pejorative sense of an unjustified favoring of certain ways of knowing over others, frequently alleging that the unjustly favoured ways are those of a dominant sex or culture (Bailin 1995). These ways favour:

• reinforcement of egocentric and sociocentric biases over dialectical engagement with opposing world-views (Paul 1981, 1984; Warren 1998)
• distancing from the object of inquiry over closeness to it (Martin 1992; Thayer-Bacon 1992)
• indifference to the situation of others over care for them (Martin 1992)
• orientation to thought over orientation to action (Martin 1992)
• being reasonable over caring to understand people’s ideas (Thayer-Bacon 1993)
• being neutral and objective over being embodied and situated (Thayer-Bacon 1995a)
• doubting over believing (Thayer-Bacon 1995b)
• reason over emotion, imagination and intuition (Thayer-Bacon 2000)
• solitary thinking over collaborative thinking (Thayer-Bacon 2000)
• written and spoken assignments over other forms of expression (Alston 2001)
• attention to written and spoken communications over attention to human problems (Alston 2001)
• winning debates in the public sphere over making and understanding meaning (Alston 2001)

A common thread in this smorgasbord of accusations is dissatisfaction with focusing on the logical analysis and evaluation of reasoning and arguments. While these authors acknowledge that such analysis and evaluation is part of critical thinking and should be part of its conceptualization and pedagogy, they insist that it is only a part. Paul (1981), for example, bemoans the tendency of atomistic teaching of methods of analyzing and evaluating arguments to turn students into more able sophists, adept at finding fault with positions and arguments with which they disagree but even more entrenched in the egocentric and sociocentric biases with which they began. Martin (1992) and Thayer-Bacon (1992) cite with approval the self-reported intimacy with their subject-matter of leading researchers in biology and medicine, an intimacy that conflicts with the distancing allegedly recommended in standard conceptions and pedagogy of critical thinking. Thayer-Bacon (2000) contrasts the embodied and socially embedded learning of her elementary school students in a Montessori school, who used their imagination, intuition and emotions as well as their reason, with conceptions of critical thinking as

thinking that is used to critique arguments, offer justifications, and make judgments about what are the good reasons, or the right answers. (Thayer-Bacon 2000: 127–128)

Alston (2001) reports that her students in a women’s studies class were able to see the flaws in the Cinderella myth that pervades much romantic fiction but in their own romantic relationships still acted as if all failures were the woman’s fault and still accepted the notions of love at first sight and living happily ever after. Students, she writes, should

be able to connect their intellectual critique to a more affective, somatic, and ethical account of making risky choices that have sexist, racist, classist, familial, sexual, or other consequences for themselves and those both near and far… critical thinking that reads arguments, texts, or practices merely on the surface without connections to feeling/desiring/doing or action lacks an ethical depth that should infuse the difference between mere cognitive activity and something we want to call critical thinking. (Alston 2001: 34)

Some critics portray such biases as unfair to women. Thayer-Bacon (1992), for example, has charged modern critical thinking theory with being sexist, on the ground that it separates the self from the object and causes one to lose touch with one’s inner voice, and thus stigmatizes women, who (she asserts) link self to object and listen to their inner voice. Her charge does not imply that women as a group are on average less able than men to analyze and evaluate arguments. Facione (1990c) found no difference by sex in performance on his California Critical Thinking Skills Test. Kuhn (1991: 280–281) found no difference by sex in either the disposition or the competence to engage in argumentative thinking.

The critics propose a variety of remedies for the biases that they allege. In general, they do not propose to eliminate or downplay critical thinking as an educational goal. Rather, they propose to conceptualize critical thinking differently and to change its pedagogy accordingly. Their pedagogical proposals arise logically from their objections. They can be summarized as follows:

• Focus on argument networks with dialectical exchanges reflecting contesting points of view rather than on atomic arguments, so as to develop “strong sense” critical thinking that transcends egocentric and sociocentric biases (Paul 1981, 1984).
• Foster closeness to the subject-matter and feeling connected to others in order to inform a humane democracy (Martin 1992).
• Develop “constructive thinking” as a social activity in a community of physically embodied and socially embedded inquirers with personal voices who value not only reason but also imagination, intuition and emotion (Thayer-Bacon 2000).
• In developing critical thinking in school subjects, treat as important neither skills nor dispositions but opening worlds of meaning (Alston 2001).
• Attend to the development of critical thinking dispositions as well as skills, and adopt the “critical pedagogy” practised and advocated by Freire (1968 [1970]) and hooks (1994) (Dalgleish, Girard, & Davies 2017).

