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1: Introduction to Critical Thinking, Reasoning, and Logic

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Page ID 29580

Golden West College via NGE Far Press

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What is thinking? It may seem strange to begin a logic textbook with this question. ‘Thinking’ is perhaps the most intimate and personal thing that people do. Yet the more you ‘think’ about thinking, the more mysterious it can appear. It is the sort of thing that one intuitively or naturally understands, and yet cannot describe to others without great difficulty. Many people believe that logic is very abstract, dispassionate, complicated, and even cold. But in fact the study of logic is nothing more intimidating or obscure than this: the study of good thinking.

1.1: Prelude to Chapter
1.2: Introduction and Thought Experiments- The Trolley Problem
1.3: Truth and Its Role in Argumentation - Certainty, Probability, and Monty Hall Only certain sorts of sentences can be used in arguments. We call these sentences propositions, statements or claims.
1.4: Distinction of Proof from Verification; Our Biases and the Forer Effect
1.5: The Scientific Method The procedure that scientists use is also a standard form of argument. Its conclusions only give you the likelihood or the probability that something is true (if your theory or hypothesis is confirmed), and not the certainty that it’s true. But when it is done correctly, the conclusions it reaches are very well-grounded in experimental evidence.
1.6: Diagramming Thoughts and Arguments - Analyzing News Media
1.7: Creating a Philosophical Outline

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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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Introduction to Logic and Critical Thinking

(10 reviews)

Matthew Van Cleave, Lansing Community College

Publisher: Matthew J. Van Cleave

Language: English

Formats Available

Conditions of use.

Learn more about reviews.

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

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

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 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 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 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, 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 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 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

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.

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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PHIL102: Introduction to Critical Thinking and Logic

Course introduction.

Time: 40 hours
College Credit Recommended ($25 Proctor Fee) -->
Free Certificate

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

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.

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. Moreover, 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 lane 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, 2021), others on the resulting judgment (Facione 1990a), and still others on responsiveness to reasons (Siegel 1988). Kuhn (2019) takes critical thinking to be more a dialogic practice of advancing and responding to arguments than an individual ability.

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 spacing 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 spacing 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 2016a) 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.

Facione (1990a: 25) divides “affective dispositions” of critical thinking into approaches to life and living in general and approaches to specific issues, questions or problems. Adapting this distinction, one can usefully divide critical thinking dispositions 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). 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. In three studies, Haran, Ritov, & Mellers (2013) found that actively open-minded thinking, including “the tendency to weigh new evidence against a favored belief, to spend sufficient time on a problem before giving up, and to consider carefully the opinions of others in forming one’s own”, led study participants to acquire information and thus to make accurate estimations.
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), Black (2012), and Blair (2021).

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. It is also helpful to be aware of the prevalence of “noise” (unwanted unsystematic variability of judgments), of how to detect noise (through a noise audit), and of how to reduce noise: make accuracy the goal, think statistically, break a process of arriving at a judgment into independent tasks, resist premature intuitions, in a group get independent judgments first, favour comparative judgments and scales (Kahneman, Sibony, & Sunstein 2021). It is helpful as well to be aware of the concept of “bounded rationality” in decision-making and of the related distinction between “satisficing” and optimizing (Simon 1956; Gigerenzer 2001).

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? In a comprehensive meta-analysis of experimental and quasi-experimental studies of strategies for teaching students to think critically, Abrami et al. (2015) found that 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), Bailin et al. (1999b), and Willingham (2019).

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.

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Library of Congress Catalog Data: ISSN 1095-5054

1 Introduction to Critical Thinking

I. what is c ritical t hinking [1].

Critical thinking is the ability to think clearly and rationally about what to do or what to believe. It includes the ability to engage in reflective and independent thinking. Someone with critical thinking skills is able to do the following:

Understand the logical connections between ideas.
Identify, construct, and evaluate arguments.
Detect inconsistencies and common mistakes in reasoning.
Solve problems systematically.
Identify the relevance and importance of ideas.
Reflect on the justification of one’s own beliefs and values.

Critical thinking is not simply a matter of accumulating information. A person with a good memory and who knows a lot of facts is not necessarily good at critical thinking. Critical thinkers are able to deduce consequences from what they know, make use of information to solve problems, and to seek relevant sources of information to inform themselves.

Critical thinking should not be confused with being argumentative or being critical of other people. Although critical thinking skills can be used in exposing fallacies and bad reasoning, critical thinking can also play an important role in cooperative reasoning and constructive tasks. Critical thinking can help us acquire knowledge, improve our theories, and strengthen arguments. We can also use critical thinking to enhance work processes and improve social institutions.

Some people believe that critical thinking hinders creativity because critical thinking requires following the rules of logic and rationality, whereas creativity might require breaking those rules. This is a misconception. Critical thinking is quite compatible with thinking “out-of-the-box,” challenging consensus views, and pursuing less popular approaches. If anything, critical thinking is an essential part of creativity because we need critical thinking to evaluate and improve our creative ideas.

II. The I mportance of C ritical T hinking

Critical thinking is a domain-general thinking skill. The ability to think clearly and rationally is important whatever we choose to do. If you work in education, research, finance, management or the legal profession, then critical thinking is obviously important. But critical thinking skills are not restricted to a particular subject area. Being able to think well and solve problems systematically is an asset for any career.

Critical thinking is very important in the new knowledge economy. The global knowledge economy is driven by information and technology. One has to be able to deal with changes quickly and effectively. The new economy places increasing demands on flexible intellectual skills, and the ability to analyze information and integrate diverse sources of knowledge in solving problems. Good critical thinking promotes such thinking skills, and is very important in the fast-changing workplace.

Critical thinking enhances language and presentation skills. Thinking clearly and systematically can improve the way we express our ideas. In learning how to analyze the logical structure of texts, critical thinking also improves comprehension abilities.

Critical thinking promotes creativity. To come up with a creative solution to a problem involves not just having new ideas. It must also be the case that the new ideas being generated are useful and relevant to the task at hand. Critical thinking plays a crucial role in evaluating new ideas, selecting the best ones and modifying them if necessary.

Critical thinking is crucial for self-reflection. In order to live a meaningful life and to structure our lives accordingly, we need to justify and reflect on our values and decisions. Critical thinking provides the tools for this process of self-evaluation.

Good critical thinking is the foundation of science and democracy. Science requires the critical use of reason in experimentation and theory confirmation. The proper functioning of a liberal democracy requires citizens who can think critically about social issues to inform their judgments about proper governance and to overcome biases and prejudice.

Critical thinking is a metacognitive skill . What this means is that it is a higher-level cognitive skill that involves thinking about thinking. We have to be aware of the good principles of reasoning, and be reflective about our own reasoning. In addition, we often need to make a conscious effort to improve ourselves, avoid biases, and maintain objectivity. This is notoriously hard to do. We are all able to think but to think well often requires a long period of training. The mastery of critical thinking is similar to the mastery of many other skills. There are three important components: theory, practice, and attitude.

III. Improv ing O ur T hinking S kills

If we want to think correctly, we need to follow the correct rules of reasoning. Knowledge of theory includes knowledge of these rules. These are the basic principles of critical thinking, such as the laws of logic, and the methods of scientific reasoning, etc.

Also, it would be useful to know something about what not to do if we want to reason correctly. This means we should have some basic knowledge of the mistakes that people make. First, this requires some knowledge of typical fallacies. Second, psychologists have discovered persistent biases and limitations in human reasoning. An awareness of these empirical findings will alert us to potential problems.

However, merely knowing the principles that distinguish good and bad reasoning is not enough. We might study in the classroom about how to swim, and learn about the basic theory, such as the fact that one should not breathe underwater. But unless we can apply such theoretical knowledge through constant practice, we might not actually be able to swim.

Similarly, to be good at critical thinking skills it is necessary to internalize the theoretical principles so that we can actually apply them in daily life. There are at least two ways to do this. One is to perform lots of quality exercises. These exercises don’t just include practicing in the classroom or receiving tutorials; they also include engaging in discussions and debates with other people in our daily lives, where the principles of critical thinking can be applied. The second method is to think more deeply about the principles that we have acquired. In the human mind, memory and understanding are acquired through making connections between ideas.

Good critical thinking skills require more than just knowledge and practice. Persistent practice can bring about improvements only if one has the right kind of motivation and attitude. The following attitudes are not uncommon, but they are obstacles to critical thinking:

I prefer being given the correct answers rather than figuring them out myself.
I don’t like to think a lot about my decisions as I rely only on gut feelings.
I don’t usually review the mistakes I have made.
I don’t like to be criticized.

To improve our thinking we have to recognize the importance of reflecting on the reasons for belief and action. We should also be willing to engage in debate, break old habits, and deal with linguistic complexities and abstract concepts.

The California Critical Thinking Disposition Inventory is a psychological test that is used to measure whether people are disposed to think critically. It measures the seven different thinking habits listed below, and it is useful to ask ourselves to what extent they describe the way we think:

Truth-Seeking—Do you try to understand how things really are? Are you interested in finding out the truth?
Open-Mindedness—How receptive are you to new ideas, even when you do not intuitively agree with them? Do you give new concepts a fair hearing?
Analyticity—Do you try to understand the reasons behind things? Do you act impulsively or do you evaluate the pros and cons of your decisions?
Systematicity—Are you systematic in your thinking? Do you break down a complex problem into parts?
Confidence in Reasoning—Do you always defer to other people? How confident are you in your own judgment? Do you have reasons for your confidence? Do you have a way to evaluate your own thinking?
Inquisitiveness—Are you curious about unfamiliar topics and resolving complicated problems? Will you chase down an answer until you find it?
Maturity of Judgment—Do you jump to conclusions? Do you try to see things from different perspectives? Do you take other people’s experiences into account?

