what is the contribution of studying language 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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Curtis Silver

The Importance of Logic and Critical Thinking

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"Critical thinking is a desire to seek, patience to doubt, fondness to meditate, slowness to assert, readiness to consider, carefulness to dispose and set in order; and hatred for every kind of imposture." - Francis Bacon (1605)

As parents, we are tasked with instilling a plethora of different values into our children. While some parents in the world choose to instill a lack of values in their kids, those of us that don't want our children growing up to be criminals and various misfits try a bit harder. Values and morality are one piece of the pie. These are important things to mold into a child's mind, but there are also other items in life to focus on as well. It starts with looking both ways to cross the street and either progresses from there, or stops.

If you stopped explaining the world to your children after they learned to cross the street, then perhaps you should stop reading and go back to surfing for funny pictures of cats. I may use some larger words that you might not understand, making you angry and causing you to leave troll-like comments full of bad grammar and moronic thought processes. However, if you looked at the crossing the street issue as I did – as a logical problem with cause and effect and a probable solution – then carry on. You are my target audience.

Or perhaps the opposite is true, as the former are the people that could benefit from letting some critical thinking into their lives. So what exactly is critical thinking? This bit by Linda Elder in a paper on CriticalThinking.org pretty much sums it up:

Through critical thinking, as I understand it, we acquire a means of assessing and upgrading our ability to judge well. It enables us to go into virtually any situation and to figure out the logic of whatever is happening in that situation. It provides a way for us to learn from new experiences through the process of continual self-assessment. Critical thinking, then, enables us to form sound beliefs and judgments, and in doing so, provides us with a basis for a 'rational and reasonable' emotional life. — Inquiry: Critical Thinking Across the Disciplines, Winter, 1996. Vol. XVI, No. 2.

The rationality of the world is what is at risk. Too many people are taken advantage of because of their lack of critical thinking, logic and deductive reasoning. These same people are raising children without these same skills, creating a whole new generation of clueless people.

Aarian Marshall

Large Language Models’ Emergent Abilities Are a Mirage

Stephen Ornes

Why the Baltimore Bridge Collapsed So Quickly

Chris Baraniuk

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Peter Guest

To wit, a personal tale of deductive reasoning:

Recently I needed a new transmission for the family van. The warranty on the power train covers the transmission up to 100,000 miles. The van has around 68,000 miles on it. Therefore, even the logic-less dimwit could easily figure that the transmission was covered. Well, this was true until the dealership told me that it wasn't, stating that because we didn't get the scheduled transmission service (which is basically a fluid change) at 30,000 and 60,000 miles the warranty was no longer valid. Now, there are many people that would argue this point, but many more that would shrug, panic, and accept the full cost of repairs.

I read the warranty book. I had a receipt that said the fluid was checked at 60,000 but not replaced. A friend on Twitter pointed out the fact that they were using 100,000 mile transmission fluid. So logically, the fluid would not have to be replaced under 100,000 miles if it wasn't needed, right? So why the stipulation that it needed to be replaced at 60,000 and the loose assumption that not doing that would void the warranty? So I asked the warranty guy to show me in the book where the two items are related. Where it explicitly says that if you don't get the service, the transmission isn't covered. There were portions where it said the service was recommended, but never connecting to actual repairs. Finally the warranty guy shrugged, admitted I was right and said the service was covered.

In this case, valid logic equaled truth and a sound argument. I used very simple reasoning and logic to determine that I was being inadvertently screwed. I say "inadvertently" because I truly believe based on their behavior that they were not intentionally trying to screw me. They believed the two items were related, they had had this argument many times before and were not prepared to be questioned. While both the service manager and the warranty guy seemed at least junior college educated, proving my argument to them took longer than it should have between three adults.

However, valid logic does not always guarantee truth or a sound argument. This is where it gets a little funky. Valid logic is when the structure of logic is correct in the way of syntax and semantics rather than truth. Truth comes from deductive reasoning of said logic. For example:

All transmissions are covered parts. All covered parts are free. Therefore, all transmissions are free. This logic is technically valid, and if the premises are true, then of course the conclusion must be true. You can see here however that it's not always true, though in some situations it could be. While the logic is valid, not all transmissions are free, only those covered by the warranty. So based on that, saying all transmissions are free is not sound logic.