A common thread in these proposals is treatment of critical thinking as a social, interactive, personally engaged activity like that of a quilting bee or a barn-raising (Thayer-Bacon 2000) rather than as an individual, solitary, distanced activity symbolized by Rodin’s The Thinker . One can get a vivid description of education with the former type of goal from the writings of bell hooks (1994, 2010). Critical thinking for her is open-minded dialectical exchange across opposing standpoints and from multiple perspectives, a conception similar to Paul’s “strong sense” critical thinking (Paul 1981). She abandons the structure of domination in the traditional classroom. In an introductory course on black women writers, for example, she assigns students to write an autobiographical paragraph about an early racial memory, then to read it aloud as the others listen, thus affirming the uniqueness and value of each voice and creating a communal awareness of the diversity of the group’s experiences (hooks 1994: 84). Her “engaged pedagogy” is thus similar to the “freedom under guidance” implemented in John Dewey’s Laboratory School of Chicago in the late 1890s and early 1900s. It incorporates the dialogue, anchored instruction, and mentoring that Abrami (2015) found to be most effective in improving critical thinking skills and dispositions.

What is the relationship of critical thinking to problem solving, decision-making, higher-order thinking, creative thinking, and other recognized types of thinking? One’s answer to this question obviously depends on how one defines the terms used in the question. If critical thinking is conceived broadly to cover any careful thinking about any topic for any purpose, then problem solving and decision making will be kinds of critical thinking, if they are done carefully. Historically, ‘critical thinking’ and ‘problem solving’ were two names for the same thing. If critical thinking is conceived more narrowly as consisting solely of appraisal of intellectual products, then it will be disjoint with problem solving and decision making, which are constructive.

Bloom’s taxonomy of educational objectives used the phrase “intellectual abilities and skills” for what had been labeled “critical thinking” by some, “reflective thinking” by Dewey and others, and “problem solving” by still others (Bloom et al. 1956: 38). Thus, the so-called “higher-order thinking skills” at the taxonomy’s top levels of analysis, synthesis and evaluation are just critical thinking skills, although they do not come with general criteria for their assessment (Ennis 1981b). The revised version of Bloom’s taxonomy (Anderson et al. 2001) likewise treats critical thinking as cutting across those types of cognitive process that involve more than remembering (Anderson et al. 2001: 269–270). For details, see the Supplement on History .

As to creative thinking, it overlaps with critical thinking (Bailin 1987, 1988). Thinking about the explanation of some phenomenon or event, as in Ferryboat , requires creative imagination in constructing plausible explanatory hypotheses. Likewise, thinking about a policy question, as in Candidate , requires creativity in coming up with options. Conversely, creativity in any field needs to be balanced by critical appraisal of the draft painting or novel or mathematical theory.

