statements in logic and critical thinking

Introduction to Logic and Critical Thinking

(10 reviews)

Matthew Van Cleave, Lansing Community College

Publisher: Matthew J. Van Cleave

Language: English

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

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

Comprehensiveness rating: 5 see less

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

Content Accuracy rating: 5

The book is accurate.

Relevance/Longevity rating: 5

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

Clarity rating: 5

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

Consistency rating: 5

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

Modularity rating: 5

This text would be easy to adapt.

Organization/Structure/Flow rating: 5

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

Interface rating: 5

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

Grammatical Errors rating: 5

The writing is excellent.

Cultural Relevance rating: 5

This is not an offensive text.

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

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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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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5.2 Logical Statements

Learning objectives.

By the end of this section, you will be able to:

Identify the necessary and sufficient conditions in conditionals and universal affirmative statements.
Describe counterexamples for statements.
Assess the truth of conditionals and universal statements using counterexamples.

Specific types of statements have a particular meaning in logic, and such statements are frequently used by philosophers in their arguments. Of particular importance is the conditional , which expresses the logical relations between two propositions. Conditional statements are used to accurately describe the world or construct a theory. Counterexamples are statements used to disprove a conditional. Universal statements are statements that assert something about every member of a set of things and are an alternative way to describe a conditional.

Conditionals

A conditional is most commonly expressed as an if–then statement, similar to the examples we discussed earlier when considering hypotheses. Additional examples of if–then statements are “If you eat your meat, then you can have some pudding” and “If that animal is a dog, then it is a mammal.” But there are other ways to express conditionals, such as “You can have pudding only if you eat your meat” or “ All dogs are mammals.” While these sentences are different, their logical meaning is the same as their correlative if–then sentences above.

All conditionals include two components—that which follows the “if” and that which follows the “then.” Any conditional can be rephrased in this format. Here is an example:

Statement 1: You must complete 120 credit hours to earn a bachelor’s degree. Statement 2: If you expect to graduate, then you must complete 120 credit hours.

Whatever follows “if” is called the antecedent ; whatever follows “then” is called the consequent . Ante means “before,” as in the word “antebellum,” which in the United States refers to anything that occurred or was produced before the American Civil War. The ante cedent is the first part of the conditional, occurring before the consequent. A consequent is a result, and in a conditional statement, it is the result of the antecedent (if the antecedent is true).

Necessary and Sufficient Conditions

All conditionals express two relations, or conditions : those that are necessary and those that are sufficient. A relation is a relationship/property that exists between at least two things. If something is sufficient, it is always sufficient for something else . And if something is necessary, it is always necessary for something else. In the conditional examples offered above, one part of the relation is required for the other. For example, 120 credit hours are required for graduation, so 120 credit hours is necessary if you expect to graduate. Whatever is the consequent—that is, whatever is in the second place of a conditional—is necessary for that particular antecedent. This is the relation/condition of necessity. Put formally, Y is a necessary condition for X if and only if X cannot be true without Y being true . In other words, X cannot happen or exist without Y. Here are a few more examples:

Being unmarried is a necessary condition for being a bachelor . If you are a bachelor, then you are unmarried.
Being a mammal is a necessary condition for being a dog. If a creature is a dog, then it is a mammal.

But notice that the necessary relation of a conditional does not automatically occur in the other direction. Just because something is a mammal does not mean that it must be a dog. Being a bachelor is not a necessary feature of being unmarried because you can be unmarried and be an unmarried woman. Thus, the relationship between X and Y in the statement “if X, then Y” is not always symmetrical (it does not automatically hold in both directions). Y is always necessary for X, but X is not necessary for Y. On the other hand, X is always sufficient for Y.

Take the example of “If you are a bachelor, then you are unmarried.” If you know that Eric is a bachelor, then you automatically know that Eric is unmarried. As you can see, the antecedent/first part is the sufficient condition, while the consequent/second part of the conditional is the necessary condition. X is a sufficient condition for Y if and only if the truth of X guarantees the truth of Y. Thus, if X is a sufficient condition for Y, then X automatically implies Y. But the reverse is not true. Oftentimes X is not the only way for something to be Y. Returning to our example, being a bachelor is not the only way to be unmarried. Being a dog is a sufficient condition for being a mammal, but it is not necessary to be a dog to be a mammal since there are many other types of mammals.

The ability to understand and use conditionals increases the clarity of philosophical thinking and the ability to craft effective arguments. For example, some concepts, such as “innocent” or “good,” must be rigorously defined when discussing ethics or political philosophy. The standard practice in philosophy is to state the meaning of words and concepts before using them in arguments. And oftentimes, the best way to create clarity is by articulating the necessary or sufficient conditions for a term. For example, philosophers may use a conditional to clarify for their audience what they mean by “innocent”: “If a person has not committed the crime for which they have been accused, then that person is innocent.”

Counterexamples

Sometimes people disagree with conditionals. Imagine a mother saying, “If you spend all day in the sun, you’ll get sunburnt.” Mom is claiming that getting sunburnt is a necessary condition for spending all day in the sun. To argue against Mom, a teenager who wants to go to the beach might offer a counterexample , or an opposing statement that proves the first statement wrong. The teenager must point out a case in which the claimed necessary condition does not occur alongside the sufficient one. Regular application of an effective sunblock with an SPF 30 or above will allow the teenager to avoid sunburn. Thus, getting sunburned is not a necessary condition for being in the sun all day.

Counterexamples are important for testing the truth of propositions. Often people want to test the truth of statements to effectively argue against someone else, but it is also important to get into the critical thinking habit of attempting to come up with counterexamples for our own statements and propositions. Philosophy teaches us to constantly question the world around us and invites us to test and revise our beliefs. And generating creative counterexamples is a good method for testing our beliefs.

Universal Statements

Another important type of statement is the universal affirmative statement . Aristotle included universal affirmative statements in his system of logic, believing they were one of only a few types of meaningful logical statements ( On Interpretation ). Universal affirmative statements take two groups of things and claim all members of the first group are also members of the second group: “All A are B.” These statements are called universal and affirmative because they assert something about all members of group A. This type of statement is used when classifying objects and/or the relationships. Universal affirmative statements are, in fact, an alternative expression of a conditional.

Universal Statements as Conditionals

Universal statements are logically equivalent to conditionals, which means that any conditional can be translated into a universal statement and vice versa. Notice that universal statements also express the logical relations of necessity and sufficiency. Because universal affirmative statements can always be rephrased as conditionals (and vice versa), the ability to translate ordinary language statements into conditionals or universal statements is helpful for understanding logical meaning. Doing so can also help you identify necessary and sufficient conditions. Not all statements can be translated into these forms, but many can.

Counterexamples to Universal Statements

Universal affirmative statements also can be disproven using counterexamples. Take the belief that “All living things deserve moral consideration.” If you wanted to prove this statement false, you would need to find just one example of a living thing that you believe does not deserve moral consideration. Just one will suffice because the categorical claim is quite strong—that all living things deserve moral consideration. And someone might argue that some parasites, like the protozoa that causes malaria, do not deserve moral consideration.

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Module Four: Delivery of Demonstration Speeches

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Is the speaker credible?

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

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

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

Does the logic employed hold up to scrutiny?

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

What questions or objections are raised by the message?

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

How will further information affect the message?

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

Will further information strengthen or weaken the claims?

Most likely Shonda’s claims will be weakened.

What questions or objections are raised by the claims?

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

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

Inference and Interpretation or Explanation

“Imply” or “Infer”?

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

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

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

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

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

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

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

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

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

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

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

Self-Regulation

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

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

The Value of Critical Thinking

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

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

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

Logic and the Role of Arguments

Billboard that says Sharia Law threatens America.

“Sharia Law Billboard” by Matt57. Public domain.

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

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

Defining Arguments

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

“Man and Woman Arguing” by mzacha. morgueFile .

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

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

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

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

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

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

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

2. Sydney cleaned the bathroom last week.

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

4. Therefore, Harrison should clean the bathroom.

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

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

Defining Deduction

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

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

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

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

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

Major premise to minor premise to conclusion.

“Deductive Reasoning” CC-BY-NC-ND .

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

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

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

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

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

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

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

The United States should invade any countries holding weapons of mass destruction. According to our experts, Iraq has weapons of mass destruction. Therefore, we should invade Iraq.

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

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

Defining Induction

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

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

Case one, Case two, and Case three in a funnel. They come out to form a conclusion.

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

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

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

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

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

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

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

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

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

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

Pursuing Truth: A Guide to Critical Thinking

Chapter 4 propositional logic.

Categorical logic is a great way to analyze arguments, but only certain kinds of arguments. It is limited to arguments that have only two premises and the four kinds of categorical sentences. This means that certain common arguments that are obviously valid will not even be well-formed arguments in categorical logic. Here is an example:

I will either go out for dinner tonight or go out for breakfast tomorrow.
I won’t go out for dinner tonight.
I will go out for breakfast tomorrow.

None of these sentences fit any of the four categorical schemes. So, we need a new logic, called propositional logic. The good news is that it is fairly simple.

4.1 Simple and Complex Sentences

The fundamental logical unit in categorical logic was a category, or class of things. The fundamental logical unit in propositional logic is a statement, or proposition 5 Simple statements are statements that contain no other statement as a part. Here are some examples:

Oklahoma Baptist University is in Shawnee, Oklahoma.
Barack Obama was succeeded as President of the US by Donald Trump.
It is 33 degrees outside.

Simple sentences are symbolized by uppercase letters. Just pick a letter that makes sense, given the sentence to be symbolized, that way you can more easily remember which letter means which sentence.