Finally, as mentioned earlier, psychologists have discovered over the years that human reasoning can be easily affected by a variety of cognitive biases. For example, people tend to be over-confident of their abilities and focus too much on evidence that supports their pre-existing opinions. We should be alert to these biases in our attitudes towards our own thinking.

IV. Defining Critical Thinking

There are many different definitions of critical thinking. Here we list some of the well-known ones. You might notice that they all emphasize the importance of clarity and rationality. Here we will look at some well-known definitions in chronological order.

1) Many people trace the importance of critical thinking in education to the early twentieth-century American philosopher John Dewey. But Dewey did not make very extensive use of the term “critical thinking.” Instead, in his book How We Think (1910), he argued for the importance of what he called “reflective thinking”:

…[when] the ground or basis for a belief is deliberately sought and its adequacy to support the belief examined. This process is called reflective thought; it alone is truly educative in value…

Active, persistent and careful consideration of any belief or supposed form of knowledge in light of the grounds that support it, and the further conclusions to which it tends, constitutes reflective thought.

There is however one passage from How We Think where Dewey explicitly uses the term “critical thinking”:

The essence of critical thinking is suspended judgment; and the essence of this suspense is inquiry to determine the nature of the problem before proceeding to attempts at its solution. This, more than any other thing, transforms mere inference into tested inference, suggested conclusions into proof.

2) The Watson-Glaser Critical Thinking Appraisal (1980) is a well-known psychological test of critical thinking ability. The authors of this test define critical thinking as:

…a composite of attitudes, knowledge and skills. This composite includes: (1) attitudes of inquiry that involve an ability to recognize the existence of problems and an acceptance of the general need for evidence in support of what is asserted to be true; (2) knowledge of the nature of valid inferences, abstractions, and generalizations in which the weight or accuracy of different kinds of evidence are logically determined; and (3) skills in employing and applying the above attitudes and knowledge.

3) A very well-known and influential definition of critical thinking comes from philosopher and professor Robert Ennis in his work “A Taxonomy of Critical Thinking Dispositions and Abilities” (1987):

Critical thinking is reasonable reflective thinking that is focused on deciding what to believe or do.

4) The following definition comes from a statement written in 1987 by the philosophers Michael Scriven and Richard Paul for the National Council for Excellence in Critical Thinking (link), an organization promoting critical thinking in the US:

Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. In its exemplary form, it is based on universal intellectual values that transcend subject matter divisions: clarity, accuracy, precision, consistency, relevance, sound evidence, good reasons, depth, breadth, and fairness. It entails the examination of those structures or elements of thought implicit in all reasoning: purpose, problem, or question-at-issue, assumptions, concepts, empirical grounding; reasoning leading to conclusions, implications and consequences, objections from alternative viewpoints, and frame of reference.

The following excerpt from Peter A. Facione’s “Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction” (1990) is quoted from a report written for the American Philosophical Association:

We understand critical thinking to be purposeful, self-regulatory judgment which results in interpretation, analysis, evaluation, and inference, as well as explanation of the evidential, conceptual, methodological, criteriological, or contextual considerations upon which that judgment is based. CT is essential as a tool of inquiry. As such, CT is a liberating force in education and a powerful resource in one’s personal and civic life. While not synonymous with good thinking, CT is a pervasive and self-rectifying human phenomenon. The ideal critical thinker is habitually inquisitive, well-informed, trustful of reason, open-minded, flexible, fairminded in evaluation, honest in facing personal biases, prudent in making judgments, willing to reconsider, clear about issues, orderly in complex matters, diligent in seeking relevant information, reasonable in the selection of criteria, focused in inquiry, and persistent in seeking results which are as precise as the subject and the circumstances of inquiry permit. Thus, educating good critical thinkers means working toward this ideal. It combines developing CT skills with nurturing those dispositions which consistently yield useful insights and which are the basis of a rational and democratic society.

V. Two F eatures of C ritical T hinking

A. how not what .

Critical thinking is concerned not with what you believe, but rather how or why you believe it. Most classes, such as those on biology or chemistry, teach you what to believe about a subject matter. In contrast, critical thinking is not particularly interested in what the world is, in fact, like. Rather, critical thinking will teach you how to form beliefs and how to think. It is interested in the type of reasoning you use when you form your beliefs, and concerns itself with whether you have good reasons to believe what you believe. Therefore, this class isn’t a class on the psychology of reasoning, which brings us to the second important feature of critical thinking.

B. Ought N ot Is ( or Normative N ot Descriptive )

There is a difference between normative and descriptive theories. Descriptive theories, such as those provided by physics, provide a picture of how the world factually behaves and operates. In contrast, normative theories, such as those provided by ethics or political philosophy, provide a picture of how the world should be. Rather than ask question such as why something is the way it is, normative theories ask how something should be. In this course, we will be interested in normative theories that govern our thinking and reasoning. Therefore, we will not be interested in how we actually reason, but rather focus on how we ought to reason.

In the introduction to this course we considered a selection task with cards that must be flipped in order to check the validity of a rule. We noted that many people fail to identify all the cards required to check the rule. This is how people do in fact reason (descriptive). We then noted that you must flip over two cards. This is how people ought to reason (normative).

Section I-IV are taken from http://philosophy.hku.hk/think/ and are in use under the creative commons license. Some modifications have been made to the original content. ↵

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Defining Critical Thinking

Partnerships

The development of the reasoning brain and how to foster logical reasoning skills

Early childhood development / Effective lifelong learning / Learning mathematics

Executive summary

Learning to reason logically is necessary for the growth of critical and scientific thinking in children. Yet, both psychological and neural evidence indicates that logical reasoning is hard even for educated adults. Here, we examine the factors that scaffold the emergence of logical reasoning in children. Evidence suggests that the development of reasoning with concrete information can be accounted for by the development of both world knowledge and self-regulation. The transition from concrete to abstract reasoning, however, is a challenge for children. Children’s development of reasoning may be supported by encouraging both divergent thinking and reasoning at levels of abstraction that are just above reasoners’ current levels, alongside activities in which children reason with others.

Introduction

It is often argued that one of the most fundamental goals of education is to nurture critical thinking, that is, to teach children to employ good reasoning skills when developing their beliefs. Therefore, fostering logical reasoning should be an important goal for education: Children should learn to provide logical reasons for their opinions and should be able to distinguish between good and bad arguments. This is likely to be important for their effective exercise of citizenship as adults. For example, logical reasoning could tell you that it is unwarranted to conclude “All Muslims are terrorists” from the assertions “All the 9/11 perpetrators are Muslims” and “All the 9/11 perpetrators are terrorists.” Yet, many educated adults still draw such a conclusion, most likely because fear and bias can overcome rational thinking. This suggests that logical reasoning is hard even for educated adults, a conclusion that is supported by a wealth of psychological studies. Perhaps the most striking demonstration of the difficulty of logical reasoning was discovered by the psychologist Peter Wason in 1966 1 . Wason designed a task in which he presented participants with four playing cards, each with a letter on one side and a number on the other side. For example, the cards could be as follow:

A B 2 3

Participants were then shown the conditional rule “If a card has the letter A on one side, then it has the number 2 on the other side.” The task consisted of selecting those cards that had to be turned over to discover whether the rule was true or false. Since Wason’s study, that task has been performed many times, and the results are always the same. Most people select either the A card alone or sometimes both the cards A and 2. However, very few adults, even highly educated, typically choose the 3 card. This is despite the fact that discovering what is on the other side of the 3 card is necessary to evaluate whether the rule is true or false (i.e., if there is an A on the other side of the 3, the rule is false). This reasoning failure has puzzled psychologists for decades because it questions the long-standing assumption that human beings are inherently rational. Why is it so hard for participants to select the 3 card? Neuroscience research suggests that it is because it is much more difficult for the brain to focus on the elements that are absent from the rule (e.g., 3) than on the elements that are present (e.g., A) 2 . Thus, selecting the 3 card requires much more extensive brain activation in several brain regions (primarily involved in attention and concentration) to overcome that tendency (see Figure 1). So, how can we get people to activate more of their reasoning brain and act more rationally on this task? One of the first ideas that comes to mind would be to teach them logic. Cheng and colleagues 3 have tested this. The researchers presented the Wason selection task to college students before and after they took a whole-semester introductory class in logic (about 40 hours of lectures). Surprisingly, they found no difference in the students’ poor performance between the beginning and the end of the semester. In other words, a whole semester of learning about logic did not help students make any less error on the task! What, then, can train the reasoning brain? To answer that question, it is interesting to turn to what we know about the development of logical reasoning in children.