• Abrami, Philip C., Robert M. Bernard, Eugene Borokhovski, David I. Waddington, C. Anne Wade, and Tonje Person, 2015, “Strategies for Teaching Students to Think Critically: A Meta-analysis”, Review of Educational Research , 85(2): 275–314. doi:10.3102/0034654314551063
• Aikin, Wilford M., 1942, The Story of the Eight-year Study, with Conclusions and Recommendations , Volume I of Adventure in American Education , New York and London: Harper & Brothers. [ Aikin 1942 available online ]
• Alston, Kal, 1995, “Begging the Question: Is Critical Thinking Biased?”, Educational Theory , 45(2): 225–233. doi:10.1111/j.1741-5446.1995.00225.x
• –––, 2001, “Re/Thinking Critical Thinking: The Seductions of Everyday Life”, Studies in Philosophy and Education , 20(1): 27–40. doi:10.1023/A:1005247128053
• American Educational Research Association, 2014, Standards for Educational and Psychological Testing / American Educational Research Association, American Psychological Association, National Council on Measurement in Education , Washington, DC: American Educational Research Association.
• Anderson, Lorin W., David R. Krathwohl, Peter W. Airiasian, Kathleen A. Cruikshank, Richard E. Mayer, Paul R. Pintrich, James Raths, and Merlin C. Wittrock, 2001, A Taxonomy for Learning, Teaching and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives , New York: Longman, complete edition.
• Bailin, Sharon, 1987, “Critical and Creative Thinking”, Informal Logic , 9(1): 23–30. [ Bailin 1987 available online ]
• –––, 1988, Achieving Extraordinary Ends: An Essay on Creativity , Dordrecht: Kluwer. doi:10.1007/978-94-009-2780-3
• –––, 1995, “Is Critical Thinking Biased? Clarifications and Implications”, Educational Theory , 45(2): 191–197. doi:10.1111/j.1741-5446.1995.00191.x
• Bailin, Sharon and Mark Battersby, 2009, “Inquiry: A Dialectical Approach to Teaching Critical Thinking”, in Juho Ritola (ed.), Argument Cultures: Proceedings of OSSA 09 , CD-ROM (pp. 1–10), Windsor, ON: OSSA. [ Bailin & Battersby 2009 available online ]
• –––, 2016, “Fostering the Virtues of Inquiry”, Topoi , 35(2): 367–374. doi:10.1007/s11245-015-9307-6
• Bailin, Sharon, Roland Case, Jerrold R. Coombs, and Leroi B. Daniels, 1999a, “Common Misconceptions of Critical Thinking”, Journal of Curriculum Studies , 31(3): 269–283. doi:10.1080/002202799183124
• –––, 1999b, “Conceptualizing Critical Thinking”, Journal of Curriculum Studies , 31(3): 285–302. doi:10.1080/002202799183133
• Berman, Alan M., Seth J. Schwartz, William M. Kurtines, and Steven L. Berman, 2001, “The Process of Exploration in Identity Formation: The Role of Style and Competence”, Journal of Adolescence , 24(4): 513–528. doi:10.1006/jado.2001.0386
• Black, Beth (ed.), 2012, An A to Z of Critical Thinking , London: Continuum International Publishing Group.
• Bloom, Benjamin Samuel, Max D. Engelhart, Edward J. Furst, Walter H. Hill, and David R. Krathwohl, 1956, Taxonomy of Educational Objectives. Handbook I: Cognitive Domain , New York: David McKay.
• Casserly, Megan, 2012, “The 10 Skills That Will Get You Hired in 2013”, Forbes , Dec. 10, 2012. Available at https://www.forbes.com/sites/meghancasserly/2012/12/10/the-10-skills-that-will-get-you-a-job-in-2013/#79e7ff4e633d ; accessed 2017 11 06.
• Center for Assessment & Improvement of Learning, 2017, Critical Thinking Assessment Test , Cookeville, TN: Tennessee Technological University.
• Cohen, Jacob, 1988, Statistical Power Analysis for the Behavioral Sciences , Hillsdale, NJ: Lawrence Erlbaum Associates, 2nd edition.
• College Board, 1983, Academic Preparation for College. What Students Need to Know and Be Able to Do , New York: College Entrance Examination Board, ERIC document ED232517.
• Commission on the Relation of School and College of the Progressive Education Association, 1943, Thirty Schools Tell Their Story , Volume V of Adventure in American Education , New York and London: Harper & Brothers.