Complex sentences have at least one sentence as a component. There are five types in propositional logic:

Conjunctions
Disjunctions
Conditionals
Biconditionals

4.1.1 Negations

Negations are “not” sentences. They assert that something is not the case. For example, the negation of the simple sentence “Oklahoma Baptist University is in Shawnee, Oklahoma” is “Oklahoma Baptist University is not in Shawnee, Oklahoma.” In general, a simple way to form a negation is to just place the phrase “It is not the case that” before the sentence to be negated.

A negation is symbolized by placing this symbol ‘ $\neg$ ’ before the sentence-letter. The symbol looks like a dash with a little tail on its right side. If $\textrm{D}$ = ‘It is 33 degrees outside,’ then $\neg \textrm{D}$ = ‘It is not 33 degrees outside.’ The negation symbol is used to translate these English phrases:

it is not the case that
it is not true that
it is false that

A negation is true whenever the negated sentence is false. If it is true that it is not 33 degrees outside, then it must be false that it is 33 degrees outside. if it is false that Tulsa is the capital of Oklahoma, then it is true that Tulsa is not the capital of Oklahoma.

When translating, try to keep the simple sentences positive in meaning. Note the warning on page 24, about the example of affirming and denying. Denying is not simply the negation of affirming.

4.2 Conjunction

Negations are “and” sentences. They put two sentences, called conjuncts, together and claim that they are both true. We’ll use the ampersand (&) to signify a negation. Other common symbols are a dot and an upside down wedge. The English words that are translated with the ampersand include:

nevertheless

For example, we would translate the sentence ‘It is raining today and my sunroof is open’ as ‘ $\textrm{R} \& \textrm{O}$ .’

4.3 Disjunction

A disjunction is an “or” sentence. It claims that at least one of two sentences, called disjuncts, is true. For example, if I say that either I will go to the movies this weekend or I will stay home and grade critical thinking homework, then I have told the truth provided that I do one or both of those things. If I do neither, though, then my claim was false.

We use this symbol, called a “vel,” for disjunctions: $\vee$ . The vel is used to translate - or - eitheror - unless

4.4 Conditional

The conditional is a common type of sentence. It claims that something is true, if something else is also. Examples of conditionals are

“If Sarah makes an A on the final, then she will get an A for the course.”
“Your car will last many years, provided you perform the required maintenance.”
“You can light that match only if it is not wet.”

We can translate those sentences with an arrow like this:

$F \rightarrow C$
$M \rightarrow L$
$L \rightarrow \neg W$

The arrow translates many English words and phrases, including

provided that
is a sufficient condition for
is a necessary condition for
on the condition that

One big difference between conditionals and other sentences, like conjunctions and disjunctions, is that order matters. Notice that there is no logical difference between the following two sentences:

Albany is the capital of New York and Austin is the capital of Texas.
Austin is the capital of Texas and Albany is the capital of New York.

They essentially assert exactly the same thing, that both of those conjuncts are true. So, changing order of the conjuncts or disjuncts does not change the meaning of the sentence, and if meaning doesn’t change, then true value doesn’t change.

That’s not true of conditionals. Note the difference between these two sentences:

If you drew a diamond, then you drew a red card.
If you drew a red card, then you drew a diamond.

The first sentence must be true. if you drew a diamond, then that guarantees that it’s a red card. The second sentence, though, could be false. Your drawing a red card doesn’t guarantee that you drew a diamond, you could have drawn a heart instead. So, we need to be able to specify which sentence goes before the arrow and which sentence goes after. The sentence before the arrow is called the antecedent, and the sentence after the arrow is called the consequent.

Look at those three examples again:

The antecedent for the first sentence is “Sarah makes an A on the final.” The consequent is “She will get an A for the course.” Note that the if and the then are not parts of the antecedent and consequent.

In the second sentence, the antecdent is “You perform the required maintenance.” The consequent is “Your car will last many years.” This tells us that the antecedent won’t always come first in the English sentence.

The third sentence is tricky. The antecedent is “You can light that match.” Why? The explanation involves something called necessary and sufficient conditions.

4.4.1 Necessary and Sufficient Conditions

A sufficient condition is something that is enough to guarantee the truth of something else. For example, getting a 95 on an exam is sufficient for making an A, assuming that exam is worth 100 points. A necessary condition is something that must be true in order for something else to be true. Making a 95 on an exam is not necessary for making an A—a 94 would have still been an A. Taking the exam is necessary for making an A, though. You can’t make an A if you don’t take the exam, or, in other words, you can make an a only if you enroll in the course.

Here are some important rules to keep in mind:

‘If’ introduces antecedents, but Only if introduces consequents.
If A is a sufficient condition for B, then $A \rightarrow B$ .
If A is a necessary condition for B, then $B \rightarrow A$ .

4.5 Biconditional

We won’t spend much time on biconditionals. There are times when something is both a necessary and a sufficient condition for something else. For example, making at least a 90 and getting an A (assuming a standard scale, no curve, and no rounding up). If you make at least a 90, then you will get an A. If you got an A, then you made at least a 90. We can use a double arrow to translate a biconditional, like this:

$N \rightarrow A$

For biconditionals, as for conjunctions and disjunctions, order doesn’t matter.

Here are some English phrases that signify biconditionals:

it and only if
when and only when
just in case
is a necessary and sufficient condition for

4.6 Translations

Propositional logic is language. Like other languages, it has a syntax and a semantics. The syntax of a language includes the basic symbols of the language plus rules for putting together proper statements in the language. To use propositional logic, we need to know how to translate English sentences into the language of propositional logic. We start with our sentence letters, which represent simple English sentences. Let’s use three borrowed from an elementary school reader:

We then build complex sentences using the sentence letters and our five logical operators, like this:

We can make even more complex sentences, but we will soon run into a problem. Consider this example:

\[ T \mathbin{\&} J \rightarrow S\]

We don’t know this means. It could be either one of the following:

Tom hit the ball, and if Jane caught the ball, then Spot chased it.
If Tom hit the ball and Jane caught it, then Spot chased it.

The first sentence is a conjunction, $T$ is the first conjunct and $M \rightarrow S$ is the second conjunct. The second sentence, though, is a conditional, $T \mathbin{\&}M$ is the antecdent, and $S$ is the consequent. Our two interpretations are not equivalent, so we need a way to clear up the ambiguity. We can do this with parentheses. Our first sentence becomes:

\[ T \mathbin{\&} (J \rightarrow S) \]

The second sentence is:

\[ (T \mathbin{\&} J) \rightarrow S\]

If we need higher level parentheses, we can use brackets and braces. For instance, this is a perfectly good formula in propositional logic:

\[ [(P \mathbin{\&} Q) \vee R] \rightarrow \{[(\neg P \leftrightarrow Q) \mathbin{\&} S] \vee \neg P\} \] 6

Every sentence in propositional logic is one of six types:

Conjunction
Disjunction
Conditional
Biconditional

What type of sentence it is will be determined by its main logical operator. Sentences can have several logical operators, but they will always have one, and only one, main operator. Here are some general rules for finding the main operator in a symbolized formula of propositional logic:

If a sentence has only one logical operator, then that is the main operator.
If a sentence has more than one logical operator, then the main operator is the one outside the parentheses.
If a sentence has two logical operators outside the parentheses, then the main operator is not the negation.

Here are some examples:

Informally, we use ‘proposition’ and ‘statement’ interchangeably. Strictly speaking, the proposition is the content, or meaning, that the statement expresses. When different sentences in different languages mean the same thing, it is because they express the same proposition. ↩︎

It may be a good formula in propositional logic, but that doesn’t mean it would be a good English sentence. ↩︎

Unit 1: What Is Philosophy?

LOGOS: Critical Thinking, Arguments, and Fallacies

Heather Wilburn, Ph.D

Critical Thinking:

With respect to critical thinking, it seems that everyone uses this phrase. Yet, there is a fear that this is becoming a buzz-word (i.e. a word or phrase you use because it’s popular or enticing in some way). Ultimately, this means that we may be using the phrase without a clear sense of what we even mean by it. So, here we are going to think about what this phrase might mean and look at some examples. As a former colleague of mine, Henry Imler, explains:

By critical thinking, we refer to thinking that is recursive in nature. Any time we encounter new information or new ideas, we double back and rethink our prior conclusions on the subject to see if any other conclusions are better suited. Critical thinking can be contrasted with Authoritarian thinking. This type of thinking seeks to preserve the original conclusion. Here, thinking and conclusions are policed, as to question the system is to threaten the system. And threats to the system demand a defensive response. Critical thinking is short-circuited in authoritarian systems so that the conclusions are conserved instead of being open for revision. [1]

A condition for being recursive is to be open and not arrogant. If we come to a point where we think we have a handle on what is True, we are no longer open to consider, discuss, or accept information that might challenge our Truth. One becomes closed off and rejects everything that is different or strange–out of sync with one’s own Truth. To be open and recursive entails a sense of thinking about your beliefs in a critical and reflective way, so that you have a chance to either strengthen your belief system or revise it if needed. I have been teaching philosophy and humanities classes for nearly 20 years; critical thinking is the single most important skill you can develop. In close but second place is communication, In my view, communication skills follow as a natural result of critical thinking because you are attempting to think through and articulate stronger and rationally justified views. At the risk of sounding cliche, education isn’t about instilling content; it is about learning how to think.