To take it one step further:

All Daleks are brown. Some brown things are Cylons . Therefore, some Daleks are Cylons. Sci-fi fan or not, you probably know that this is not true. The basic lesson here is that, while the logic above might seem valid because of the structure of the statement, it takes a further understanding to figure out why it's not necessarily true: That is, based on the first two statements it's possible that some Daleks are Cylons, but it's not logically concludable. That's where deductive reasoning comes on top of the logic. The underlying lesson here is not to immediately assume everything you read or are told is true, something all children need to and should learn.

This is the direct lesson that needs to be passed on to our children: that of not accepting the immediately visible logic. While not all problems are complex enough to require the scientific method, some of them need some deduction to determine if they are true. Take the example above — how many kids would immediately be satisfied with the false conclusion? Sure, it's a bit geeky with the examples, but switch out bears for Daleks and puppies for Cylons. That makes it easier, and takes the actual research out of it (to find out what Daleks and Cylons are respectively) but many people would just accept that in fact some bears are puppies, if presented with this problem in the context of a textbook or word problem.

Maybe I'm being paranoid or thinking too doomsday, whatever, but I think this is an epidemic. Children are becoming lazier and not as self sufficient because their parents have a problem with watching a three year old cry after they tell her to remove her own jeans, or ask her to put away her own toys (yes, organizational logic falls under the main topic). These are the same parents who do their kid's science project while the kid is playing video games. These kids grow up lacking the simple problem solving skills that make navigating life much easier. Remember when you were growing up and you had the plastic stacking toys ? Well, instead of toys for early development like that, parents are just plopping their kids down in front of the television. While there is some educational type programming on television, it's just not the same as hands-on experience.

My father is an engineer, and he taught me logic and reasoning by making me solve simple, then complex, problems on my own. Or at least giving me the opportunity to solve them on my own. This helped develop critical thinking and problem solving skills, something a lot of children lack these days. Too often I see children that are not allowed to solve problems on their own; instead their parents simply do it for them without argument or discussion. Hell, I am surrounded by adults every day that are unable to solve simple problems, instead choosing to immediately ask me at which point I have to fill the role that their parents never did and – knowing the solution – tell them to solve it themselves, or at least try first.

One of the things I like to work on with my kids is math. There is nothing that teaches deductive reasoning and logic better than math word problems. They are at the age where basic algebra can come into play, which sharpens their reasoning skills because they start to view real world issues with algebraic solutions. Another thing is logic puzzles , crossword puzzles and first person shooters. Actually, not that last one. That's just the reward.

Since I weeded out the folks that don't teach their kids logic in the first two paragraphs, as representatives of the real world it's up to the rest of us to spread the knowledge. It won't be easy. The best thing we can do is teach these thought processes to our children, so that they may look at other children with looks of bewilderment when other children are unable to solve simple tasks. Hopefully, they will not simply do the task for them, but teach them to think. I'm not saying we need to build a whole new generation of project managers and analysts, but it would be better than a generation of task-oriented mindless office drones with untied shoelaces, shoving on a door at the Midvale School for the Gifted .

h/t to @aubreygirl22 for the logical conversation. Image: Flickr user William Notowidagdo. Used under Creative Commons License.

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2: Language, Meaning, and Definition

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Critical thinking, on one understanding of the idea, is the ability to ask the right questions. Some of the right questions are questions about the words used in an argument or used to express a position. What do they mean? No, what, specifically , do they mean? When someone says something like “immigration is a problem.” What do they mean by “immigration”? Are they referring to illegal immigration? Legal Immigration? All immigration? A specific nationality? A specific subset of illegal immigrants? What do they mean by “a problem”? Do they mean “we need to find out how to support these people as they struggle to survive?” or do they mean “we need to protect ourselves from these people”? We don’t really know exactly what they mean until we’ve clarified it with them (or sometimes looked at the other things they’re saying and inferred what they mean).