Figure 1. The reasoning brain. Location of the brain regions (in red, blue, and white) that are activated when participants reason with elements that are not present in the rule in the Wason card task. Activations are displayed on pictures of the brain taken using a magnetic resonance imaging scanner. (Reproduced from Ref. 2 )

The development of concrete logical reasoning in children

It is clear that even young children can use some logical reasoning when concrete information is involved. For instance, most 6-year-olds can draw the conclusion “The person is hurt” from the statements “If the person breaks his arm, the person will be hurt” and “The person breaks his arm.” However, the reasoning abilities of young children are limited. For example, many 6-year-olds would also draw the conclusion “The person broke his arm” from the statements “If the person breaks his arm, the person will be hurt” and “The person is hurt.” This, however, is an invalid conclusion because there may be many other reasons why a person could be hurt. Children will progressively understand this and will make this type of reasoning error less and less as they get older. By the time they reach the end of elementary school, most children are able to refrain from concluding “The person broke his arm” from the statements “If the person breaks his arm, the person will be hurt” and “The person is hurt” 4 . Critically, this increased reasoning ability is mirrored by an increase in the ability to think about alternate causes for a given consequence. For example, older children are much more able than younger children to think about the many other reasons why someone would be hurt, like getting sick, breaking a leg, cutting a finger, etc. In other words, better reasoning ability with age is associated with a better ability to consider alternatives from stored knowledge. Clearly, however, children differ in terms of what they know about the world. This predicts that those who have better world knowledge and can think about more alternatives should be better reasoners than the others. And this is exactly what has been shown in several studies 4 .

Interestingly, the importance of world knowledge for reasoning has a paradoxical effect: It can make children poorer reasoners on some occasions. For example, children who can think about a lot of alternatives would be less inclined to draw the logically valid conclusion “The person will be tired” from the statements “If a person goes to sleep late, then he will be tired” and “The person goes to sleep late.” This is because a child with significant world knowledge can think of several circumstances that would make the conclusion unwarranted, such as waking up later the next day. Thus, more world knowledge needs to be associated with more ability to suppress the alternatives that might come to mind if the task requires it. This self-regulation ability relies on a part of the brain that also massively develops during childhood, i.e., the prefrontal cortex (see Figure 2). Overall, then, the development of concrete logical reasoning in children can be largely accounted for by the development of both world knowledge and self-regulation skills that are associated with the frontal cortex.

Figure 2. The prefrontal cortex. Location of the prefrontal cortex on a 3D rendering of the human brain. Polygon data were generated by Database Center for Life Science(DBCLS), distributed under a CC-BY-SA-2.1-jp license.

From concrete to abstract reasoning

There is, however, an important difference between the reasoning skills described above and the task developed by Peter Wason about the four cards. What we just described relates to reasoning with very concrete information, whereas the card task involves reasoning with purely abstract information. Abstract reasoning is difficult because it requires one to manipulate information without any referent in the real world. Knowledge is of no help. In fact, neuroscience research indicates that abstract and concrete reasoning rely on two different parts of the brain 5 (see Figure 3). The ability to reason logically with an abstract premise is generally only found during late adolescence 4 . Transitioning from concrete to abstract reasoning may require extensive practice with concrete reasoning. With mastery, children may extract from the reasoning process abstract strategies that could be applied to abstract information. A recent study, however, suggests a trick to help facilitate this transition in children 6 . The researchers discovered that abstract reasoning in 12- to 15-year-olds is much improved when these adolescents are previously engaged in a task in which they have to reason with information that is concrete but empirically false, such as “If a shirt is rubbed with mud, then the shirt will be clean.” No such effect was observed when adolescents are asked to reason with concrete information that is empirically true, such as “If a shirt is washed with detergent, then the shirt will be clean.” Therefore, reasoning with information that contradicts what we know about the world might constitute an intermediary step in transitioning from concrete to abstract reasoning.

Figure 3. Brain regions activated when reasoning with concrete (left) and abstract (right) information. Activations are displayed on pictures of the brain taken using a magnetic resonance imaging scanner. (Reproduced from Ref. 5 )

What can we do to foster logical reasoning skills?

What, then, can we do to help foster the development of logical reasoning skills in children? The research described above suggests several potentially fruitful ways. First, it is clear that the development of concrete reasoning—the very first type of reasoning children can engage in—relies on an increased ability to think about counter-examples for a given statement. This implies that knowledge about the world is critical to the emergence of logical reasoning in children, at least when concrete information is involved. Therefore, all activities that would expand such world knowledge (e.g., reading informational books, learning new vocabulary, exploring new environments and places) are likely to be beneficial to the development of children’s reasoning skills. Second, it is important to consider that the more world knowledge a child possesses, the more he/she will need to juggle with this knowledge. For example, generating counter-examples when solving a reasoning problem will require maintaining pieces of information in memory for a short period of time, a type of memory called working memory . World knowledge can also sometimes be detrimental to reasoning and needs to be inhibited , such as when recognizing that the conclusion “The person will be tired” logically follows from the statements “If a person goes to sleep late, then he will be tired” and “The person goes to sleep late” (even if one might think of several conditions that would make the conclusion untrue based on what we know about the world). Fostering these types of self-regulation skills (working memory and inhibition) should thus be beneficial to the development of logical reasoning. Several studies suggest that these functions could be promoted by targeting children’s emotional and social development, such as in curricula involving social pretend play (requiring children to act out of character and adjusting to improvisation of others), self-discipline, orderliness, and meditation exercises 7 . Studies also indicate positive effects of various physical activities emphasizing self-control and mindfulness, such as yoga or traditional martial arts 7 . Third, studies indicate that the transition from concrete to abstract reasoning occurring around adolescence is challenging. Although more research is needed in this domain, one promising way to help this transition is by encouraging children’s thinking about alternatives with content that contradicts what they know about the world (e.g., “If a shirt is rubbed with mud, then the shirt will be clean”). In sum, as stated by Henry Markovits, “the best way to encourage the development of more abstract ways of logical reasoning is to gradually encourage both divergent thinking and reasoning at levels of abstraction that are just above reasoners’ current levels” 4 .

Fostering the development of logical reasoning should be an important goal of education. Yet, studies indicate that logical reasoning is hard even for educated adults and relies on the activation of an extensive network of brain regions. Neuroscience studies also demonstrate that reasoning with concrete information involves brain regions that qualitatively differ from those involved in reasoning with more abstract information, explaining why transitioning from concrete to abstract reasoning is challenging for children. We nonetheless reviewed here the more recent research on the development of reasoning skills and suggest several important factors that scaffold children’s reasoning abilities, such as world knowledge and self-regulation functions. On a final note, it is important to consider that logical reasoning is not something that we always do on our own, isolated from our peers. In fact, some have argued that the very function of reasoning is to argue with our peers (i.e., to find the best arguments to convince others and to evaluate arguments made by others) 8 . This idea is interesting from an educational point of view because it suggests that reasoning with others might be easier than reasoning in isolation—a hypothesis validated by several studies. For example, performance on the card task developed by Peter Wason is much higher when participants solve it as a group rather than alone 8 . Therefore, encouraging activities in which children reason with others might also be a fruitful avenue for stimulating the reasoning brain.

Wason, P. C. Reasoning. In New Horizons in Psychology (ed. Foss, B. M.). (Penguin: Harmondsworth, 1966).
Prado, J., & Noveck, I. A. Overcoming perceptual features in logical reasoning: A parametric functional magnetic resonance imaging study. J Cogn Neurosci . 19(4): 642-57 (2007).
Cheng, P. W. et al. Pragmatic versus syntactic approaches to training deductive reasoning. Cogn Psychol . 18(3): 293-328 (1986).
Markovits, H. How to develop a logical reasoner. In The Developmental Psychology of Reasoning and Decision-Making (ed. Markovits, H.) 148-164. (Psychology Press: Hove, UK, 2014).
Goel, V. Anatomy of deductive reasoning. Trends Cogn. Sci. (Reg. Ed.) 11(10): 435-41 (2007).
Markovits, H., & Lortie-Forgues, H. Conditional reasoning with false premises facilitates the transition between familiar and abstract reasoning. Child Development 82(2): 646-660 (2011).
Diamond, A., & Lee, K. Interventions shown to aid executive function development in children 4 to 12 years old. Science 333(6045): 959-964 (2011).
Mercier, H., & Sperber, D. Why do humans reason? Arguments for an argumentative theory. Behav Brain Sci . 34(2): 57-74; discussion 74-111 (2011).

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Critical Thinking and Decision-Making - Logical Fallacies

Critical thinking and decision-making -, logical fallacies, critical thinking and decision-making logical fallacies.

Critical Thinking and Decision-Making: Logical Fallacies

Lesson 7: logical fallacies.

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Logical fallacies

If you think about it, vegetables are bad for you. I mean, after all, the dinosaurs ate plants, and look at what happened to them...

illustration of a dinosaur eating leaves while a meteor falls in the background

Let's pause for a moment: That argument was pretty ridiculous. And that's because it contained a logical fallacy .

A logical fallacy is any kind of error in reasoning that renders an argument invalid . They can involve distorting or manipulating facts, drawing false conclusions, or distracting you from the issue at hand. In theory, it seems like they'd be pretty easy to spot, but this isn't always the case.

Watch the video below to learn more about logical fallacies.

Sometimes logical fallacies are intentionally used to try and win a debate. In these cases, they're often presented by the speaker with a certain level of confidence . And in doing so, they're more persuasive : If they sound like they know what they're talking about, we're more likely to believe them, even if their stance doesn't make complete logical sense.

illustration of a politician saying, "I know for a fact..."