In your philosophy classes your own ideas and beliefs will very likely be challenged. This does not mean that you will be asked to abandon your beliefs, but it does mean that you might be asked to defend them. Additionally, your mind will probably be twisted and turned about, which can be an uncomfortable experience. Yet, if at all possible, you should cherish these experiences and allow them to help you grow as a thinker. To be challenged and perplexed is difficult; however, it is worthwhile because it compels deeper thinking and more significant levels of understanding. In turn, thinking itself can transform us not only in thought, but in our beliefs, and our actions. Hannah Arendt, a social and political philosopher that came to the United States in exile during WWII, relates the transformative elements of philosophical thinking to Socrates. She writes:

Socrates…who is commonly said to have believed in the teachability of virtue, seems to have held that talking and thinking about piety, justice, courage, and the rest were liable to make men more pious, more just, more courageous, even though they were not given definitions or “values” to direct their further conduct. [2]

Thinking and communication are transformative insofar as these activities have the potential to alter our perspectives and, thus, change our behavior. In fact, Arendt connects the ability to think critically and reflectively to morality. As she notes above, morality does not have to give a predetermined set of rules to affect our behavior. Instead, morality can also be related to the open and sometimes perplexing conversations we have with others (and ourselves) about moral issues and moral character traits. Theodor W. Adorno, another philosopher that came to the United States in exile during WWII, argues that autonomous thinking (i.e. thinking for oneself) is crucial if we want to prevent the occurrence of another event like Auschwitz, a concentration camp where over 1 million individuals died during the Holocaust. [3] To think autonomously entails reflective and critical thinking—a type of thinking rooted in philosophical activity and a type of thinking that questions and challenges social norms and the status quo. In this sense thinking is critical of what is, allowing us to think beyond what is and to think about what ought to be, or what ought not be. This is one of the transformative elements of philosophical activity and one that is useful in promoting justice and ethical living.

With respect to the meaning of education, the German philosopher Hegel uses the term bildung, which means education or upbringing, to indicate the differences between the traditional type of education that focuses on facts and memorization, and education as transformative. Allen Wood explains how Hegel uses the term bildung: it is “a process of self-transformation and an acquisition of the power to grasp and articulate the reasons for what one believes or knows.” [4] If we think back through all of our years of schooling, particularly those subject matters that involve the teacher passing on information that is to be memorized and repeated, most of us would be hard pressed to recall anything substantial. However, if the focus of education is on how to think and the development of skills include analyzing, synthesizing, and communicating ideas and problems, most of us will use those skills whether we are in the field of philosophy, politics, business, nursing, computer programming, or education. In this sense, philosophy can help you develop a strong foundational skill set that will be marketable for your individual paths. While philosophy is not the only subject that will foster these skills, its method is one that heavily focuses on the types of activities that will help you develop such skills.

Let’s turn to discuss arguments. Arguments consist of a set of statements, which are claims that something is or is not the case, or is either true or false. The conclusion of your argument is a statement that is being argued for, or the point of view being argued for. The other statements serve as evidence or support for your conclusion; we refer to these statements as premises. It’s important to keep in mind that a statement is either true or false, so questions, commands, or exclamations are not statements. If we are thinking critically we will not accept a statement as true or false without good reason(s), so our premises are important here. Keep in mind the idea that supporting statements are called premises and the statement that is being supported is called the conclusion. Here are a couple of examples:

Example 1: Capital punishment is morally justifiable since it restores some sense of

balance to victims or victims’ families.

Let’s break it down so it’s easier to see in what we might call a typical argument form:

Premise: Capital punishment restores some sense of balance to victims or victims’ families.

Conclusion: Capital punishment is morally justifiable.

Example 2 : Because innocent people are sometimes found guilty and potentially

executed, capital punishment is not morally justifiable.

Premise: Innocent people are sometimes found guilty and potentially executed.

Conclusion: Capital punishment is not morally justifiable.

It is worth noting the use of the terms “since” and “because” in these arguments. Terms or phrases like these often serve as signifiers that we are looking at evidence, or a premise.

Check out another example:

Example 3 : All human beings are mortal. Heather is a human being. Therefore,

Heather is mortal.

Premise 1: All human beings are mortal.

Premise 2: Heather is a human being.

Conclusion: Heather is mortal.

In this example, there are a couple of things worth noting: First, there can be more than one premise. In fact, you could have a rather complex argument with several premises. If you’ve written an argumentative paper you may have encountered arguments that are rather complex. Second, just as the arguments prior had signifiers to show that we are looking at evidence, this argument has a signifier (i.e. therefore) to demonstrate the argument’s conclusion.

So many arguments!!! Are they all equally good?

No, arguments are not equally good; there are many ways to make a faulty argument. In fact, there are a lot of different types of arguments and, to some extent, the type of argument can help us figure out if the argument is a good one. For a full elaboration of arguments, take a logic class! Here’s a brief version:

Deductive Arguments: in a deductive argument the conclusion necessarily follows the premises. Take argument Example 3 above. It is absolutely necessary that Heather is a mortal, if she is a human being and if mortality is a specific condition for being human. We know that all humans die, so that’s tight evidence. This argument would be a very good argument; it is valid (i.e the conclusion necessarily follows the premises) and it is sound (i.e. all the premises are true).

Inductive Arguments : in an inductive argument the conclusion likely (at best) follows the premises. Let’s have an example:

Example 4 : 98.9% of all TCC students like pizza. You are a TCC student. Thus, you like pizza.

Premise 1: 98.9% of all TCC students like pizza

Premise 2: You are a TCC student.

Conclusion: You like pizza. (*Thus is a conclusion indicator)

In this example, the conclusion doesn’t necessarily follow; it likely follows. But you might be part of that 1.1% for whatever reason. Inductive arguments are good arguments if they are strong. So, instead of saying an inductive argument is valid, we say it is strong. You can also use the term sound to describe the truth of the premises, if they are true. Let’s suppose they are true and you absolutely love Hideaway pizza. Let’s also assume you are a TCC student. So, the argument is really strong and it is sound.

There are many types of inductive argument, including: causal arguments, arguments based on probabilities or statistics, arguments that are supported by analogies, and arguments that are based on some type of authority figure. So, when you encounter an argument based on one of these types, think about how strong the argument is. If you want to see examples of the different types, a web search (or a logic class!) will get you where you need to go.

Some arguments are faulty, not necessarily because of the truth or falsity of the premises, but because they rely on psychological and emotional ploys. These are bad arguments because people shouldn’t accept your conclusion if you are using scare tactics or distracting and manipulating reasoning. Arguments that have this issue are called fallacies. There are a lot of fallacies, so, again, if you want to know more a web search will be useful. We are going to look at several that seem to be the most relevant for our day-to-day experiences.

Inappropriate Appeal to Authority : We are definitely going to use authority figures in our lives (e.g. doctors, lawyers, mechanics, financial advisors, etc.), but we need to make sure that the authority figure is a reliable one.

Things to look for here might include: reputation in the field, not holding widely controversial views, experience, education, and the like. So, if we take an authority figure’s word and they’re not legit, we’ve committed the fallacy of appeal to authority.

Example 5 : I think I am going to take my investments to Voya. After all, Steven Adams advocates for Voya in an advertisement I recently saw.

If we look at the criteria for evaluating arguments that appeal to authority figures, it is pretty easy to see that Adams is not an expert in the finance field. Thus, this is an inappropropriate appeal to authority.

Slippery Slope Arguments : Slippery slope arguments are found everywhere it seems. The essential characteristic of a slippery slope argument is that it uses problematic premises to argue that doing ‘x’ will ultimately lead to other actions that are extreme, unlikely, and disastrous. You can think of this type of argument as a faulty chain of events or domino effect type of argument.

Example 6 : If you don’t study for your philosophy exam you will not do well on the exam. This will lead to you failing the class. The next thing you know you will have lost your scholarship, dropped out of school, and will be living on the streets without any chance of getting a job.

While you should certainly study for your philosophy exam, if you don’t it is unlikely that this will lead to your full economic demise.

One challenge to evaluating slippery slope arguments is that they are predictions, so we cannot be certain about what will or will not actually happen. But this chain of events type of argument should be assessed in terms of whether the outcome will likely follow if action ‘x” is pursued.

Faulty Analogy : We often make arguments based on analogy and these can be good arguments. But we often use faulty reasoning with analogies and this is what we want to learn how to avoid.

When evaluating an argument that is based on an analogy here are a few things to keep in mind: you want to look at the relevant similarities and the relevant differences between the things that are being compared. As a general rule, if there are more differences than similarities the argument is likely weak.

Example 7 : Alcohol is legal. Therefore, we should legalize marijuana too.

So, the first step here is to identify the two things being compared, which are alcohol and marijuana. Next, note relevant similarities and differences. These might include effects on health, community safety, economic factors, criminal justice factors, and the like.

This is probably not the best argument in support for marijuana legalization. It would seem that one could just as easily conclude that since marijuana is illegal, alcohol should be too. In fact, one might find that alcohol is an often abused and highly problematic drug for many people, so it is too risky to legalize marijuana if it is similar to alcohol.

Appeal to Emotion : Arguments should be based on reason and evidence, not emotional tactics. When we use an emotional tactic, we are essentially trying to manipulate someone into accepting our position by evoking pity or fear, when our positions should actually be backed by reasonable and justifiable evidence.

Example 8 : Officer please don’t give me a speeding ticket. My girlfriend broke up with me last night, my alarm didn’t go off this morning, and I’m late for class.

While this is a really horrible start to one’s day, being broken up with and an alarm malfunctioning is not a justifiable reason for speeding.

Example 9 : Professor, I’d like you to remember that my mother is a dean here at TCC. I’m sure that she will be very disappointed if I don’t receive an A in your class.

This is a scare tactic and is not a good way to make an argument. Scare tactics can come in the form of psychological or physical threats; both forms are to be avoided.

Appeal to Ignorance : This fallacy occurs when our argument relies on lack of evidence when evidence is actually needed to support a position.