• Council for Aid to Education, 2017, CLA+ Student Guide . Available at http://cae.org/images/uploads/pdf/CLA_Student_Guide_Institution.pdf ; accessed 2017 09 26.
• Dalgleish, Adam, Patrick Girard, and Maree Davies, 2017, “Critical Thinking, Bias and Feminist Philosophy: Building a Better Framework through Collaboration”, Informal Logic , 37(4): 351–369. [ Dalgleish et al. available online ]
• Dewey, John, 1910, How We Think , Boston: D.C. Heath. [ Dewey 1910 available online ]
• –––, 1916, Democracy and Education: An Introduction to the Philosophy of Education , New York: Macmillan.
• –––, 1933, How We Think: A Restatement of the Relation of Reflective Thinking to the Educative Process , Lexington, MA: D.C. Heath.
• –––, 1936, “The Theory of the Chicago Experiment”, Appendix II of Mayhew & Edwards 1936: 463–477.
• –––, 1938, Logic: The Theory of Inquiry , New York: Henry Holt and Company.
• Dominguez, Caroline (coord.), 2018a, A European Collection of the Critical Thinking Skills and Dispositions Needed in Different Professional Fields for the 21st Century , Vila Real, Portugal: UTAD. Available at http://bit.ly/CRITHINKEDUO1 ; accessed 2018 04 09.
• ––– (coord.), 2018b, A European Review on Critical Thinking Educational Practices in Higher Education Institutions , Vila Real: UTAD. Available at http://bit.ly/CRITHINKEDUO2 ; accessed 2018 04 14.
• Dumke, Glenn S., 1980, Chancellor’s Executive Order 338 , Long Beach, CA: California State University, Chancellor’s Office. Available at https://www.calstate.edu/eo/EO-338.pdf ; accessed 2017 11 16.
• Ennis, Robert H., 1958, “An Appraisal of the Watson-Glaser Critical Thinking Appraisal”, The Journal of Educational Research , 52(4): 155–158. doi:10.1080/00220671.1958.10882558
• –––, 1962, “A Concept of Critical Thinking: A Proposed Basis for Research on the Teaching and Evaluation of Critical Thinking Ability”, Harvard Educational Review , 32(1): 81–111.
• –––, 1981a, “A Conception of Deductive Logical Competence”, Teaching Philosophy , 4(3/4): 337–385. doi:10.5840/teachphil198143/429
• –––, 1981b, “Eight Fallacies in Bloom’s Taxonomy”, in C. J. B. Macmillan (ed.), Philosophy of Education 1980: Proceedings of the Thirty-seventh Annual Meeting of the Philosophy of Education Society , Bloomington, IL: Philosophy of Education Society, pp. 269–273.
• –––, 1984, “Problems in Testing Informal Logic, Critical Thinking, Reasoning Ability”. Informal Logic , 6(1): 3–9. [ Ennis 1984 available online ]
• –––, 1987, “A Taxonomy of Critical Thinking Dispositions and Abilities”, in Joan Boykoff Baron and Robert J. Sternberg (eds.), Teaching Thinking Skills: Theory and Practice , New York: W. H. Freeman, pp. 9–26.
• –––, 1989, “Critical Thinking and Subject Specificity: Clarification and Needed Research”, Educational Researcher , 18(3): 4–10. doi:10.3102/0013189X018003004
• –––, 1991, “Critical Thinking: A Streamlined Conception”, Teaching Philosophy , 14(1): 5–24. doi:10.5840/teachphil19911412
• –––, 1996, “Critical Thinking Dispositions: Their Nature and Assessability”, Informal Logic , 18(2–3): 165–182. [ Ennis 1996 available online ]
• –––, 1998, “Is Critical Thinking Culturally Biased?”, Teaching Philosophy , 21(1): 15–33. doi:10.5840/teachphil19982113
• –––, 2011, “Critical Thinking: Reflection and Perspective Part I”, Inquiry: Critical Thinking across the Disciplines , 26(1): 4–18. doi:10.5840/inquiryctnews20112613
• –––, 2013, “Critical Thinking across the Curriculum: The Wisdom CTAC Program”, Inquiry: Critical Thinking across the Disciplines , 28(2): 25–45. doi:10.5840/inquiryct20132828
• –––, 2016, “Definition: A Three-Dimensional Analysis with Bearing on Key Concepts”, in Patrick Bondy and Laura Benacquista (eds.), Argumentation, Objectivity, and Bias: Proceedings of the 11th International Conference of the Ontario Society for the Study of Argumentation (OSSA), 18–21 May 2016 , Windsor, ON: OSSA, pp. 1–19. Available at http://scholar.uwindsor.ca/ossaarchive/OSSA11/papersandcommentaries/105 ; accessed 2017 12 02.