False cause

One common logical fallacy is the false cause . This is when someone incorrectly identifies the cause of something. In my argument above, I stated that dinosaurs became extinct because they ate vegetables. While these two things did happen, a diet of vegetables was not the cause of their extinction.

illustration showing that extinction was not caused by some dinosaurs being vegetarians

Maybe you've heard false cause more commonly represented by the phrase "correlation does not equal causation ", meaning that just because two things occurred around the same time, it doesn't necessarily mean that one caused the other.

A straw man is when someone takes an argument and misrepresents it so that it's easier to attack . For example, let's say Callie is advocating that sporks should be the new standard for silverware because they're more efficient. Madeline responds that she's shocked Callie would want to outlaw spoons and forks, and put millions out of work at the fork and spoon factories.

illustration of Maddie accusing Callie of wanting to outlaw spoons and forks

A straw man is frequently used in politics in an effort to discredit another politician's views on a particular issue.

Begging the question

Begging the question is a type of circular argument where someone includes the conclusion as a part of their reasoning. For example, George says, “Ghosts exist because I saw a ghost in my closet!"

illustration of George claiming that ghosts exists and him seeing one in his closet

George concluded that “ghosts exist”. His premise also assumed that ghosts exist. Rather than assuming that ghosts exist from the outset, George should have used evidence and reasoning to try and prove that they exist.

illustration of George using math and reasoning to try and prove that ghosts exist

Since George assumed that ghosts exist, he was less likely to see other explanations for what he saw. Maybe the ghost was nothing more than a mop!

illustration of a splitscreen showing a ghost in a closet on the left, and that same closet with a mop in it on the right

False dilemma

The false dilemma (or false dichotomy) is a logical fallacy where a situation is presented as being an either/or option when, in reality, there are more possible options available than just the chosen two. Here's an example: Rebecca rings the doorbell but Ethan doesn't answer. She then thinks, "Oh, Ethan must not be home."

Rebecca posits that either Ethan answers the door or he isn't home. In reality, he could be sleeping, doing some work in the backyard, or taking a shower.

illustration of Ethan sleeping, doing yard work, and taking a shower

Most logical fallacies can be spotted by thinking critically . Make sure to ask questions: Is logic at work here or is it simply rhetoric? Does their "proof" actually lead to the conclusion they're proposing? By applying critical thinking, you'll be able to detect logical fallacies in the world around you and prevent yourself from using them as well.

Logical Reasoning in Formal and Everyday Reasoning Tasks

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Published: 26 December 2019
Volume 18 , pages 1673–1694, ( 2020 )

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Hugo Bronkhorst ORCID: orcid.org/0000-0002-8181-1299 1 ,
Gerrit Roorda 2 ,
Cor Suhre 2 &
Martin Goedhart 1

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Logical reasoning is of great societal importance and, as stressed by the twenty-first century skills framework, also seen as a key aspect for the development of critical thinking. This study aims at exploring secondary school students’ logical reasoning strategies in formal reasoning and everyday reasoning tasks. With task-based interviews among 4 16- and 17-year-old pre-university students, we explored their reasoning strategies and the reasoning difficulties they encounter. In this article, we present results from linear ordering tasks, tasks with invalid syllogisms and a task with implicit reasoning in a newspaper article. The linear ordering tasks and the tasks with invalid syllogisms are presented formally (with symbols) and non-formally in ordinary language (without symbols). In tasks that were familiar to our students, they used rule-based reasoning strategies and provided correct answers although their initial interpretation differed. In tasks that were unfamiliar to our students, they almost always used informal interpretations and their answers were influenced by their own knowledge. When working on the newspaper article task, the students did not use strong formal schemes, which could have provided a clear overview. At the end of the article, we present a scheme showing which reasoning strategies are used by students in different types of tasks. This scheme might increase teachers’ awareness of the variety in reasoning strategies and can guide classroom discourse during courses on logical reasoning. We suggest that using suitable formalisations and visualisations might structure and improve students’ reasoning as well.

Probabilistic literacy and reasoning of prospective secondary school teachers when interpreting media news

Developing a diagnostic framework for primary and secondary students’ reasoning difficulties during mathematical problem solving

Enhancing students’ critical thinking skills: is comparing correct and erroneous examples beneficial?

Avoid common mistakes on your manuscript.

Introduction

P21's Framework for twenty-first Century Learning describes critical thinking as an important skill to be successful in professional and everyday life situations in an increasingly complex world (P21, 2015 ). Of great value for critical thinking is ‘reason effectively’, which is explained in the twenty-first century skills framework as “[using] various types of reasoning (inductive, deductive, etc.) as appropriate to the situation” (P21, 2015 , p. 4). Liu, Ludu, and Holton ( 2015 ) support this view and consider valid logical reasoning as a key element for sound critical thinking. Other authors suggest that improving logical reasoning skills as part of higher order thinking skills is an important objective of education (Zohar & Dori, 2003 ).

To support the development of critical thinking, it seems essential that teachers devote attention to students’ strategies to reason logically. So far, not much is known about the reasoning processes of secondary school students in different logical reasoning tasks. Therefore, this article addresses this issue by exploring how 16- and 17-year-old students reason within formal reasoning and everyday reasoning tasks. The information provided by this study seems important to increase teachers’ awareness of reasoning strategies used by students and reasoning difficulties they encounter, as well as to be able to develop instruction materials to support and improve students’ logical reasoning skills.

Theoretical Background

Halpern ( 2014 ) describes critical thinking as “purposeful, reasoned, and goal-directed” (p. 8) and contends that many definitions of critical thinking in literature use the term “reasoning/logic” (p. 8), so being able to apply the rules of logic can be seen as a requirement for critical thinking. Many studies report difficulties with logical reasoning for different age groups (e.g. Daniel & Klaczynski, 2006 ; Galotti, 1989 ; O’Brien, Shapiro, & Reali, 1971 ; Stanovich, West, & Toplak, 2016 ). Because of those difficulties, it is by no means certain that secondary school students are able to reason logically and thus develop their critical thinking abilities autonomously.

Formal Reasoning.

The area of logic can be divided into formal logic and informal logic. Aristotle already differentiated between formal logic with syllogisms described in Analytica Priora and ‘dialectics’ in his combined work Topica exploring arguments and opinions (Aristotle, 2015 version). Almost 2000 years later, Gottlob Frege (1848 – 1925) studied and developed formal systems to analyse thoughts, reasoning, and inferences. Also, he developed the so-called ‘predicate logic’, inspired by Leibniz (1646 – 1716), which is more advanced than the ‘propositional logic’ (Look, 2013 ; Zalta, 2016 ). Nowadays, those types of systems are often called ‘symbolic logic’ with strict validity as a key aspect (De Pater & Vergauwen, 2005 ) in which formal deductive reasoning is applied.

In general, formal systems contain a set of rules and symbols and the reasoning within these systems will provide valid results as long as one follows the defined rules (Schoenfeld, 1991 ). The corresponding reasoning is often called formal reasoning and “characterized by rules of logic and mathematics, with fixed and unchanging premises” (Teig & Scherer, 2016 , p. 1). The same use of formal procedures can be found in definitions of logical reasoning as well. For instance “Logical reasoning involves determining what would follow from stated premises if they were true” (Franks et al., 2013 , p. 146), and “When we reason logically, we are following a set of rules that specify how we ‘ought to’ derive conclusions” (Halpern, 2014 , p. 176).

However, there is no consensus on the term reasoning and it is not exclusively used for formal deductive reasoning or mathematical situations only. Although reasoning in mathematics differs immensely from everyday reasoning (Yackel & Hanna, 2003 ), even reasoning in mathematical proof is not only a formal procedure, but involves discussion, discovery, and exploration (Lakatos, 1976 ) and shows us a need for more informal methods when approaching formal reasoning problems.

Informal Reasoning.

In the previous section, we indicated that, dependent on the situation, reasoning demands more than applying rules of logic. For instance, the importance of transforming information as stated by Galotti ( 1989 ): “[Reasoning is a] mental activity that consists of transforming given information … in order to reach conclusions” (p. 333) and the role of samenesses as stated by Grossen ( 1991 ): “Analogical and logical reasoning are strategies for finding and using samenesses. … logical reasoning applies these derived samenesses in order to understand and control our experience” (p. 343).

The notion of broadening formal methods with more informal methods is not new. Toulmin already discusses the limitations of formal logic for all sorts of arguments in his famous book The Uses of Argument ( 1958 ). He distinguishes different logical types to emphasise how logic is used in different fields, such as law, science, and daily-life situations. In his layout of an argument, he schematises the grounds for a claim balanced with reasons that rebut a claim. He also uses qualifiers to indicate the probability of a claim.

Philosophers and educators were also dissatisfied with the dominance of formal logic, that they considered as inappropriate for evaluating real-life arguments, and started in the 1970s an informal logic movement for another approach of analysing arguments stated in ordinary, daily-life language (Van Eemeren et al., 2014 ). One of the major textbooks still in print today is Logical Self-Defense (Johnson & Blair, 2006 ), which covers an introduction in “logical thinking, reasoning, or critical thinking … that focuses on the interpretation and assessment of ‘real life’ arguments” (p. xix). In literature, this is often indicated as informal or everyday reasoning, but this term has various meanings, from reasoning originating from formal systems to all reasoning related to everyday life events (Blair & Johnson, 2000 ; Voss, Perkins, & Segal, 1991 ). Different from formal reasoning, the reasoning and the conclusions depend on the context and can be questioned on their validity as already shown by Toulmin. Therefore, the topics are open for debate and invite to ponder on justifications and objections. The argument, as the result of the reasoning, often concerns open-ended, ill-structured real world problems without one conclusive, correct response (Cerbin, 1988 ; Kuhn, 1991 ). For this, Johnson and Blair ( 2006 ) use “acceptable premises that are relevant to the conclusion and supply sufficient evidence to justify accepting it” (p. xiii). The use of acceptable premises can arise from practical reasons to reach a certain goal and often includes presumptions or presuppositions. Walton ( 1996 ) uses the term ‘presumptive reasoning’ for this kind of arguments, which he sees as dialogues.