Example 10 : No one has proven that sasquatch doesn’t exist; therefore it does exist.

Example 11 : No one has proven God exists; therefore God doesn’t exist.

The key here is that lack of evidence against something cannot be an argument for something. Lack of evidence can only show that we are ignorant of the facts.

Straw Man : A straw man argument is a specific type of argument that is intended to weaken an opponent’s position so that it is easier to refute. So, we create a weaker version of the original argument (i.e. a straw man argument), so when we present it everyone will agree with us and denounce the original position.

Example 12 : Women are crazy arguing for equal treatment. No one wants women hanging around men’s locker rooms or saunas.

This is a misrepresentation of arguments for equal treatment. Women (and others arguing for equal treatment) are not trying to obtain equal access to men’s locker rooms or saunas.

The best way to avoid this fallacy is to make sure that you are not oversimplifying or misrepresenting others’ positions. Even if we don’t agree with a position, we want to make the strongest case against it and this can only be accomplished if we can refute the actual argument, not a weakened version of it. So, let’s all bring the strongest arguments we have to the table!

Red Herring : A red herring is a distraction or a change in subject matter. Sometimes this is subtle, but if you find yourself feeling lost in the argument, take a close look and make sure there is not an attempt to distract you.

Example 13 : Can you believe that so many people are concerned with global warming? The real threat to our country is terrorism.

It could be the case that both global warming and terrorism are concerns for us. But the red herring fallacy is committed when someone tries to distract you from the argument at hand by bringing up another issue or side-stepping a question. Politicians are masters at this, by the way.

Appeal to the Person : This fallacy is also referred to as the ad hominem fallacy. We commit this fallacy when we dismiss someone’s argument or position by attacking them instead of refuting the premises or support for their argument.

Example 14 : I am not going to listen to what Professor ‘X’ has to say about the history of religion. He told one of his previous classes he wasn’t religious.

The problem here is that the student is dismissing course material based on the professor’s religious views and not evaluating the course content on its own ground.

To avoid this fallacy, make sure that you target the argument or their claims and not the person making the argument in your rebuttal.

Hasty Generalization : We make and use generalizations on a regular basis and in all types of decisions. We rely on generalizations when trying to decide which schools to apply to, which phone is the best for us, which neighborhood we want to live in, what type of job we want, and so on. Generalizations can be strong and reliable, but they can also be fallacious. There are three main ways in which a generalization can commit a fallacy: your sample size is too small, your sample size is not representative of the group you are making a generalization about, or your data could be outdated.

Example 15 : I had horrible customer service at the last Starbucks I was at. It is clear that Starbucks employees do not care about their customers. I will never visit another Starbucks again.

The problem with this generalization is that the claim made about all Starbucks is based on one experience. While it is tempting to not spend your money where people are rude to their customers, this is only one employee and presumably doesn’t reflect all employees or the company as a whole. So, to make this a stronger generalization we would want to have a larger sample size (multiple horrible experiences) to support the claim. Let’s look at a second hasty generalization:

Example 16 : I had horrible customer service at the Starbucks on 81st street. It is clear that Starbucks employees do not care about their customers. I will never visit another Starbucks again.

The problem with this generalization mirrors the previous problem in that the claim is based on only one experience. But there’s an additional issue here as well, which is that the claim is based off of an experience at one location. To make a claim about the whole company, our sample group needs to be larger than one and it needs to come from a variety of locations.

Begging the Question : An argument begs the question when the argument’s premises assume the conclusion, instead of providing support for the conclusion. One common form of begging the question is referred to as circular reasoning.

Example 17 : Of course, everyone wants to see the new Marvel movie is because it is the most popular movie right now!

The conclusion here is that everyone wants to see the new Marvel movie, but the premise simply assumes that is the case by claiming it is the most popular movie. Remember the premise should give reasons for the conclusion, not merely assume it to be true.

Equivocation : In the English language there are many words that have different meanings (e.g. bank, good, right, steal, etc.). When we use the same word but shift the meaning without explaining this move to your audience, we equivocate the word and this is a fallacy. So, if you must use the same word more than once and with more than one meaning you need to explain that you’re shifting the meaning you intend. Although, most of the time it is just easier to use a different word.

Example 18 : Yes, philosophy helps people argue better, but should we really encourage people to argue? There is enough hostility in the world.

Here, argue is used in two different senses. The meaning of the first refers to the philosophical meaning of argument (i.e. premises and a conclusion), whereas the second sense is in line with the common use of argument (i.e. yelling between two or more people, etc.).

Henry Imler, ed., Phronesis An Ethics Primer with Readings, (2018). 7-8. ↵
Arendt, Hannah, “Thinking and Moral Considerations,” Social Research, 38:3 (1971: Autumn): 431. ↵
Theodor W. Adorno, “Education After Auschwitz,” in Can One Live After Auschwitz, ed. by Rolf Tiedemann, trans. by Rodney Livingstone (Stanford: Stanford University Press, 2003): 23. ↵
Allen W. Wood, “Hegel on Education,” in Philosophers on Education: New Historical Perspectives, ed. Amelie O. Rorty (London: Routledge 1998): 302. ↵

LOGOS: Critical Thinking, Arguments, and Fallacies Copyright © 2020 by Heather Wilburn, Ph.D is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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8 Arguments and Critical Thinking

J. anthony blair, introduction [1].

This chapter discusses two different conceptions of argument, and then discusses the role of arguments in critical thinking. It is followed by a chapter in which David Hitchcock carefully analyses one common concept of an argument.

1. Two meanings of ‘argument’

The word ‘argument’ is used in a great many ways. Any thorough understanding of arguments requires understanding ‘argument’ in each of its senses or uses. These may be divided into two large groupings: arguments had or engaged in , and arguments made or used . I begin with the former.

1.1 A n ‘a rgument’ as something two parties have with each othe r, something they get into, the kind of ‘argument’ one has in mind in de scribing two people as “arguing all the time ”

For many people outside academia or the practice of law, an argument is a quarrel . It is usually a verbal quarrel, but it doesn’t have to use words. If dishes are flying or people are glaring at each other in angry silence, it can still be an argument. What makes a quarrel an argument is that it involves a communication between two or more parties (however dysfunctional the communication may be) in which the parties disagree and in which that disagreement and reasons, actual or alleged, motivating it are expressed—usually in words or other communicative gestures.

Quarrels are emotional. The participants experience and express emotions, although that feature is not exclusive to arguments that are quarrels. People can and do argue emotionally, and (or) when inspired by strong emotions, when they are not quarrelling. Heated arguments are not necessarily quarrels; but quarrels tend to be heated.

What makes quarrels emotional in some cases is that at least one party experiences the disagreement as representing some sort of personal attack, and so experiences his or her ego or sense of self-worth as being threatened. Fear is a reaction to a perceived threat, and anger is a way of coping with fear and also with embarrassment and shame. In other cases, the argument about the ostensible disagreement is a reminder of or a pretext for airing another, deeper grievance. Jealousy and resentment fuel quarrels. Traces of ego-involvement often surface even in what are supposed to be more civilized argumentative exchanges, such as scholarly disputes. Quarrels tend not to be efficient ways of resolving the disagreements that gives rise to them because the subject of a disagreement changes as the emotional attacks escalate or because the quarrel was often not really about that ostensible disagreement in the first place.

In teaching that ‘argument’ has different senses, it is misleading to leave the impression (as many textbooks do) that quarrels are the only species of argument of this genus. In fact they are just one instance of a large class of arguments in this sense of extended, expressed, disagreements between or among two or more parties.

A dispute is an argument in this sense that need not be a quarrel. It is a disagreement between usually two parties about the legality, or morality, or the propriety on some other basis, of a particular act or policy. It can be engaged in a civil way by the disputants or their proxies (e.g., their spokespersons or their lawyers). Sometimes only the disputing parties settle their difference; sometimes a third party such as a mediator, arbitrator or judge is called in to impose a settlement.

A debate is another argument of this general kind. Debates are more or less formalized or regimented verbal exchanges between parties who might disagree, but in any case who take up opposing sides on an issue. Procedural rules that govern turn-taking, time available for each turn, and topics that may be addressed are agreed to when political opponents debate one another. Strict and precise rules of order govern who may speak, who must be addressed, sometimes time limits for interventions, in parliamentary or congressional debates in political decision-making bodies, or in formal intercollegiate competitive debates. Usually the “opponent” directly addressed in the debate is not the party that each speaker is trying to influence, so although the expressed goal is to “win” the debate, winning does not entail getting the opponent to concede. Instead, it calls for convincing an on-looking party or audience—the judge of the debate or the jury in a courtroom or the television audience or the press or the electorate as a whole—of the superior merits of one’s case for the opinion being argued for in the debate.

To be distinguished from a debate and a dispute by such factors as scale is a controversy . Think of such issues as the abortion controversy, the climate change controversy, the same-sex marriage controversy, the LGBT rights controversy, the animal rights controversy. The participants are many—often millions. The issues are complex and there are many disputes about details involved, including sometimes even formal debates between representatives of different sides. Typically there is a range of positions, and there might be several different sides each with positions that vary one from another. A controversy typically occurs over an extended period of time, often years and sometime decades long. But an entire controversy can be called an argument, as in, “the argument over climate change.” Controversies tend to be unregulated, unlike debates but like quarrels, although they need not be particularly angry even when they are emotional. Like quarrels, and unlike debates, the conditions under which controversies occur, including any constraints on them, are shaped by the participants.