• –––, 2018, “Critical Thinking Across the Curriculum: A Vision”, Topoi , 37(1): 165–184. doi:10.1007/s11245-016-9401-4
• Ennis, Robert H., and Jason Millman, 1971, Manual for Cornell Critical Thinking Test, Level X, and Cornell Critical Thinking Test, Level Z , Urbana, IL: Critical Thinking Project, University of Illinois.
• Ennis, Robert H., Jason Millman, and Thomas Norbert Tomko, 1985, Cornell Critical Thinking Tests Level X & Level Z: Manual , Pacific Grove, CA: Midwest Publication, 3rd edition.
• –––, 2005, Cornell Critical Thinking Tests Level X & Level Z: Manual , Seaside, CA: Critical Thinking Company, 5th edition.
• Ennis, Robert H. and Eric Weir, 1985, The Ennis-Weir Critical Thinking Essay Test: Test, Manual, Criteria, Scoring Sheet: An Instrument for Teaching and Testing , Pacific Grove, CA: Midwest Publications.
• Facione, Peter A., 1990a, Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction , Research Findings and Recommendations Prepared for the Committee on Pre-College Philosophy of the American Philosophical Association, ERIC Document ED315423.
• –––, 1990b, California Critical Thinking Skills Test, CCTST – Form A , Millbrae, CA: The California Academic Press.
• –––, 1990c, The California Critical Thinking Skills Test--College Level. Technical Report #3. Gender, Ethnicity, Major, CT Self-Esteem, and the CCTST , ERIC Document ED326584.
• –––, 1992, California Critical Thinking Skills Test: CCTST – Form B, Millbrae, CA: The California Academic Press.
• –––, 2000, “The Disposition Toward Critical Thinking: Its Character, Measurement, and Relationship to Critical Thinking Skill”, Informal Logic , 20(1): 61–84. [ Facione 2000 available online ]
• Facione, Peter A. and Noreen C. Facione, 1992, CCTDI: A Disposition Inventory , Millbrae, CA: The California Academic Press.
• Facione, Peter A., Noreen C. Facione, and Carol Ann F. Giancarlo, 2001, California Critical Thinking Disposition Inventory: CCTDI: Inventory Manual , Millbrae, CA: The California Academic Press.
• Facione, Peter A., Carol A. Sánchez, and Noreen C. Facione, 1994, Are College Students Disposed to Think? , Millbrae, CA: The California Academic Press. ERIC Document ED368311.
• Fisher, Alec, and Michael Scriven, 1997, Critical Thinking: Its Definition and Assessment , Norwich: Centre for Research in Critical Thinking, University of East Anglia.
• Freire, Paulo, 1968 [1970], Pedagogia do Oprimido . Translated as Pedagogy of the Oppressed , Myra Bergman Ramos (trans.), New York: Continuum, 1970.
• Glaser, Edward Maynard, 1941, An Experiment in the Development of Critical Thinking , New York: Bureau of Publications, Teachers College, Columbia University.
• Halpern, Diane F., 1998, “Teaching Critical Thinking for Transfer Across Domains: Disposition, Skills, Structure Training, and Metacognitive Monitoring”, American Psychologist , 53(4): 449–455. doi:10.1037/0003-066X.53.4.449
• –––, 2016, Manual: Halpern Critical Thinking Assessment , Mödling, Austria: Schuhfried. Available at https://drive.google.com/file/d/0BzUoP_pmwy1gdEpCR05PeW9qUzA/view ; accessed 2017 12 01.
• Hamby, Benjamin, 2014, The Virtues of Critical Thinkers , Doctoral dissertation, Philosophy, McMaster University. [ Hamby 2014 available online ]
• –––, 2015, “Willingness to Inquire: The Cardinal Critical Thinking Virtue”, in Martin Davies and Ronald Barnett (eds.), The Palgrave Handbook of Critical Thinking in Higher Education , New York: Palgrave Macmillan, pp. 77–87.
• Haynes, Ada, Elizabeth Lisic, Kevin Harris, Katie Leming, Kyle Shanks, and Barry Stein, 2015, “Using the Critical Thinking Assessment Test (CAT) as a Model for Designing Within-Course Assessments: Changing How Faculty Assess Student Learning”, Inquiry: Critical Thinking Across the Disciplines , 30(3): 38–48. doi:10.5840/inquiryct201530316