Although presumptive reasoning is not always conclusive or accepted by everyone, it is, in particular if full knowledge is unavailable or unobtainable, according to Walton, the best supplement to describe and discuss everyday life reasoning, for which he uses argumentation schemes. Even though Blair ( 1999 ) acknowledges the importance of presumptive reasoning for describing human reasoning and the strength of conclusions derived from the premises, he questions if all arguments are dialogues and discusses the completeness of the schemes.

To sum up, we define informal reasoning as reasoning in ordinary language to construct an argument which requires a critical review of the given premises and transforming of information, as well as finding additional or similar information provided by the problem solver or by external sources.

Towards a Definition for Logical Reasoning in This Study.

Now, we have seen that for well-founded reasoning, formal and informal methods are useful, we need to formulate a definition of logical reasoning for this study, which captures both aspects. A definition of logical reasoning should contain both the context and the way of reasoning, which can consist of formal and informal strategies. In other words, a definition of logical reasoning should not be synonymous with formal deductive reasoning. Important key words taken from the previous sections are ‘derive conclusions’ from Halpern and ‘transforming information’ from Galotti. That can be done with rules derived from formal systems, but that is not a necessity, so informal reasoning will also be part of our definition and thus seen as a valid reasoning process. Therefore, we conclude that logical reasoning involves several steps and define logical reasoning for this study as selecting and interpreting information from a given context , making connections and verifying and drawing conclusions based on provided and interpreted information and the associated rules and processes.

Formal and Everyday Reasoning Tasks.

Until now, we focused on the ways of reasoning and stressed the importance of the context. If we want to study how students reason in a variety of contexts, we have to differentiate between closed tasks with one correct answer and more open tasks. For this, we will use Galotti’s ( 1989 , p. 335) division: ‘formal reasoning tasks’ and ‘everyday reasoning tasks’. Formal reasoning tasks are self-contained, in which all premises are provided. For those tasks, established procedures are often available which lead to one conclusive answer. In everyday reasoning tasks, premises might be implicit or not provided at all. For those tasks, established procedures are often not available and it depends on the situation when an answer is good enough. In daily-life situations, everyday reasoning problems “are [often] not self-contained” and “the content of the problem typically has potential personal relevance” (Galotti, 1989 , p. 335). For both types of tasks, but for everyday reasoning tasks in particular, selecting and encoding relevant information is of great importance. We will call that the interpretation of the task.

Formal reasoning tasks may be provided in different forms: with symbols and completely in ordinary language without symbols. As shown in Fig. 1 , we differentiate formal reasoning tasks in formally stated and in non-formally stated tasks. Formally stated tasks are stated with a certain set of symbols, for example a task with the premises ‘(1) All A are B. (2) All B are C.’ Non-formally stated tasks are tasks stated in ordinary language, for example a task with the premises ‘(1) All mandarins are oranges. (2) All oranges are fruits.’ For each task, students’ reasoning starts with an interpretation of the given information. That might be either a formal interpretation, in other words, an interpretation within a certain set of symbols (e.g. A ⊆ B ⊆ C ⇒ “All A are C”), or an informal interpretation in ordinary language.

Types of tasks and interpretation

Everyday reasoning tasks are not translatable to formal reasoning tasks and often contain implicit premises as, for instance, in everyday life stories. Like in formal reasoning tasks, students will need to interpret the information in everyday reasoning tasks as well. That can be done completely informally, but a formal representation, such as a schematic overview, might help students to get an overview of the given situation. In this study, we focus both on students’ interpretation and the reasoning strategies that follow from there.

Formalisations.

From prior research among university students (e.g. Lehman, Lempert, & Nisbett, 1988 ; Stenning, 1996 ), we conjecture that reasoning in all kinds of situations will benefit from the use of formal representations or formalisations. We will use the term formalisation in its broadest sense, including all sorts of symbols, schematisations, visualisations, formal notations and (formal) reasoning schemes. Stenning ( 1996 ) gives support for the role of (elementary) formal notations and rules by mentioning that “learning elementary logic can [emphasis added] improve reasoning skills” (p. 227) and can help to understand formal thoughts and arguments. Also, Lehman et al. ( 1988 ) found support for the notion that reasoning in general can improve as a result of teaching formal rules within a particular field. Nonetheless, this does not imply that every formalisation is helpful: The chosen representation should support the thinking process for the specific context, rather than that it should capture all aspects (McKendree, Small, Stenning, & Conlon, 2002 ). In this study, we will investigate which formalisations are used by the participants and if those formalisations are beneficial.

Research Questions

Since little is known about the reasoning processes of 16- and 17-year-old students in logical reasoning tasks, our aim is to explore their reasoning strategies. Because of its exploratory nature, we selected, according to the division provided in Fig. 1 , three elementary types of reasoning tasks: two formal reasoning tasks, to be presented with (formally stated) and without (non-formally stated) symbols, and an everyday reasoning task. Our exploratory study was guided by the following research questions: (1) How do students reason towards a conclusion in formal reasoning and everyday reasoning tasks, whether or not by using formalisations? And (2) what kind of reasoning difficulties do they encounter when proceeding to a conclusion?

For this exploratory study, we selected closed tasks (formal reasoning tasks) concerning linear ordering and syllogisms and an open-ended newspaper comprehension task (everyday reasoning task). The formal reasoning tasks were presented formally and non-formally, of which the non-formally stated task is a counter-item of the formally stated one. A non-formally stated counter-item is a translation of the corresponding formally stated task in ordinary language and vice versa. Both tasks have similar conclusions as final answer, so that the reasoning processes can be compared. Figures 2 and 3 show these formal reasoning tasks, both formally stated and non-formally stated.

Formal reasoning tasks about linear ordering, formally and non-formally stated

Formal reasoning tasks about invalid syllogisms, formally and non-formally stated

Figure 4 shows the everyday reasoning task and this task does not have a counter-item. This newspaper task is an open-ended task with implicit premises and hidden assumptions. In this task, students have to reconstruct the line of the argument. An expert in logic validated all items by checking wording and comprehensibility of the tasks.

Everyday reasoning task, reasoning in a newspaper article

This selection of tasks captures each category shown in Fig. 1 in which we expect different reasoning strategies and contains familiar and unfamiliar tasks to our students. For each task, we provide example interpretations and solutions below. These solutions are used as reference solutions to check the correctness of students’ answers, but, of course, the reasoning towards a conclusion can differ. In the everyday reasoning task in particular, different formulations are possible.

The linear ordering tasks (see Fig. 2 ), which are formal reasoning tasks, have ‘P > S’ and ‘Peter is older than Sally’ as correct answers respectively. If taken a formal interpretation, the reasoning can be P > Q > R > S for the order of the letters. If taken an informal interpretation, you can take example ages for the four persons. For example, if Peter is 50 years old, then Quint can be 20 years old, because Peter is older than Quint. Rosie is younger than Quint, so Rosie can be 10 years old. Rosie is older than Sally, so Sally can be 5 years old. In conclusion, if Peter is 50 years old and Sally 5 years old, then Peter must be older than Sally.

The syllogism tasks (see Fig. 3 ), which are formal reasoning tasks too, should have ‘does not follow necessarily from the given premises’ as correct answer as the only valid conclusive option. For the formally stated version of the syllogism task, possible formal and informal interpretations are visualised in Fig. 5 . At the left, the given syllogism is translated into ordinary language completely and thus called an informal interpretation. In this case, it is example-based with a counterexample in ordinary language, which is, of course, a sufficient explanation why the conclusion does not necessarily follow from these premises. However, it is important to recognise that an example does not always lead to a general conclusion, in particular for valid syllogisms, so in that case, there must be a translation back to the formal setting.

Formal and informal interpretations of the formally stated syllogism task

The formal interpretation with Euler diagrams at the right of Fig. 5 shows that C does not necessarily overlap with A. In this interpretation, the original given set of letter symbols is used. Similar diagrams can be drawn for the non-formally stated version of the task.

The everyday reasoning task (Fig. 4 ) requires students to (1) identify the premises (reasons) leading to the author’s conclusion, and (2) to hypothesise how these premises might be connected to the conclusion by using general knowledge or evidence that might support the author’s conclusion. Our example solution (see Fig. 6 ) is scheme-based with phrases in ordinary language. We analyse such a scheme as a formal interpretation in which the three reasons (the identified premises) are linked directly or indirectly to the author’s conclusion. For the third reason, one needs an additional reasoning step by mentioning another hidden assumption to make the argument complete. We assume that there is sufficient general knowledge on this subject among the participants. The arrows represent if-then statements and are not only part of the formal scheme, but also formalisations in themselves.