Somewhere among quarrels, debates and controversies lie the theoretical arguments that theorists in academic disciplines engage in, in academic journals and scholarly monographs. In such arguments theorists take positions, sometimes siding with others and sometimes standing alone, and they argue back and forth about which theoretical position is the correct one. In a related type of argument, just two people argue back and forth about what is the correct position on some issue (including meta-level arguments about what is the correct way to frame the issue in the first place).

The stakes don’t have to be theories and the participants don’t have to be academics. Friends argue about which team will win the championship, where the best fishing spot is located, or what titles to select for the book club. Family members argue about how to spend their income, what school to send the children to, or whether a child is old enough to go on a date without a chaperone. Co-workers argue about the best way to do a job, whether to change service providers, whether to introduce a new product line, and so on. These arguments are usually amicable, whether or not they settle the question in dispute.

All of these kinds of “argument” in this sense of the term—quarrels, friendly disputes, arguments at work, professional arguments about theoretical positions, formal or informal debates, and various kinds of controversy—share several features.

They involve communications between or among two or more people. Something initiates the communication, and either something ends it or there are ways for participants to join and to exit the conversation. They entail turn-taking (less or more regimented), each side addressing the other side and in turn construing and assessing what the other has to say in reply and formulating and communicating a response to the replies of the other side. And, obviously, they involve the expression, usually verbal, of theses and of reasons for them or against alternatives and criticisms.
They have a telos or aim, although there seems to be no single end in mind for all of them or even for each of them. In a quarrel the goal might be to have one’s point of view prevail, to get one’s way, but it might instead (or in addition) be to humiliate the other person or to save one’s own self-respect. Some quarrels—think of the ongoing bickering between some long-married spouses—seem to be a way for two people to communicate, merely to acknowledge one another. In a debate, each side seeks to “win,” which can mean different things in different contexts ( cf. a collegiate debate vs. a debate between candidates in an election vs. a parliamentary debate). Some arguments seemed designed to convince the other to give up his position or accept the interlocutor’s position, or to get the other to act in some way or to adopt some policy. Some have the more modest goal of getting a new issue recognized for future deliberation and debate. Still others are clearly aimed not at changing anyone’s mind but at reinforcing or entrenching a point of view already held (as is usually the case with religious sermons or with political speeches to the party faithful). Some are intended to establish or to demonstrate the truth or reasonableness of some position or recommendation and (perhaps) also to get others to “see” that the truth has been established. Some seem designed to maintain disagreement, as when representatives of competing political parties argue with one another.
All these various kinds of argument are more or less extended, both in the sense that they occur over time, sometimes long stretches of time, and also in the sense that they typically involved many steps: extensive and complex support for a point of view and critique of its alternatives.
In nearly every case, the participants give reasons for the claims they make and they expect the other participants in the argument to give reasons for their claims. This is even a feature of quarrels, at least at the outset, although such arguments can deteriorate into name-calling and worse. (Notice that even the “yes you did; no I didn’t;…; did; didn’t” sequence of the Monty Python “Having an argument” skit breaks down and a reason is sought.)

The kinds of argument listed so far are all versions of having an argument (see Daniel J. O’Keefe, 1977, 1982). Some might think that this is not the sense of ‘argument’ that is pertinent to critical thinking instruction, but such arguments are the habitat of the kinds of argument that critical thinkers need to be able to identify, analyze and evaluate.

1.2 An argument a s something a person makes (or constructs, invents, borrows) consisting of purported reasons alleged to suggest, or support or prove a point and that is used for some purpose such as to persuade someone of some claim, to justify someone in maintaining the position claimed, or to test a claim .

When people have arguments—when they engage in one or another of the activities of arguing described above—one of the things they routinely do is present or allege or offer reasons in support of the claims that they advance, defend, challenge, dispute, question, or consider. That is, in having “arguments,” we typically make and use “arguments.” The latter obviously have to be arguments in different sense from the former. They are often called “reason-claim” complexes. If arguments that someone has had constitute a type of communication or communicative activity, arguments that someone has made or used are actual or potential contributions to such activities. Reason-claim complexes are typically made and used when engaged in an argument in the first sense, trying to convince someone of your point of view during a disagreement or dispute with them. Here is a list of some of the many definitions found in textbooks of ‘argument’ in this second sense.

“… here [the word ‘argument’] … is used in the … logical sense of giving reasons for or against some claim.” Understanding Arguments, Robert Fogelin and Walter Sinnott-Armstrong, 6th ed., p. 1. “Thus an argument is a discourse that contains at least two statements, one of which is asserted to be a reason for the other.” Monroe Beardsley, Practical Logic, p. 9. “An argument is a set of claims a person puts forward in an attempt to show that some further claim is rationally acceptable.” Trudy Govier. A Practical Study of Arguments, 5th ed., p. 3. An argument is “a set of clams some of which are presented as reasons for accepting some further claim.” Alec Fisher, Critical Thinking, An Introduction, p. 235. Argument: “A conclusion about an issue that is supported by reasons.” Sherry Diestler, Becoming a Critical Thinker, 4th ed., p. 403. “ Argument: An attempt to support a conclusion by giving reasons for it.” Robert Ennis, Critical Thinking, p. 396. “Argument – A form of thinking in which certain statements (reasons) are offered in support of another statement (conclusion).” John Chaffee, Thinking Critically, p. 415 “When we use the word argument in this book we mean a message which attempts to establish a statement as true or worthy of belief on the basis of other statements.” James B. Freeman, Thinking Logically, p. 20 “Argument. A sequence of propositions intended to establish the truth of one of the propositions.” Richard Feldman, Reason and Argument, p. 447. “Arguments consist of conclusions and reasons for them, called ‘premises’.” Wayne Grennan, Argument Evaluation, p. 5. Argument: “A set of claims, one of which, the conclusion is supported by [i.e., is supposed to provide a reason for] one or more of the other claims. Reason in the Balance, Sharon Bailin & Mark Battersby, p. 41.

These are not all compatible, and most of them define ‘argument’ using other terms—‘reasons’, ‘claims’, ‘propositions’, ‘statements’, ‘premises’ and ‘conclusions’—that are in no less need of definition than it is. In the next chapter, David Hitchcock offers a careful analysis of this concept of an argument.

Some define argument in this second sense as a kind of communication; others conceive it as a kind of set of propositions that can serve communicative functions, but others as well (such as inquiry). Either way, the communicative character, or function, of arguments has been the subject of much of the research in the past several decades. Most recently what some have called “multi-modal” argument has attracted attention, focusing on the various ways arguments can be communicated, especially visually or in a mix of verbal and visual modes of communication. Some have contended that smells and sounds can play roles in argument communication as well. This area of research interest would seem to have relevance for the analysis of arguments on the web.

1.3 Argumentation

‘Argumentation’ is another slippery term. It is used in several different senses.

Sometimes it is used to mean the communicative activity in which arguments are exchanged: “During their argumentation they took turns advancing their own arguments and criticizing one another’s arguments.” Sometimes ‘argumentation’ denotes the body of arguments used in an argumentative exchange: “The evening’s argumentation was of high quality.” And occasionally you will find it used to refer to the reasons or premises supporting a conclusion, as in: “The argumentation provided weak support for the thesis.” ‘Argumentation theory’ is the term often used to denote theory about the nature of arguments and their uses, including their uses in communications involving exchanges of arguments.

2 The relation between critical thinking and argument

2 .1 arguments are both tools of critical thinking and objects of critical thinking.

In … [one] sense, thought denotes belief resting upon some basis, that is, real or supposed knowledge going beyond what is directly present. … Some beliefs are accepted when their grounds have not themselves been considered …. … such thoughts may mean a supposition accepted without reference to its real grounds. These may be adequate, they may not; but their value with reference to the support they afford the belief has not been considered. Such thoughts grow up unconsciously and without reference to the attainment of correct belief. They are picked up—we know not how. From obscure sources and by unnoticed channels they insinuate themselves into acceptance and become unconsciously a part of our mental furniture. Tradition, instruction, imitation—all of which depend upon authority in some form, or appeal to our advantage, or fall in with strong passions—are responsible for them. Such thoughts are prejudices, that is, prejudgments, not judgments proper that rest upon a survey of evidence. (John Dewey, How We Think , pp. 4-5, emphasis added.)

People—all of us—routinely adopt beliefs and attitudes that are prejudices in Dewey’s sense of being prejudgments, “not judgments proper that rest upon a survey of evidence.” One goal of critical thinking education is to provide our students with the means to be able, when it really matters, to “properly survey” the grounds for beliefs and attitudes.

Arguments supply one such means. The grounds for beliefs and attitudes are often expressed, or expressible, as arguments for them. And the “proper survey” of these arguments is to test them by subjecting them to the critical scrutiny of counter-arguments.

Arguments also come into play when the issue is not what to believe about a contentious issue, but in order just to understand the competing positions. Not only are we not entitled to reject a claim to our belief if we cannot counter the arguments that support it; we are not in possession of an understanding of that claim if we cannot formulate the arguments that support it to the satisfaction of its proponents.

Furthermore, arguments can be used to investigate a candidate for belief by those trying “to make up their own minds” about it. The investigator tries to find and express the most compelling arguments for and against the candidate. Which arguments count as “most compelling” are the ones that survive vigorous attempts, using arguments, to refute or undermine them. These survivors are then compared against one another, the pros weighed against the cons. More arguments come into play in assessing the attributed weights.

In these ways, a facility with arguments serves a critical thinker well. Such a facility includes skill in recognizing, interpreting and evaluating arguments, as well as in formulating them. That includes skill in laying out complex arguments, in recognizing argument strengths and weaknesses, and in making a case for one’s critique. It includes the ability to distinguish the more relevant evidence from the less, and to discriminate between minor, fixable flaws and major, serious problems, in arguments. Thus the critical thinker is at once adept at using arguments in various ways and at the same time sensitive in judging arguments’ merits, applying the appropriate criteria.