• Hitchcock, David, 2017, “Critical Thinking as an Educational Ideal”, in his On Reasoning and Argument: Essays in Informal Logic and on Critical Thinking , Dordrecht: Springer, pp. 477–497. doi:10.1007/978-3-319-53562-3_30
• hooks, bell, 1994, Teaching to Transgress: Education as the Practice of Freedom , New York and London: Routledge.
• –––, 2010, Teaching Critical Thinking: Practical Wisdom , New York and London: Routledge.
• Johnson, Ralph H., 1992, “The Problem of Defining Critical Thinking”, in Stephen P, Norris (ed.), The Generalizability of Critical Thinking , New York: Teachers College Press, pp. 38–53.
• Kahane, Howard, 1971, Logic and Contemporary Rhetoric: The Use of Reason in Everyday Life , Belmont, CA: Wadsworth.
• Kahneman, Daniel, 2011, Thinking, Fast and Slow , New York: Farrar, Straus and Giroux.
• Kenyon, Tim, and Guillaume Beaulac, 2014, “Critical Thinking Education and Debasing”, Informal Logic , 34(4): 341–363. [ Kenyon & Beaulac 2014 available online ]
• Krathwohl, David R., Benjamin S. Bloom, and Bertram B. Masia, 1964, Taxonomy of Educational Objectives, Handbook II: Affective Domain , New York: David McKay.
• Kuhn, Deanna, 1991, The Skills of Argument , New York: Cambridge University Press. doi:10.1017/CBO9780511571350
• Lipman, Matthew, 1987, “Critical Thinking–What Can It Be?”, Analytic Teaching , 8(1): 5–12. [ Lipman 1987 available online ]
• Loftus, Elizabeth F., 2017, “Eavesdropping on Memory”, Annual Review of Psychology , 68: 1–18. doi:10.1146/annurev-psych-010416-044138
• Martin, Jane Roland, 1992, “Critical Thinking for a Humane World”, in Stephen P. Norris (ed.), The Generalizability of Critical Thinking , New York: Teachers College Press, pp. 163–180.
• Mayhew, Katherine Camp, and Anna Camp Edwards, 1936, The Dewey School: The Laboratory School of the University of Chicago, 1896–1903 , New York: Appleton-Century. [ Mayhew & Edwards 1936 available online ]
• McPeck, John E., 1981, Critical Thinking and Education , New York: St. Martin’s Press.
• Nickerson, Raymond S., 1998, “Confirmation Bias: A Ubiquitous Phenomenon in Many Guises”, Review of General Psychology , 2(2): 175–220. doi:10.1037/1089-2680.2.2.175
• Nieto, Ana Maria, and Jorge Valenzuela, 2012, “A Study of the Internal Structure of Critical Thinking Dispositions”, Inquiry: Critical Thinking across the Disciplines , 27(1): 31–38. doi:10.5840/inquiryct20122713
• Norris, Stephen P., 1985, “Controlling for Background Beliefs When Developing Multiple-choice Critical Thinking Tests”, Educational Measurement: Issues and Practice , 7(3): 5–11. doi:10.1111/j.1745-3992.1988.tb00437.x
• Norris, Stephen P. and Robert H. Ennis, 1989, Evaluating Critical Thinking (The Practitioners’ Guide to Teaching Thinking Series), Pacific Grove, CA: Midwest Publications.
• Norris, Stephen P. and Ruth Elizabeth King, 1983, Test on Appraising Observations , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland.
• –––, 1984, The Design of a Critical Thinking Test on Appraising Observations , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland. ERIC Document ED260083.
• –––, 1985, Test on Appraising Observations: Manual , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland.
• –––, 1990a, Test on Appraising Observations , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland, 2nd edition.
• –––, 1990b, Test on Appraising Observations: Manual , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland, 2nd edition.
• Obama, Barack, 2014, State of the Union Address , January 28, 2014. [ Obama 2014 available online ]
• OCR [Oxford, Cambridge and RSA Examinations], 2011, AS/A Level GCE: Critical Thinking – H052, H452 , Cambridge: OCR. Information available at http://www.ocr.org.uk/qualifications/as-a-level-gce-critical-thinking-h052-h452/ ; accessed 2017 10 12.