Formal scheme for the everyday reasoning task

Nevertheless, the if-then statements in the scheme can be explained in full sentences too. For the first two reasons, that will look like ‘If people smoke or inhale particulate matter, then it will affect their health and thus shorten their life.’ Such considerations based on common knowledge still show the connection, but it is not yet formalised, neither with a scheme, nor with any symbols and thus considered as a completely informal interpretation (see Fig. 1 ). As soon as one introduces logical symbols, we will call those symbols formalisations. In combination with the if-then rule, the sentence can be represented as ‘(smoking ∨ inhaling particulate matter) ⇒ unhealthy ⇒ shorter life’.

Participants

Our participants are Dutch secondary school students in their penultimate year of pre-university secondary education (11th graders) and volunteered to participate in think-aloud sessions. The first author of this article was their teacher and they all signed an informed consent. These students did not take advanced mathematics or science, but followed a mathematics course in which logical reasoning has recently become a compulsory domain (College voor Toetsen en Examens, 2016 ). This study was conducted before the participants received teaching in logical reasoning. In this article, work is discussed from two male (Edgar, James) and two female students (Anne, Susan).

We conducted task-based interviews in which students solved logical reasoning tasks aloud (Goldin, 2000 ; Van Someren, Barnard, & Sandberg, 1994 ). The interviews were conducted in Dutch and recorded with a smartpen so that verbal and written information could be connected. The students were asked to say aloud everything they were thinking of. The interviewer, who is the first author of this article, refrained from commenting as much as possible, so that ‘free problem-solving’ was a key aspect of the sessions. If a student did not understand the task or thought it was done, the interviewer would ask additional (clarification) questions, but did never provide feedback on the given answers.

The transcripts of the interviews were analysed in Dutch and selected parts were translated to English for this article. Students’ task solving was analysed qualitatively in an interpretive way and data-driven (Cohen, Manion, & Morrison, 2007 ). To get a clear picture of the reasoning process, the data sources, interview transcripts and students’ written notes, were analysed according to our definition of logical reasoning. Our analysis included the following steps: (1) students’ understanding of the task, (2) students’ interpretation of the task, (3) students’ reasoning process and strategies used, (4) students’ use of formalisations and (5) the correctness of students’ final answers. If students switch between interpretations, we will call the predominant interpretation, their main interpretation.

Students’ reasoning in counter-items is intended as an exploration of possible variation in reasoning. Because students worked on only one of each two counter-items, we cannot analyse the differences between individual students’ strategies on alternative versions of similar closed tasks.

To judge the correctness of their final answers, students’ written notes, as well as the interview transcripts, are used and compared. Possible differences are marked and combined with their interpretations and reasoning. We have to note that the verbal explanations in itself can be seen as informal, because if students are asked to do tasks aloud, they use ordinary language, but if explained with a (given) set of symbols, the interpretation of the task can still be formal. Furthermore, the verbal explanations are linked to written notes, in which possible use of formalisations is clearly visible.

Table 1 provides an overview of the results. Thereafter, for each task students’ reasoning will be illustrated in detail.

Reasoning with Linear Ordering

Formal reasoning tasks with linear ordering (see Fig. 2 ) are familiar to the students because these types of tasks are common in primary and secondary education. We summarise the findings first: All four students used rule-based strategies, but their initial interpretation differed. All answers were correct and well-reasoned. Only one student came up with an additional formalisation other than the given symbols. She used a very suitable tool, a number line representation with formal letters symbols, to get a clear overview of the order. We will present a detailed description of the four students.

Formally Stated, Edgar.

Edgar interprets the task in a formal way by copying the formal notation, see first three lines in Fig. 7 . After writing that down, his first statements are switching to example-based reasoning (informal interpretation) that involves filling in some numbers (line [1] in transcript). After that, he quickly weighs his two interpretations (lines [2] and [3]) and switches back to the formal situation, by comparing the given letters P, R and S with the symbol for ‘greater than’ (line [4] and Fig. 7 ). Although the verbal explanations are in words, inherent to thinking aloud, he solves the task by following mathematical rules by staying in the formal system with the corresponding formal symbols. This way of reasoning provides the correct answer quickly and using the given symbols only gives a clear structure: P > R, R > S, P > S.

Formally stated linear ordering task at the left, Edgar’s written notes at the right

Edgar: [1] well, yes, you could just fill in numbers of course as an example, [2] well oh no, let's wait[3] we are not going to do that at first [4] uhm, P is greater than Q, so P is also greater than R, …

Formally Stated, Anne.

After reading the task, Anne starts immediately with a translation of the formal symbols into expressions in ordinary language by writing down ‘greater than’ and ‘less than’ in full, thus giving an informal transformation of most of the formally stated task (see Fig. 8 ). Although she still reasons with the given formal letters, she switches to ordinary language for applying the mathematical rules. She provides the correct answer.

Anne’s written notes at the left, English translation at the right

Non-formally Stated, Susan.

Susan translates the non-formally stated version of this formal reasoning task immediately into a formal situation with letter abbreviations for the names and the symbols > and < for ‘older than’ and ‘younger than’. Besides these formal symbols, she puts the letters in sequential order horizontally, which can be seen as a ‘number line’ representation with formal letter symbols, starting with P-Q-R reasoning that Q must be in the middle, see Fig. 9 . We call that another formalisation. After adding S as well, she comes to the right conclusion that Peter must be older than Sally, which is a translation from her formal system to the conclusion asked for in ordinary language.

Susan’s written notes

Non-formally Stated, James.

James reasons in words within the non-formally stated version of this task leading to a correct conclusion. We call his interpretation informal with a correct application of mathematical rules. After the confirmation that he has to write his reasoning down, his written explanation is completely in ordinary language, using the given names and the phrases ‘older than’ and ‘younger than’ (see Fig. 10 ). So, James’s interpretation is completely informal without switching.

James’s written notes at the left, English translation at the right

Reasoning with an Invalid Syllogism

Formal reasoning tasks with syllogisms (see Fig. 3 ) are unfamiliar tasks to these students because they are not used to reasoning within syllogisms. We summarise the findings first: Three of the four students used an informal interpretation, but only two students provided a correct answer. The formally stated version caused difficulties due to not understanding the task or due to incomplete translations to an informal example. Also, the misinterpretation of ‘are’ and the confusion between ‘all’ and ‘some’ are noteworthy. We also found that a recognisable non-formally stated context can support the reasoning, despite some hindrance of real-life experiences concerning the context as well. We present a detailed description of the four students.

Formally Stated, Susan.

Susan shows that she understands that she has to accept the two premises in this formal reasoning task, regardless of their truths by writing “true” behind it, see Fig. 11 . Her next step is formalising the given statements even further by introducing the equality sign, see first lines in her written notes in Fig. 12 , so she interprets the task completely formally.

Susan accepts the given premises, English translation at the right

Formalisations used by Susan, English translation at the right

Susan tries to reason with the given letters four times (see four sections transcript) before she gives up. Again, her verbal explanations are in ordinary language, of course, inherent to thinking aloud, but she uses the given letters and stays in the formal system, so we call that a formal interpretation. In her first try (lines [1] – [7] in transcript), she states that A and B are equal (line [5]), but she cannot connect this with C. In her second try (lines [8] – [14]), she starts with stating that A and B are equal, but cannot connect C with that although saying that some B are not C (line [10]). In her third try (lines [15] – [17]), she says, once more, that A and B are equal, but she cannot connect that with C, because she does not know which B’s are C. The fourth time she writes down the last two lines shown in Fig. 12 , connecting some with a symbol for approximately, but that does not help either (lines [18] – [25]). It is important to notice that she uses the equality sign each time as equal to which conflicts with the original premise containing an inclusion.

After underlining her conclusion ‘A ≈ C’ in the fourth try, she gives up and sighs: “I just do not understand the logic of all this” (line [25]). Susan only reasoned with the given letters and formal symbols and did not switch to an informal situation.

Susan: [1] all A are B, …, so is equal [2] but some of those are C[3] so some are not, some A are not either, some A are [4] … mmm … [5] all A are B, so A and B are equal [6] some B are C, so some B are only A [7] and some B are C … mmm … [start reasoning from the beginning again] [8] all A are B, A and B are equal [9] some of those are C and some are not [10] some B are not C [11] some A, that is also B [12] some B … some A are C [13] … but all A are B, and some B are C, some A are C [rereading given syllogism] [14] no, I don’t think so [start reasoning from the beginning again] [15] I think that, … uhm …, if all A are B, A and B are equal [16] but some B are C, so some of those B’s, that has to be the case, do not necessarily have to be A, because you do not know which B’s are C, because those are equal to C, and A and B are equal, some A are C [17] ow, I really think this is difficult … [start reasoning from the beginning once more] [18] okay, all A are B [writes down A=B] [19] some B are C, so approximately [writes down B≈C] [20] and some A are C, but A and B are equal[21] some of those B are C [writes down behind A=B: ➔ B≈C] [22] and some A are C [writes down A≈C] [23] so, my conclusion, … mmm … [underlines A≈C] [24] I really don’t know [25] I just do not understand the logic of all this

Formally Stated, James.

James recognises that he does not know how to solve this task in a formal way by expressing “I don’t know”, so he switches to an informal interpretation of the formally stated task: starting with searching for an example in ordinary language. This can be seen as analogy- and example-based reasoning. His explanation is closely related to our example in Fig. 5 , but James only looks for one valid example instead of a counterexample. He chooses an example in which ‘some’ represents all apes (line [3] in transcript), because the set of apes not being mammals is empty. We assume that he did not recognise that because of his incorrect conclusion. He tries to use a logical structure ‘if-then’ (lines [2] – [4]) as well, but that does not solve the problem. After the valid conclusion of his example in ordinary language, he tries to explain the validity of his conclusion in a more formal way with the given letters (lines [5] – [7]) and writes that down as well (see Fig. 13 ). For this, James also states that A and B are equal (line [5]) in the same way as Susan did, and is not able to provide a more precise explanation after clarification questions by the interviewer.