2.1: Breakdown of meaning
2.2: How does meaning work? Definition and Concepts
2.3: Necessary and Sufficient Conditions
2.4: Chapter 2 - Key Terms
2.E: Chapter Two (Exercises)

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al-Farabi’s Philosophy of Logic and Language

Abū Naṣr al-Fārābī (Iraq, c. 870–c. 950) devoted his career to introducing the work of Aristotle to educated Arabic-speaking citizens of the Islamic Empire. Several of his major writings are lost in whole or part. But many of his books explaining Aristotle’s Organon (the collection of Aristotle’s writings on logic and related subjects) have survived, and the number of them available in Western translations is increasing steadily. For general information on al-Fārābī see the entry on Al-Farabi .

Al-Fārābī studies the various roles of language in human life and society. He emphasises the use of language to convey information, to ask questions and resolve disagreements, and to describe distinctions and classifications. He believes that language in some sense copies meanings, and that mismatches between language and meanings need to be avoided. He presents Aristotle’s logic as a collection of methods for exercising persuasion, regulating debate, discovering truth and achieving certainty. He also explores its applications in poetry. Along the way he makes many acute observations on issues ranging from the sources of metaphysical questions to the temporal structure of events and the relationship between poetry and music.

1. Al-Fārābī’s Writings and Their Background

2. the origin of languages, 3. the origins of syllogistic arts, 4.1 questions in debate, 4.2 questions seeking information, 5. the definition of logic, 6.1 categorical logic, 6.2 hypothetical logic, 6.3 modal logic, 6.4 demonstrative logic, 7. logical consequence, 8. truth and falsehood, 9. foundations of arabic, 10. poetry and music, works of al-fārābī, works of other authors, other internet resources, related entries.

Al-Fārābī’s surviving works contain well over a thousand pages that are devoted to explaining the contents of Aristotle’s logical writings and aimed at educated readers of Arabic. Much of this material reveals al-Fārābī’s strong interest in the nature of language.

Al-Fārābī’s intellectual background was not so much Aristotle himself. Rather it was the Aristotelian part of the syllabus of the Neoplatonic school of philosophy that flourished in Alexandria (in Egypt) in the fifth and sixth centuries (see D’Ancona 2022). Al-Fārābī tells us that eventually “instruction was moved from Alexandria to Antioch” (in Syria), until the last members of the school scattered “taking their books with them”. He says that he himself studied with one of these last members, Yūḥannā bin Ḥaylān, and together they read Aristotle up to the end of Posterior Analytics. He adds that the Alexandrian school came to describe the part of Aristotle’s Organon from modal logic onwards as “the part that is not read”, since under the Christians the modal material had been kept hidden. (Al-Fārābī’s account is in a lost work quoted by the historian Ibn Abī Usaybi‘a [ ‘Uyūn 604f]; see the translation in Fakhry 2002: 159.)

Al-Fārābī has oversimplified the history (see Lameer 1997 and Watt 2008). But he correctly implies that his understanding of Aristotle is based on the Alexandrian syllabus and its later offshoots in the Middle East. For example, the account of logic in his influential [ Catalogue ] has been shown to be an edited translation of a work from the Alexandrian teaching materials. [ 1 ] So for understanding al-Fārābī it becomes important to know when he is giving his own considered view and when he is merely passing on parts of the Alexandrian syllabus. As yet there is no consensus about this, or about the order in which he wrote his works.

The Alexandrian Neoplatonists saw philosophy as an avenue by which we can achieve happiness through knowledge of The One (see Wildberg 2021). To add intellectual rigor to this mystical endeavor they included the logical writings of Aristotle in the early stages of their teaching syllabus. They devised a body of introductory texts to explain how Aristotle’s logic saves us from incorrect thinking and acting, and why Aristotle devised his logic syllabus—his Organon —in the form that he gave it. [ 2 ] Some features of al-Fārābī’s presentation are most easily explained in terms of the Alexandrians. For example, the Aristotelian part of their syllabus, after Porphyry’s Eisagoge , began with Aristotle’s Categories , so al-Fārābī duly seeks reasons why categories are an essential first step in logic. Their Organon also included Aristotle’s Rhetoric and his Poetics ; so al-Fārābī explains why the arts of rhetoric and poetry are really parts of logic. If their Organon had contained a book on music, al-Fārābī would have explained why musical theory is a branch of logic. [ 3 ] (On music see Section 10 below.)