• OECD [Organization for Economic Cooperation and Development] Centre for Educational Research and Innovation, 2018, Fostering and Assessing Students’ Creative and Critical Thinking Skills in Higher Education , Paris: OECD. Available at http://www.oecd.org/education/ceri/Fostering-and-assessing-students-creative-and-critical-thinking-skills-in-higher-education.pdf ; accessed 2018 04 22.
• Ontario Ministry of Education, 2013, The Ontario Curriculum Grades 9 to 12: Social Sciences and Humanities . Available at http://www.edu.gov.on.ca/eng/curriculum/secondary/ssciences9to122013.pdf ; accessed 2017 11 16.
• Passmore, John Arthur, 1980, The Philosophy of Teaching , London: Duckworth.
• Paul, Richard W., 1981, “Teaching Critical Thinking in the ‘Strong’ Sense: A Focus on Self-Deception, World Views, and a Dialectical Mode of Analysis”, Informal Logic , 4(2): 2–7. [ Paul 1981 available online ]
• –––, 1984, “Critical Thinking: Fundamental to Education for a Free Society”, Educational Leadership , 42(1): 4–14.
• –––, 1985, “McPeck’s Mistakes”, Informal Logic , 7(1): 35–43. [ Paul 1985 available online ]
• Paul, Richard W. and Linda Elder, 2006, The Miniature Guide to Critical Thinking: Concepts and Tools , Dillon Beach, CA: Foundation for Critical Thinking, 4th edition.
• Payette, Patricia, and Edna Ross, 2016, “Making a Campus-Wide Commitment to Critical Thinking: Insights and Promising Practices Utilizing the Paul-Elder Approach at the University of Louisville”, Inquiry: Critical Thinking Across the Disciplines , 31(1): 98–110. doi:10.5840/inquiryct20163118
• Possin, Kevin, 2008, “A Field Guide to Critical-Thinking Assessment”, Teaching Philosophy , 31(3): 201–228. doi:10.5840/teachphil200831324
• –––, 2013a, “Some Problems with the Halpern Critical Thinking Assessment (HCTA) Test”, Inquiry: Critical Thinking across the Disciplines , 28(3): 4–12. doi:10.5840/inquiryct201328313
• –––, 2013b, “A Serious Flaw in the Collegiate Learning Assessment (CLA) Test”, Informal Logic , 33(3): 390–405. [ Possin 2013b available online ]
• –––, 2014, “Critique of the Watson-Glaser Critical Thinking Appraisal Test: The More You Know, the Lower Your Score”, Informal Logic , 34(4): 393–416. [ Possin 2014 available online ]
• Rawls, John, 1971, A Theory of Justice , Cambridge, MA: Harvard University Press.
• Rousseau, Jean-Jacques, 1762, Émile , Amsterdam: Jean Néaulme.
• Scheffler, Israel, 1960, The Language of Education , Springfield, IL: Charles C. Thomas.
• Scriven, Michael, and Richard W. Paul, 1987, Defining Critical Thinking , Draft statement written for the National Council for Excellence in Critical Thinking Instruction. Available at http://www.criticalthinking.org/pages/defining-critical-thinking/766 ; accessed 2017 11 29.
• Sheffield, Clarence Burton Jr., 2018, “Promoting Critical Thinking in Higher Education: My Experiences as the Inaugural Eugene H. Fram Chair in Applied Critical Thinking at Rochester Institute of Technology”, Topoi , 37(1): 155–163. doi:10.1007/s11245-016-9392-1
• Siegel, Harvey, 1985, “McPeck, Informal Logic and the Nature of Critical Thinking”, in David Nyberg (ed.), Philosophy of Education 1985: Proceedings of the Forty-First Annual Meeting of the Philosophy of Education Society , Normal, IL: Philosophy of Education Society, pp. 61–72.
• –––, 1988, Educating Reason: Rationality, Critical Thinking, and Education , New York: Routledge.
• –––, 1999, “What (Good) Are Thinking Dispositions?”, Educational Theory , 49(2): 207–221. doi:10.1111/j.1741-5446.1999.00207.x
• Simpson, Elizabeth, 1966–67, “The Classification of Educational Objectives: Psychomotor Domain”, Illinois Teacher of Home Economics , 10(4): 110–144, ERIC document ED0103613. [ Simpson 1966–67 available online ]
• Skolverket, 2011, Curriculum for the Compulsory School, Preschool Class and the Recreation Centre , Stockholm: Ordförrådet AB. Available at http://malmo.se/download/18.29c3b78a132728ecb52800034181/pdf2687.pdf ; accessed 2017 11 16.