James: [1] okay, well, I am going to have a look with a similar example I think [2] if, uhm, all humans are apes [3] some apes are mammals [4] then some humans are … also mammals [5] so, I think it is correct, because A and B are equal, [6] because that is necessarily true, [7] so if that’s the case for some B, it is also the case for A

Non-formally Stated, Edgar.

Edgar’s interpretation of the non-formally stated version of this formal reasoning task is informal. He draws the correct conclusion quite easily (line [2] in transcript). He also explains, although this is not necessarily true, the possibility that some flowers might refer to roses as well as to other flowers (line [6]), which shows a notion of the rules of logic. In his written notes (see Fig. 14 ) he also shows that the word flower could contain more than one type of flowers. This reflection is quite strong and shows insight in the generality of a syllogism.

Edgar’s written notes at the left, English translation at the right

Edgar: [1] uhm… well… let’s see… [2] yes, you would say that this does not follow logically, because some flowers does not necessarily refer to all roses [3] let’s see [4] some, yes, [5] uhm… [6] it does not have to mean that roses fade quickly since some flowers might also be daisies or, well, something, or other flowers consequently

Non-formally Stated, Anne.

Anne also draws the right conclusion in the non-formally stated version of this task. She uses an informal interpretation and comes up with a correct answer quickly (line [1] in transcript) and provides a more complete explanation in her next sentence (line [2]), which is similar to her written answer (see Fig. 15 ). However, Anne is not completely sure about her answer. Asked for an explanation, she says that her uncertainty comes from her knowledge about fading flowers (line [8] and [9]), although she recognises that one cannot conclude that from these premises, which shows that she understands the rules of logic.

Anne: [1] You do not know if it’s the roses that fade, so you also don’t know if some roses fade quickly. [2] All roses can still be flowers, and some flowers can still fade quickly, but that does not have to mean that roses [sighs] fade quickly. [3] Yes, I think so. [4] I am less certain about this one. … [5] because roses can still be flowers, but, ow wait, and [6] … that does not have to mean that, per se, the roses fade quickly, … Intvwr: [7] And why are you less sure than in the previous task? Anne: [8] uhm… yes, because, some flowers fade quickly, yes, I don’t know, I know, I think it’s difficult to explain, but I am just more in doubt here, because … [9] I was thinking because I know, of course, that there are many other species of flowers than only roses, only from these premises you cannot see that of course

Reasoning in a Newspaper Article

An everyday reasoning task about the analysis of a newspaper article (see Fig. 4 ) is considered unfamiliar to these students. We summarise the findings first: Both students used informal interpretations and only some basic formalisations to sum up reasons or make connections even though one of the students (Susan) provided to some extent a schematic overview. Although not essential, they did not build a (strong) formal scheme as, for example, shown in Fig. 6 . We present a detailed description of the two students.

Susan starts this task with identifying the three premises (step 1) in a structured way by writing down the three reasons mentioned in the article behind bullets (see first three lines Fig. 16 ). Thereafter, she takes her time to reconsider these reasons, the wording of the task and the phrase ‘hidden assumption’. She writes down “the hidden assumption is that people from Rotterdam live less healthy”, which hypothesises how the premises are linked to the conclusion (step 2). She explains that “it has to do with people’s health” because of the first two reasons, smoking and worse environment, but Susan struggles with an explanation for the third reason: lower education and income level (see line [1] in transcript). This reason demands more evidence. Susan implies that poorer families are the missing connection for the lower income (line [4]). For that, she uses another formalisation, which structures her written notes: an arrow to make the connection. Verbally, she provides a further explanation for the assumption ‘poorer families’ (line [5]), but she did not write that down.

Susan’s written notes at the left, English translation at the right

Overall, in her verbal explanation, she has connected all the mentioned reasons with a hidden assumption leading to her main assumption ‘poorer health’, which she underlines as well. In her written notes, she uses formalisations at three moments: at the beginning (bullets) for the first step involving identifying the premises, and arrows at two times for connections, either with hypothesised evidence based on her own knowledge (step 2), or to emphasise the main hidden assumption. Her notes provide more or less a schematic overview, but Susan did not compile a complete formal scheme.

Susan: [1] ... mmm, so ... the lower education and income level what does that have to do with ... lower level of education, ... mmm ..., yes, the amount of smokers has to do with health and the high concentration of particulate matter in the air, so it means that the health of people from Rotterdam is worse than the health of other people in the Netherlands [2] uh, to link, explain how the reasons mentioned are linked to the shorter life, by describing the hidden assumption, uhm ... [3] The shorter life is caused by ... the ... poorer health in Rotterdam compared to other Dutch people. [4] Then, the hidden assumption is that poorer health and ... maybe, uh ... lower education and income level, so perhaps poorer families [draws an arrow to connect this with lower education and income level] [5] ... and they may not buy very expensive and organic food and everything, so they would live less healthy or something, I think the hidden assumption is that they eat less healthy, or live less healthy lives especially, yes that’s what I think [6] This is what I think, the poorer health [underlines poorer health], that’s the hidden assumption. [adds arrow]

Anne underlines the three main reasons in the text: smokers, particulate matter, lower education and income level, which shows that she identified the premises (step 1). After that, she lists the three reasons behind bullets (see Fig. 17 ). That is the only formalisation she uses. The rest of the reasoning, verbal and written, is done in ordinary language. For the second and third reason, she provides a hidden assumption: “particulate matter is bad for someone and thus shortens one’s life, and the lower education level and the lower income level leads to poorer living conditions and thus shortens one’s life”. She uses her own knowledge to state that particulate matter is bad for someone’s health and to hypothesise that a lower income level leads to poorer living conditions (step 2). However, she forgets to provide a connection for the first reason, so the interviewer asked for further explanations before she added “bad for you and thus” (see top line Fig. 17 ) for the connection between smoking and shortening one’s life.

Overal, Anne identified the premises quite quickly and provided support for the reasons easily. Probably, she assumed that the connection between smoking and a shorter life was generally known, so that she only provided additional evidence after a clarification question by the interviewer.

Conclusions and Discussion

The purpose of this study was to gain insights into the reasoning processes of 16- and 17-year-old pre-university secondary school students on logical reasoning tasks, aimed at fostering their critical thinking skills as an important objective in the twenty-first century skills framework (P21, 2015 ). In this exploratory study, we investigated (1) the way of reasoning students used in formal reasoning and everyday reasoning tasks and their use of formalisations, and (2) the difficulties they encounter in their reasoning.

In the linear ordering tasks and in the syllogism tasks, students used rule-, analogy- and example-based reasoning strategies. In the newspaper article task, students reasoned partly scheme-based, but mainly in ordinary language only. Except for the formally stated syllogism task, students used appropriate strategies to find correct answers. Although the linear ordering tasks are familiar to the students, both formats (formally and non-formally stated) led to formal and informal interpretations.

Students do not always feel certain about their method and answer, in particular in the syllogism tasks and in the everyday reasoning task. The incomplete written answers in the everyday reasoning task show that our students probably have doubts if their answers are good enough, because they have the feeling that more answers are possible. Even though the newspaper task is taken from an everyday life context and—we expect—recognisable and meaningful, students still fulfil a task for which they expect that there should be one correct answer, as is common in mathematics tasks (e.g. Jäder, Sidenvall, & Sumpter, 2017 ). The doubt students express is in line with Galotti’s ( 1989 ) description for everyday reasoning tasks, because she states that “it is often unclear whether the current ‘best’ solution is good enough” (p. 335) in contrast to formal reasoning tasks where “it is typically unambiguous when the problem is solved” (p. 335).

In our formally stated syllogism task, the students misinterpreted the phrases ‘all…are…’ and ‘some…are…’. Consequently, they did not see that their representations, such as the use of the equality sign as a formal symbol, were not suitable. Susan was completely stuck in the formally stated version and could not find a way out. The misuse of the equality sign (=) for ‘all… are…’ is a common mistake (e.g. Galotti, 1989 , p. 336). Stenning and Van Lambalgen ( 2008 ) also describe difficulties with understanding and interpreting syllogisms.

An overview of our findings is visualised in a scheme (Fig. 18 ) as an extension of Fig. 1 . We showed that students’ initial interpretations, their first thoughts, do not always match with their later choices, so students seem to switch between formal and informal interpretations. This is visualised by the arrow in the scheme. The strategies included in this scheme are derived from our exploratory study among 16- and 17-year-old students and might not provide a complete overview. Consequently, the overview can be supplemented with argumentation schemes based on presumptive reasoning (Walton, 1996 ; Walton, Reed, & Macagno, 2008 ) in further research. Our everyday reasoning task gives only a limited view of students’ possible reasoning strategies, because students were only asked to identify the premises and to use their own knowledge to find connections with the conclusion. They were not asked to find rebuttals or further backing of the claims. The connections provided by the students should be sufficient for justifiable reasoning. This correspondents to the earlier mentioned description from Johnson and Blair ( 2006 ) about acceptable premises.