Moreover, arguments in the sense of “reasons-claim” complexes surround us in our daily lives. Our “familiars”, as Gilbert (2014) has dubbed them—our family members, the friends we see regularly, shopkeepers and others whose services we patronize daily, our co-workers—engage us constantly in argumentative discussions in which they invoke arguments to try to get us to do things, to agree, to judge, to believe. The public sphere—the worlds of politics, commerce, entertainment, leisure activities, social media (see Jackson’s chapter)—is another domain in which arguments can be found, although (arguably) mere assertion predominates there. In the various roles we play as we go through life—child, parent, spouse or partner, student, worker, patient, subordinate or supervisor, citizen (voter, jurist, community member), observer or participant, etc.—we are invited with arguments to agree or disagree, approve or disapprove, seek or avoid. We see others arguing with one another and are invited to judge the merits of the cases they make. Some of these arguments are cogent and their conclusions merit our assent, but others are not and we should not be influenced by them. Yet others are suggestive and deserve further thought.

We can simply ignore many of these arguments, but others confront us and force us to decide whether or not to accept them. Often it is unclear whether someone has argued or done something else: just vented, perhaps, or explained rather than argued, or merely expressed an opinion without arguing for it, or was confused. So we initially might have to decide whether there is an argument that we need to deal with. When it is an argument, often in order to make up our minds about it we need first to get clear about exactly what the argument consists of. So even before we evaluate this argument we have to identify and analyze it. (These operations are discussed in Chapter 12.)

In the end we have to decide for ourselves whether the argument makes its case or falls short. Does the conclusion really follow from the premises? Is there enough evidence to justify the conclusion? Is it the right kind of evidence? Are there well-known objections or arguments against the conclusion that haven’t been acknowledged and need to be answered satisfactorily? Can they be answered? And are the premises themselves believable or otherwise acceptable? Are there other arguments, as good or better, that support the claim?

Critical thinking can (and should!) come into all of these decisions we need to make in the identification, the analysis and the assessment of arguments.

2 .2 Critical thinking about things other than arguments

Many critical thinking textbooks focus exclusively on the analysis and evaluation of arguments. While the centrality of arguments to the art of critical thinking is unquestionable, a strong case can be made that critical thinking has other objectives in addition to appreciating arguments. In their analysis of the concept of critical thinking, Fisher and Scriven suggest the following definition:

Critical thinking is skilled and active interpretation and evaluation of o b servations and communications , information and argumentation. (1997, p. 21, emphasis added)

We agree with the gist of this claim, but notice what Fisher and Scriven propose as the objects to which critical thinking applies. Not just argumentation, but as well observations, communications and information. About observations, they note that:

What one sees (hears, etc.) are usually things and happenings, and one often has to interpret what one sees, sometimes calling on critical thinking skills to do so, most obviously in cases where the context involves weak lighting, strong emotions, possible drug effects, or putatively magical or parapsychological phenomena. Only after the application of critical thinking—and sometimes not even then—does one know what one “really saw”. … When the filter of critical thinking has been applied to the observations, and only then, one can start reasoning towards further conclusions using these observations as premises. ( Ibid ., p, 37)

An example is the recent large number of convictions in the U.S.A. that originally relied on eyewitness testimony but that have been overturned on the basis of DNA evidence. [2] , [3]

The DNA evidence proved that the accused was not the culprit, so the moral certainty of the eyewitness had to have been mistaken. The observation of the eyewitness was flawed. He or she did not think critically about whether the conditions need ed to make a reliable o b servation were present (e.g., were strong emotions like fear involved? was the lighting good? has he or she ordinarily a good memory for faces? was there time to observe carefully? were there distractions present?). Neither, probably, did the lawyers on either side, or else they immorally suppressed what should have been their doubts. As a consequence, innocent people languished in jail for years and guilty parties went free.

Communications are another object for critical thought. When in reply to Harry’s question, “How are you doing?” Morgan says, in a clipped and dull voice and a strained expression on her face, “I’m fine”, Harry needs to be aware that “How are you doing?” often functions as equivalent to a simple greeting, like “Hi” and so the response “Fine” could similarly be functioning as a polite return of the greeting, like “Hi back to you”, and not as an accurate report of the speaker’s condition. Harry needs to notice and interpret other aspects of Morgan’s communication—her lethargic tone of voice and her anxious facial expression—and to recognize the incompatibility between those signals and the interpretation of her response as an accurate depiction of Morgan’s state of well-being. He needs to employ critical interpretive skills to realize that Morgan has communicated that she is not fine at all, but for some reason isn’t offering to talk about it.

If President Trump did in fact say to his then F.B.I. director James Comey, about the F.B.I. investigation of former National Security Advisor Michaell Flynn “I hope you can let this go”, was it legitimate for Comey to interpret the President’s comment as a directive? And was Comey’s response, which was simply to ignore President Trump’s alleged comment, an appropriate response? What was going on? It takes critical thinking to try to sort out these issues. Taking the President’s alleged comment literally, it just expresses his attitude towards the FBI investigation of Flynn. But communications from the President in a tête-à-tête in the White House with the Director of the FBI are not occasions for just sharing attitudes. This was not an occasion on which they could step out of their political roles and chat person-to-person. The President can legitimately be presumed to be communicating his wishes as to what his FBI Director should do, and such expressions of wishes are, in this context, to be normally understood as directives. On the other hand, for the President to direct that an ongoing investigation by the FBI be stopped, or that it come up with a pre-determined finding, is illegal: it’s obstruction of justice. So Comey seemed faced with at least two possible interpretations of what he took the President to be saying: either an out-of-place expression of his attitude towards the outcome of the Flynn investigation or an illegal directive. Which was the President’s intention? However, there are other possibilities.

Was President Trump a political tyro whose lack of political experience might have left him ignorant of the fact that the FBI Director has to keep investigations free of political interference? Or might Trump have thought that the Presidency conveys the authority to influence the outcome of criminal investigations? Or might President Trump have been testing Mr. Comey to see if he could be manipulated? And Mr. Comey could have responded differently. He could have said, “I wish we could let this go too, Mr. President, but there are questions about General Flynn’s conduct that have to be investigated, and as you know, we cannot interfere with an ongoing FBI investigation”. Such a response would have forced the President to take back what he allegedly said, withdrawing any suggestion that his comment was a directive, or else to make it plain that he was indeed directing Comey to obstruct justice. In the event, apparently Mr. Comey did not take this way out, which would at once have displayed loyalty to the President (by protecting him from explicitly obstructing justice) and also have affirmed the independence of the FBI from interference from the White House. Perhaps he thought that the President clearly had directed him to obstruct justice, and judged that giving him an opportunity explicitly to withdraw that directive amounted to overlooking that illegal act, which would be a violation of his responsibilities as Director of the FBI. If so, however, simply not responding to the President’s comment, the path Comey apparently chose, also amounted to turning a blind eye to what he judged to be President Trump’s illegal directive.

As these two examples illustrate, the interpretation of communications, and the appropriate response to them can require critical thinking: recognizing different functions of communication, and being sensitive to the implications of different contexts of communication; being sensitive to the roles communicators occupy and to the rights, obligations, and limits attached to such roles.

As Fisher and Scriven acknowledge, “defining information is itself a difficult task.” They make a useful start by distinguishing information from raw data (“the numbers or bare descriptions obtained from measurements or observations”, op . cit., p. 41). No critical thinking is required for the latter; just the pains necessary to record raw data accurately, In many cases, though, the interpretation of raw data, the meaning or significance that they are said to have, can require critical thinking.

One might go beyond Fisher and Scriven’s list of other things besides arguments to which critical thinking can be applied. A thoughtful appreciation of novels or movies, plays or poetry, paintings or sculptures requires skilled interpretation, imagining alternatives, thoughtful selection of appropriate criteria of evaluation and then the selection and application of appropriate standards, and more. A good interior designer must consider the effects and interactions of space and light and color and fabrics and furniture design, and coordinate these with clients’ lifestyles, habits and preferences. Advanced practical skills in various sciences come into play. A coach of a sports team must think about each individual team member’s skills and deficiencies, personality and life situation; about plays and strategies, opponents’ skills sets; approaches to games; and much more. Conventional approaches need to be reviewed as to their applicability to the current situation. Alternative possibilities need to be creatively imagined and critically assessed. And all of this is time-sensitive, sometimes calling for split-second decisions. The thinking involved in carrying out the tasks of composing a review of some work of literature or art or of coaching a sports team can be routine and conventional, or it can be imaginative, invoking different perspectives and challenging standard criteria.

The list could go on. The present point is that, while argument is central to critical thinking, critical thinking about and using arguments is not all there is to critical thinking. [4]

Bailin, Sharon & Battersby, Mark. (2010). Reason in the Balance , An I n quiry Approach to Critical Thinking , 1 st ed. Toronto: McGraw-Hill Ryerson.

Beardsley, Monroe C. (1950). Practical L ogic . Englewood Cliffs, NJ: Prentice-Hall.

Chaffee, John. 1985. Thinking Critically . Boston: Houghton Mifflin.

Dewey, John. (1910, 1991). How We Think . Lexington, MAD.C. Heath; Buffalo, NY: Prometheus Books.

Diestler, Sherry. (2005). Becoming a Critical Thinker , 4 th ed. Upper Saddle River, NJ: Pearson Education.

Ennis, Robert H. (1996). Critical Thinking . Upper Saddle River, NJ: Prentice-Hall.