• Smith, B. Othanel, 1953, “The Improvement of Critical Thinking”, Progressive Education , 30(5): 129–134.
• Smith, Eugene Randolph, Ralph Winfred Tyler, and the Evaluation Staff, 1942, Appraising and Recording Student Progress , Volume III of Adventure in American Education , New York and London: Harper & Brothers.
• Splitter, Laurance J., 1987, “Educational Reform through Philosophy for Children”, Thinking: The Journal of Philosophy for Children , 7(2): 32–39. doi:10.5840/thinking1987729
• Stanovich Keith E., and Paula J. Stanovich, 2010, “A Framework for Critical Thinking, Rational Thinking, and Intelligence”, in David D. Preiss and Robert J. Sternberg (eds), Innovations in Educational Psychology: Perspectives on Learning, Teaching and Human Development , New York: Springer Publishing, pp 195–237.
• Stanovich Keith E., Richard F. West, and Maggie E. Toplak, 2011, “Intelligence and Rationality”, in Robert J. Sternberg and Scott Barry Kaufman (eds.), Cambridge Handbook of Intelligence , Cambridge: Cambridge University Press, 3rd edition, pp. 784–826. doi:10.1017/CBO9780511977244.040
• Tankersley, Karen, 2005, Literacy Strategies for Grades 4–12: Reinforcing the Threads of Reading , Alexandria, VA: Association for Supervision and Curriculum Development.
• Thayer-Bacon, Barbara J., 1992, “Is Modern Critical Thinking Theory Sexist?”, Inquiry: Critical Thinking Across the Disciplines , 10(1): 3–7. doi:10.5840/inquiryctnews199210123
• –––, 1993, “Caring and Its Relationship to Critical Thinking”, Educational Theory , 43(3): 323–340. doi:10.1111/j.1741-5446.1993.00323.x
• –––, 1995a, “Constructive Thinking: Personal Voice”, Journal of Thought , 30(1): 55–70.
• –––, 1995b, “Doubting and Believing: Both are Important for Critical Thinking”, Inquiry: Critical Thinking across the Disciplines , 15(2): 59–66. doi:10.5840/inquiryctnews199515226
• –––, 2000, Transforming Critical Thinking: Thinking Constructively , New York: Teachers College Press.
• Toulmin, Stephen Edelston, 1958, The Uses of Argument , Cambridge: Cambridge University Press.
• Turri, John, Mark Alfano, and John Greco, 2017, “Virtue Epistemology”, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Winter 2017 Edition). URL = < https://plato.stanford.edu/archives/win2017/entries/epistemology-virtue/ >
• Warren, Karen J. 1988. “Critical Thinking and Feminism”, Informal Logic , 10(1): 31–44. [ Warren 1988 available online ]
• Watson, Goodwin, and Edward M. Glaser, 1980a, Watson-Glaser Critical Thinking Appraisal, Form A , San Antonio, TX: Psychological Corporation.
• –––, 1980b, Watson-Glaser Critical Thinking Appraisal: Forms A and B; Manual , San Antonio, TX: Psychological Corporation,
• –––, 1994, Watson-Glaser Critical Thinking Appraisal, Form B , San Antonio, TX: Psychological Corporation.
• Weinstein, Mark, 1990, “Towards a Research Agenda for Informal Logic and Critical Thinking”, Informal Logic , 12(3): 121–143. [ Weinstein 1990 available online ]
• –––, 2013, Logic, Truth and Inquiry , London: College Publications.
• Zagzebski, Linda Trinkaus, 1996, Virtues of the Mind: An Inquiry into the Nature of Virtue and the Ethical Foundations of Knowledge , Cambridge: Cambridge University Press. doi:10.1017/CBO9781139174763

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• Association for Informal Logic and Critical Thinking (AILACT)
• Center for Teaching Thinking (CTT)
• Critical Thinking Across the European Higher Education Curricula (CRITHINKEDU)
• Critical Thinking Definition, Instruction, and Assessment: A Rigorous Approach (criticalTHINKING.net)
• Critical Thinking Research (RAIL)
• Foundation for Critical Thinking
• Insight Assessment
• Partnership for 21st Century Learning (P21)
• The Critical Thinking Consortium
• The Nature of Critical Thinking: An Outline of Critical Thinking Dispositions and Abilities , by Robert H. Ennis

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