Types of tasks combined with students’ interpretations and reasoning strategies

Each of the strategies shown in Fig. 18 can be supported by the use of formalisations. For example, in the non-formally stated linear ordering task, Susan used letter abbreviations, mathematical symbols and a number line representation. For cases in which students reason in ordinary language without clearly showing causality, comparison or examples, we added the category ‘informal reasoning’. This category is based on our definition of informal reasoning in the corresponding section in the Theoretical Background. We believe it is important to present ‘informal reasoning’ as separate category in the scheme, because students still managed to construct an argument in ordinary language, but without clearly showing a visible reasoning strategy, such as rule-based, example-based, scheme-based, et cetera.. Therefore, we used a dotted line in Fig. 18 . Consequently, in that case, formalisations can only be used to a certain extent as, for example, shown by Anne in her analysis of the newspaper article where she separated her three informal arguments by bullets.

In this article, we hypothesised that suitable formalisations can support the reasoning process and summarised those tools at the right-hand side of Fig. 18 . We believe that our hypothesis is strengthened by the findings in this exploratory study. Symbols (like ‘greater than’ and ‘less than’, or the equality sign) and letter abbreviations are suitable tools to shorten notations, while other tools (like a number line representation) are strong tools to visualise information. Although not used by our students, Venn and Euler diagrams are also strong tools to visualise data. However, it is our conviction that the use of formalisations, including visualisations such as Venn and Euler diagrams, is teachable and can be linked to the strategies used by the students, also in everyday reasoning tasks.

A limitation of the study is related to our choice of tasks. In our selection of tasks, we used formally stated tasks and non-formally stated tasks as counter-items for similar reasoning problems. In our design, different students worked on one of the counter-items and therefore, we could not compare the performance of an individual student on both tasks. The non-formally stated tasks were more easily to interpret by the students and led to other strategies, because their prior knowledge was helpful. Hintikka ( 2001 ) explains that “in real-life reasoning, even when it is purely deductive, familiarity with the subject matter can be strategically helpful” (p. 46). On the other hand, sometimes our students may doubt their answers, because premises in the task (e.g. Anne in the non-formally stated syllogism task) might conflict with their prior knowledge. In general, this means that our counter-items (formally versus non-formally stated tasks) cannot be considered as equivalent.

Despite the fact that our study has a limitation in the number of participants (small and selective sample) and a limited number of tasks, the information in Fig. 18 shows a variety of reasoning strategies, which is important for teachers to understand the diversity of students’ reasoning and possible difficulties in the interpretations of tasks, in particular for tasks that are not familiar to students or lead to incorrect answers.

Future Research and Recommendations

This study not only shows the complex matter of reasoning and everyday life reasoning in particular, it also confirms that more research is needed as already mentioned by Galotti ( 1989 , 2017 ). Our exploratory study is a first step to get insights in the reasoning process of 16- and 17-year-old pre-university students and shows a gap between their verbal and written explanations. We will continue our research for an in-depth understanding. Unfamiliar tasks, such as all sorts of non-formally stated syllogisms (formal reasoning tasks) and everyday reasoning tasks seem to be useful contexts to investigate how students solve reasoning tasks and which formalisations, including visualisations, they use. Our definition of logical reasoning, mentioned in the Theoretical Background, fits this future research.

Our results show that students do not structure everyday life contexts automatically, so it is plausible that similar difficulties occur in authentic everyday life reasoning too. In future research, we intend to show that students may be supported by learning more structured reasoning strategies and the use of formalisations and visualisations.

One of the key aspects for lessons in logical reasoning must be classroom discourse when solving reasoning tasks. Lakatos ( 1976 ) already stressed the importance of dialogue in the construction of mathematical and logical reasoning. Our research might increase teachers’ awareness of that importance and, more practically, for which Fig. 18 serves as a guideline for discussion. Different interpretations and possible strategies used by students are made explicit and can be used as input for classroom discussions. We suggest that formalisations and visualisations are part of those discussions and might establish a deeper understanding. Above all, logical reasoning tasks where several ways of reasoning are possible, are highly connected to the twenty-first century skills (P21, 2015 ), and thus with the development of critical thinking skills.

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Acknowledgements

This work is part of the research programme Doctoral Grant for Teachers with project number 023.007.043, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).

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Institute for Science Education and Communication, Faculty of Science and Engineering, University of Groningen, P.O. Box 407, 9700 AK, Groningen, The Netherlands

Hugo Bronkhorst & Martin Goedhart

Teacher Education, Faculty of Behavioural and Social Sciences, University of Groningen, Grote Kruisstraat 2/1, 9712 TS, Groningen, The Netherlands

Gerrit Roorda & Cor Suhre

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Bronkhorst, H., Roorda, G., Suhre, C. et al. Logical Reasoning in Formal and Everyday Reasoning Tasks. Int J of Sci and Math Educ 18 , 1673–1694 (2020). https://doi.org/10.1007/s10763-019-10039-8

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Received : 07 February 2019

Accepted : 01 December 2019

Published : 26 December 2019

Issue Date : December 2020

DOI : https://doi.org/10.1007/s10763-019-10039-8

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Brain teaser: How many animals do you see in this picture?

A brain teaser shared on social media has left netizens baffled. The challenge is to find the number of animals hidden in this picture. At first glance, only 4-5 animals would be visible. However, when one looks carefully more animals appear.

"The more you look at the picture, the more animals appear," writes one user.

Brain teasers are challenging due to their ability to provoke critical thinking and problem-solving skills. They often involve complex scenarios or puzzles that require deciphering patterns, making logical deductions, and thinking creatively. Additionally, brain teasers may intentionally mislead or present information in a way that requires careful interpretation. Their difficulty stems from the need to navigate through layers of ambiguity, uncertainty, and sometimes unconventional reasoning. These teasers are designed to push individuals beyond their comfort zones, encouraging them to explore alternative perspectives and solutions. Ultimately, it's this blend of complexity and mental agility that makes brain teasers inherently difficult yet rewarding to solve.

The answer:

There are 9 animals embedded in this single picture. If you look carefully you can notice a bear, a cow, a wolf, a crow, a cat, a rabbit, a butterfly, a bird and a snail.

READ ALSO: Brain Teaser: You are among the elite 1 percent if you can identify the box that contains the car

READ ALSO: Brain teaser: Can you solve this simple maths puzzle?

Solving brain teasers requires a combination of logical thinking, creativity, and sometimes even thinking outside the box. Here's a step-by-step approach to tackling a brain teaser:

Read carefully: Begin by thoroughly understanding the question or scenario presented in the brain teaser. Pay attention to all the details provided.

Identify patterns or clues: Look for any patterns, clues, or hints within the teaser that might lead to a solution. These could be numerical sequences, word associations, or visual patterns.

Break it down: If the teaser seems complex, try breaking it down into smaller, more manageable parts. Simplifying the problem can often make it easier to solve.

Use logic and reasoning: Employ logical reasoning to analyze the information given and deduce potential solutions. This may involve making educated guesses or eliminating unlikely options.

Think creatively: Don't be afraid to think creatively or consider unconventional approaches. Sometimes, the solution to a brain teaser lies outside conventional thinking.

Trial and error: In some cases, trial and error may be necessary to test different hypotheses or approaches until the correct solution is found.

Stay persistent: Brain teasers are designed to be challenging, so don't get discouraged if you don't immediately find the answer. Stay persistent and keep exploring different strategies until you succeed.

Verify the solution: Once you believe you've found the solution, double-check your reasoning and ensure that it satisfies all the conditions or requirements given in the teaser.

By following these steps and employing a mix of logical thinking, creativity, and persistence, you can effectively tackle and solve brain teasers of varying difficulty levels.

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Brain teaser: How many animals do you see in this picture?

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1: Introduction to Critical Thinking, Reasoning, and Logic
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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 ]: Universal. Crucial for the economy. Essential for improving language and presentation skills.
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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 ...
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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 ...
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Critical thinking is widely regarded as a species of informal logic, although critical thinking makes use of some formal methods. ... Approaches to Improving Reasoning through Critical Thinking. ... critical thinkers attempt to interpret statements or arguments clearly and charitably, and then they apply the tools of formal and informal logic ...
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This specialization introduces general standards of good reasoning and offers tools to improve your critical thinking skills. These skills will help you determine when an argument is being given, what its crucial parts are, and what it assumes implicitly. You will also learn how to apply deductive and inductive standards for assessing arguments ...
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Critical thinking is the ability to effectively analyze information and form a judgment. To think critically, you must be aware of your own biases and assumptions when encountering information, and apply consistent standards when evaluating sources. Critical thinking skills help you to: Identify credible sources. Evaluate and respond to arguments.
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Free Certificate. This course will introduce you to critical thinking, informal logic, and a small amount of formal logic. Its purpose is to provide you with the basic tools of analytical reasoning, which will give you a distinctive edge in a wide variety of careers and courses of study. While many university courses focus on presenting content ...
Critical Thinking
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 ...
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Critical thinking, in educational theory, mode of cognition using deliberative reasoning and impartial scrutiny of information to arrive at a possible solution to a problem. From the perspective of educators, critical thinking encompasses both a set of logical skills that can be taught and a
Defining Critical Thinking
Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action.
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Critical thinking is the ability to analyze, evaluate, and synthesize information from various sources and perspectives. It involves applying logic, reasoning, and creativity to solve problems, make decisions, and form judgments. Critical thinking also requires being open-minded, curious, and respectful of different views and evidence.
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CHAPTER 1
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