Feldman, Richard. (1993). Reason and Argument , 2 nd ed. Upper Saddle River, NJ: Prentice-Hall.

Fisher, Alex.(2001). Critical Thinking, An Introduction . Cambridge: Cambridge University Press.

Fisher, Alec & Scriven, Michael. (1997). Critical Thinking, Its Definition and Assessment . Point

Reyes, CA: EdgePress; Norwich, UK: Center for Research in Critical Thinking.

Fogelin, Robert & Sinnott-Armstrong, Walter. (2001). Understanding A r guments , An Introduction to Informal Logic , 6 th ed. Belmont, CA: Wadsworth.

Freeman, James B. (1988.) Thinking Logically , Basic Concepts of Reaso n ing . Englewood Cliffs, NJ: Prentice-Hall.

Grennan, Wayne . (1984). Argument Evaluation . Lanham, MD: University Press of America.

Govier, Trudy. (2001). A Practical Study of Argument , 5 th ed. Belmont, CA: Wadsworth.

O’Keefe, Daniel J. (1977). Two concepts of argument. Journal of the Amer i can Forensic Association , 13 , 121-128.

O‘Keefe, Daniel J. (1982). The concepts of argument and arguing. In J. R. Cox & C. A. Willard (Eds.), Advances in Argumentation Theory and R e search , pp. 3-23. Carbondale, IL: Southern Illinois University Press.

According to the Innocence Project, “Eyewitness misidentification is the greatest contributing factor to wrongful convictions proven by DNA testing, playing a role in more than 70% of convictions [in the U.S.A.] overturned through DNA testing nationwide.” (https://www.innocenceproject.org/causes/eyewitness-misidentification/, viewed August 2017). ↵
I owe the general organization and many of the specific ideas of this chapter to a series of lectures by Jean Goodwin at the Summer Institute on Argumentation sponsored by the Centre for Research in Reasoning, Argumentation and Rhetoric at the University of Windsor. ↵

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What Is Critical Thinking? | Definition & Examples

What Is Critical Thinking? | Definition & Examples

Published on May 30, 2022 by Eoghan Ryan . Revised on May 31, 2023.

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
Assess alternative viewpoints
Test hypotheses against relevant criteria

Why is critical thinking important, critical thinking examples, how to think critically, other interesting articles, frequently asked questions about critical thinking.

Critical thinking is important for making judgments about sources of information and forming your own arguments. It emphasizes a rational, objective, and self-aware approach that can help you to identify credible sources and strengthen your conclusions.

Critical thinking is important in all disciplines and throughout all stages of the research process . The types of evidence used in the sciences and in the humanities may differ, but critical thinking skills are relevant to both.

In academic writing , critical thinking can help you to determine whether a source:

Is free from research bias
Provides evidence to support its research findings
Considers alternative viewpoints

Outside of academia, critical thinking goes hand in hand with information literacy to help you form opinions rationally and engage independently and critically with popular media.

Prevent plagiarism. Run a free check.

Critical thinking can help you to identify reliable sources of information that you can cite in your research paper . It can also guide your own research methods and inform your own arguments.

Outside of academia, critical thinking can help you to be aware of both your own and others’ biases and assumptions.

Academic examples

However, when you compare the findings of the study with other current research, you determine that the results seem improbable. You analyze the paper again, consulting the sources it cites.

You notice that the research was funded by the pharmaceutical company that created the treatment. Because of this, you view its results skeptically and determine that more independent research is necessary to confirm or refute them. Example: Poor critical thinking in an academic context You’re researching a paper on the impact wireless technology has had on developing countries that previously did not have large-scale communications infrastructure. You read an article that seems to confirm your hypothesis: the impact is mainly positive. Rather than evaluating the research methodology, you accept the findings uncritically.

Nonacademic examples

However, you decide to compare this review article with consumer reviews on a different site. You find that these reviews are not as positive. Some customers have had problems installing the alarm, and some have noted that it activates for no apparent reason.

You revisit the original review article. You notice that the words “sponsored content” appear in small print under the article title. Based on this, you conclude that the review is advertising and is therefore not an unbiased source. Example: Poor critical thinking in a nonacademic context You support a candidate in an upcoming election. You visit an online news site affiliated with their political party and read an article that criticizes their opponent. The article claims that the opponent is inexperienced in politics. You accept this without evidence, because it fits your preconceptions about the opponent.

There is no single way to think critically. How you engage with information will depend on the type of source you’re using and the information you need.

However, you can engage with sources in a systematic and critical way by asking certain questions when you encounter information. Like the CRAAP test , these questions focus on the currency , relevance , authority , accuracy , and purpose of a source of information.

When encountering information, ask:

Who is the author? Are they an expert in their field?
What do they say? Is their argument clear? Can you summarize it?
When did they say this? Is the source current?
Where is the information published? Is it an academic article? Is it peer-reviewed ?
Why did the author publish it? What is their motivation?
How do they make their argument? Is it backed up by evidence? Does it rely on opinion, speculation, or appeals to emotion ? Do they address alternative arguments?

Critical thinking also involves being aware of your own biases, not only those of others. When you make an argument or draw your own conclusions, you can ask similar questions about your own writing:

Am I only considering evidence that supports my preconceptions?
Is my argument expressed clearly and backed up with credible sources?
Would I be convinced by this argument coming from someone else?

If you want to know more about ChatGPT, AI tools , citation , and plagiarism , make sure to check out some of our other articles with explanations and examples.

ChatGPT vs human editor
ChatGPT citations
Is ChatGPT trustworthy?
Using ChatGPT for your studies
What is ChatGPT?
Chicago style
Paraphrasing

Plagiarism

Types of plagiarism
Self-plagiarism
Avoiding plagiarism
Academic integrity
Consequences of plagiarism
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statements in logic and critical thinking

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Critical thinking refers to the ability to evaluate information and to be aware of biases or assumptions, including your own.

Like information literacy , it involves evaluating arguments, identifying and solving problems in an objective and systematic way, and clearly communicating your ideas.

Critical thinking skills include the ability to:

You can assess information and arguments critically by asking certain questions about the source. You can use the CRAAP test , focusing on the currency , relevance , authority , accuracy , and purpose of a source of information.

Ask questions such as:

Who is the author? Are they an expert?
How do they make their argument? Is it backed up by evidence?

A credible source should pass the CRAAP test and follow these guidelines:

The information should be up to date and current.
The author and publication should be a trusted authority on the subject you are researching.
The sources the author cited should be easy to find, clear, and unbiased.
For a web source, the URL and layout should signify that it is trustworthy.

Information literacy refers to a broad range of skills, including the ability to find, evaluate, and use sources of information effectively.

Being information literate means that you:

Know how to find credible sources
Use relevant sources to inform your research
Understand what constitutes plagiarism
Know how to cite your sources correctly

Confirmation bias is the tendency to search, interpret, and recall information in a way that aligns with our pre-existing values, opinions, or beliefs. It refers to the ability to recollect information best when it amplifies what we already believe. Relatedly, we tend to forget information that contradicts our opinions.

Although selective recall is a component of confirmation bias, it should not be confused with recall bias.

On the other hand, recall bias refers to the differences in the ability between study participants to recall past events when self-reporting is used. This difference in accuracy or completeness of recollection is not related to beliefs or opinions. Rather, recall bias relates to other factors, such as the length of the recall period, age, and the characteristics of the disease under investigation.

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How to apply critical thinking in learning

Sometimes your university classes might feel like a maze of information. Consider critical thinking skills like a map that can lead the way.

Why do we need critical thinking?

Critical thinking is a type of thinking that requires continuous questioning, exploring answers, and making judgments. Critical thinking can help you:

analyze information to comprehend more thoroughly
approach problems systematically, identify root causes, and explore potential solutions
make informed decisions by weighing various perspectives
promote intellectual curiosity and self-reflection, leading to continuous learning, innovation, and personal development

What is the process of critical thinking?

1. understand .

Critical thinking starts with understanding the content that you are learning.

This step involves clarifying the logic and interrelations of the content by actively engaging with the materials (e.g., text, articles, and research papers). You can take notes, highlight key points, and make connections with prior knowledge to help you engage.

Ask yourself these questions to help you build your understanding:

What is the structure?
What is the main idea of the content?
What is the evidence that supports any arguments?
What is the conclusion?

2. Analyze

You need to assess the credibility, validity, and relevance of the information presented in the content. Consider the authors’ biases and potential limitations in the evidence.

Ask yourself questions in terms of why and how:

What is the supporting evidence?
Why do they use it as evidence?
How does the data present support the conclusions?
What method was used? Was it appropriate?

3. Evaluate

After analyzing the data and evidence you collected, make your evaluation of the evidence, results, and conclusions made in the content.

Consider the weaknesses and strengths of the ideas presented in the content to make informed decisions or suggest alternative solutions:

What is the gap between the evidence and the conclusion?
What is my position on the subject?
What other approaches can I use?

When do you apply critical thinking and how can you improve these skills?

1. reading academic texts, articles, and research papers.

analyze arguments
assess the credibility and validity of evidence
consider potential biases presented
question the assumptions, methodologies, and the way they generate conclusions

2. Writing essays and theses

demonstrate your understanding of the information, logic of evidence, and position on the topic
include evidence or examples to support your ideas
make your standing points clear by presenting information and providing reasons to support your arguments
address potential counterarguments or opposing viewpoints
explain why your perspective is more compelling than the opposing viewpoints

3. Attending lectures

understand the content by previewing, active listening , and taking notes
analyze your lecturer’s viewpoints by seeking whether sufficient data and resources are provided
think about whether the ideas presented by the lecturer align with your values and beliefs
talk about other perspectives with peers in discussions

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Critical thinking definition

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

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

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

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

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

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

Is critical thinking useful in writing?

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

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

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

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

Are there any services that can help me use more critical thinking?

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2.2: Propositional Logic and the Four Basic Truth Functional Connectives

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Matthew Van Cleave
Lansing Community College

Propositional logic (also called “sentential logic”) is the area of formal logic that deals with the logical relationships between propositions. A proposition is simply what I called in section 1.1 a statement. 1 Some examples of propositions are:

Snow is white

Snow is cold

Tom is an astronaut

The floor has been mopped

The dishes have been washed

We can also connect propositions together using certain English words, such as “and” like this:

The floor has been mopped and the dishes have been washed.

This proposition is called a complex proposition because it contains the connective “and” which connects two separate propositions. In contrast, “the floor has been mopped” and “the dishes have been washed” are what are called atomic propositions. Atomic propositions are those that do not contain any truth-functional connectives. The word “and” in this complex proposition is a truth-functional connective. A truth-functional connective is a way of connecting propositions such that the truth value of the resulting complex proposition can be determined by the truth value of the propositions that compose it. Suppose that the floor has not been mopped but the dishes have been washed. In that case, if I assert the conjunction, “the floor has been mopped and the dishes have been washed,” then I have asserted something that is false. The reason is that a conjunction, like the one above, is only true when each conjunct (i.e., each statement that is conjoined by the “and”) is true. If either one of the conjuncts is false, then the whole conjunction is false. This should be pretty obvious. If Bob and Sally split chores and Bob’s chore was to both vacuum and dust whereas Sally’s chore was to both mop and do the dishes, then if Sally said she mopped the floor and did the dishes when in reality she only did the dishes (but did not mop the floor), then Bob could rightly complain that it isn’t true that Sally both mopped the floor and did the dishes! What this shows is that conjunctions are true only if both conjuncts are true. This is true of all conjunctions. The conjunction above has a certain form—the same form as any conjunction. We can represent that form using placeholders—lowercase letters like p and q to stand for any statement whatsoever. Thus, we represent the form of a conjunction like this:

Any conjunction has this same form. For example, the complex proposition, “it is sunny and hot today,” has this same form which we can see by writing the conjunction this way:

It is sunny today and it is hot today .

Although we could write the conjunction that way, it is more natural in English to conjoin the adjectives “sunny” and “hot” to get “it is sunny and hot today.” Nevertheless, these two sentences mean the same thing (it’s just that one sounds more natural in English than the other). In any case, we can see that “it is sunny today” is the proposition in the “p” place of the form of the conjunction, whereas “it is hot today” is the proposition in the “q” place of the form of the conjunction. As before, this conjunction is true only if both conjuncts are true. For example, suppose that it is a sunny but bitterly cold winter’s day. In that case, while it is true that it is sunny today, it is false that it is hot today—in which case the conjunction is false. If someone were to assert that it is sunny and hot today in those circumstances, you would tell them that isn’t true. Conversely, if it were a cloudy but hot and humid summer’s day, the conjunction would still be false. The only way the statement would be true is if both conjuncts were true.

In the formal language that we are developing in this chapter, we will represent conjunctions using a symbol called the “dot,” which looks like this: “⋅” Using this symbol, here is how we will represent a conjunction in symbolic notation:

In the following sections we will introduce four basic truth-functional connectives, each of which have their own symbol and meaning. The four basic truth-functional connectives are: conjunction, disjunction, negation, and conditional. In the remainder of this section, we will discuss only conjunction. As we’ve seen, a conjunction conjoins two separate propositions to form a complex proposition. The conjunction is true if and only if both conjuncts are true. We can represent this information using what is called a truth table . Truth tables represent how the truth value of a complex proposition depends on the truth values of the propositions that compose it. Here is the truth table for conjunction:

Here is how to understand this truth table. The header row lists the atomic propositions, p and q, that the conjunction is composed of, as well as the conjunction itself, p ⋅ q. Each of the following four rows represents a possible scenario regarding the truth of each conjunct, and there are only four possible scenarios: either p and q could both be true (as in row 1), p and q could both be false (as in row 4), p could be true while q is false (row 2), or p could be false while q is true (row 3). The final column (the truth values under the conjunction, p ⋅ q) represents how the truth value of the conjunction depends on the truth value of each conjunct (p and q). As we have seen, a conjunction is true if and only if both conjuncts are true. This is what the truth table represents. Since there is only one row (one possible scenario) in which both p and q are true (i.e., row 1), that is the only circumstance in which the conjunction is true. Since in every other row at least one of the conjuncts is false, the conjunction is false in the remaining three scenarios.

At this point, some students will start to lose a handle on what we are doing with truth tables. Often, this is because one thinks the concept is much more complicated than it actually is. (For some, this may stem, in part, from a math phobia that is triggered by the use of symbolic notation.) But a truth table is actually a very simple idea: it is simply a representation of the meaning of a truth-functional operator. When I say that a conjunction is true only if both conjuncts are true, that is just what the table is representing. There is nothing more to it than that. (Later on in this chapter we will use truth tables to prove whether an argument is valid or invalid. Understanding that will require more subtlety, but what I have so far introduced is not complicated at all.)

There is more than one way to represent conjunctions in English besides the English word “and.” Below are some common English words and phrases that commonly function as truth-functional conjunctions.

It is important to point out that many times English conjunctions carry more information than simply that the two propositions are true (which is the only information carried by our symbolic connective, the dot). We can see this with English conjunctions like “but” and “however” which have a contrastive sense. If I were to say, “Bob voted, but Caroline didn’t,” then I am contrasting what Bob and Caroline did. Nevertheless, I am still asserting two independent propositions. Another kind of information that English conjunctions represent but the dot connective doesn’t is temporal information. For example, in the conjunction:

Bob brushed his teeth and got into bed

There is clearly a temporal implication that Bob brushed his teeth first and then got into bed. It might sound strange to say:

Bob got into bed and brushed his teeth

since this would seem to imply that Bob brushed his teeth while in bed. But each of these conjunctions would be represented in the same way by our dot connective, since the dot connective does not care about the temporal aspects of things. If we were to represent “Bob got into bed” with the capital letter A and “Bob brushed his teeth” with the capital letter B, then both of these propositions would be represented exactly the same, namely, like this:

Sometimes a conjunction can be represented in English with just a comma or semicolon, like this:

While Bob vacuumed the floor, Sally washed the dishes.

Bob vacuumed the floor; Sally washed the dishes.

Both of these are conjunctions that are represented in the same way. You should see that both of them have the form, p ⋅ q.

Not every conjunction is a truth-function conjunction. We can see this by considering a proposition like the following:

Maya and Alice are married.

If this were a truth-functional proposition, then we should be able to identify the two, independent propositions involved. But we cannot. What would those propositions be? You might think two propositions would be these:

Maya is married

Alice is married

But that cannot be right since the fact that Maya is married and that Alice is married is not the same as saying that Maya and Alice are married to each other, which is clearly the implication of the original sentence. Furthermore, if you tried to add “to each other” to each proposition, it would no longer make sense:

Maya is married to each other

Alice is married to each other

Perhaps we could say that the two conjuncts are “Maya is married to Alice” and “Alice is married to Maya,” but the truth values of those two conjuncts are not independent of each other since if Maya is married to Alice it must also be true that Alice is married to Maya. In contrast, the following is an example of a truth-functional conjunction:

Maya and Alice are women.

Unlike the previous example, in this case we can clearly identify two propositions whose truth values are independent of each other:

Maya is a woman

Alice is a woman

Whether or not Maya is a woman is an issue that is totally independent of whether Alice is a woman (and vice versa). That is, the fact that Maya is a woman tells us nothing about whether Alice is a woman. In contrast, the fact that Maya is married to Alice implies that Alice is married to Maya. So the way to determine whether or not a conjunction is truth-functional is to ask whether it is formed from two propositions whose truth is independent of each other. If there are two propositions whose truth is independent of each other, then the conjunction is truth-functional; if there are not two propositions whose truth is independent of each other, the conjunction is not truth-functional.

Identify which of the following sentences are truth-functional conjunctions. If the sentence is a truth-functional conjunction, identify the two conjuncts (by writing them down).

1. Jack and Jill are coworkers. 2. Tom is a fireman and a father. 3. Ringo Starr and John Lennon were bandmates. 4. Lucy loves steak and onion sandwiches. 5. Cameron Dias has had several relationships, although she has never married. 6. Bob and Sally kissed. 7. A person who plays both mandolin and guitar is a multi- instrumentalist. 8. No one has ever contracted rabies and lived. 9. Jack and Jill are cowboys. 10. Josiah is Amish; nevertheless, he is also a drug dealer. 11. The Tigers are the best baseball team in the state, but they are not as good as the Yankees. 12. Bob went to the beach to enjoy some rest and relaxation. 13. Lauren isn’t the fastest runner on the team; still, she is fast enough to have made it to the national championship. 14. The ring is beautiful, but expensive. 15. It is sad, but true that many Americans do not know where their next meal will come from.

1 Some philosophers would claim that a proposition is not the same as a statement, but the reasons for doing so are not relevant to what we’ll be doing in this chapter. Thus, for our purposes, we can treat a proposition as the same thing as a statement.

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Pursuing Truth: A Guide to Critical Thinking

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1.1 A n ‘a rgument’ as something two parties have with each othe r, something they get into, the kind of ‘argument’ one has in mind in de scribing two people as “arguing all the time ”

1.3 Argumentation

2 The relation between critical thinking and argument

2 .2 Critical thinking about things other than arguments

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2.2: Propositional Logic and the Four Basic Truth Functional Connectives

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