Al-Fārābī’s logical writings take various forms. Some of them are Long Commentaries on works of Aristotle, which dissect Aristotle’s text in sometimes excruciating detail; only the Long Commentary on De Interpretatione survives in full, though we have parts of others. More friendly are the Epitomes, in which al-Fārābī rewrites works in the Organon from his own point of view. There are also a number of texts that serve as introductions to the Organon , though they are not necessarily elementary. We call attention to three works in this last group. The first, [ Indication ], teaches that logic is the art of making correct discriminations, and hence is the key to happiness in life as a whole. It also explains that we must study language before we study logic. The second, [ Expressions ], is a sequel to [ Indication ] and introduces the vocabulary of logic.

The third work is the extraordinarily original and insightful [ Letters ], which weaves together language, logic, and metaphysics. We will take this work as the best basis for understanding al-Fārābī’s overall view of language and logic. Sections 2 to 5 below will review what we take to be the core of this view. The remaining Sections 6 to 10 will pick up particular themes.

Besides the Alexandrian material, al-Fārābī was able to call on highly professional Arabic translations of the books of the Organon . He also had translations of some logical writers from the Roman Empire, such as Alexander of Aphrodisias and Themistius. He is not known to have made any use of earlier Arabic texts relating to logic, such as the Logic of Ibn al-Muqaffa‘ and writings of al-Kindī. (Zimmermann [1981: lxviii–xcviii] and Lameer [1994: Chapter 1] discuss what earlier logical writings were available to al-Fārābī. See also Walzer [1962: 129–136] for al-Fārābī’s sources on Aristotle’s poetics.)

Al-Fārābī’s work on logic and language had a direct effect on several Arabic authors in the two hundred years after his death. [ 4 ] These include Ibn Bājja (in Latin Avempace), Ibn Sīnā (Avicenna), Al-Ghazālī (Algazel), and Ibn Rushd (Averroes). He also influenced a number of medieval Jewish authors including Maimonides. The Latins knew him as Alfarabius or Alpharabius or Abunaser. His influence can be seen in Scholastic treatments of determinism, poetic argument, and the classification of sciences. [ 5 ]

Al-Fārābī describes how a language develops within a community. In [ Letters ] (114, 115) 134.16–135.14 he pictures a community whose members have concepts ( ma‘qūlāt , literally “intellected things”, or “intelligibles” in Scholastic terminology) that allow them to pick out identifiable objects in the external world, either individually or as kinds of thing. He refers to these concepts drawn from perception of the external world as “primary concepts”. These people have beliefs, and they are able to reason about the world, to deliberate about their actions, and to communicate by pointing. But as yet these people have no language.

The first development towards language is that the people come to realize that they can communicate their needs to each other better if they agree to label some objects and concepts with vocal sounds. This sets up a conventional correlation between simple (i.e., uncompounded) primary concepts and words, and eventually this correlation comes to be accepted by the whole community. The words are said to “signify” the concepts to which they are correlated. Al-Fārābī envisages that a lawmaker will regulate the correlation and add some words to it for the benefit of the community ([ Letters ] (120) 138.4–8). Thus a national lexicon is created; the sounds that are used form a national alphabet.

Once the idea has become established that words signify meanings, the community will aim to develop the language so that words imitate the “ordering” or “regime” ( intiẓām ) of the primary concepts ([ Letters ] (122) 139.2–4). This regime includes any relationships that the concepts have as concepts. For example, two concepts may be similar; so an effort will be made to find a pair of similar words to express these concepts. Al-Fārābī notes that this effort may misfire and result in homonymy—a single word being used for two different concepts ([ Letters ] (124) 140.8–10). The pressure to copy similarities also leads to metaphors ([ Letters ] (127) 141.10).

Also some concepts are derived from others; the word for the derived concept should be grammatically derived from the word for the other concept. The words for underived concepts should not be grammatically derived. Al-Fārābī notes that in practice this correlation sometimes fails. For example, he takes it that the participle “living” ( ḥayy ) is derived, but it is sometimes used to signify the underived concept “animal” ([ Letters ] (26) 74.16, (36) 81.18f). Likewise the underived concept “is” is sometimes signified by the derived passive participle mawjūd ([ Letters ] (84) 113.9).

Also concepts can be combined into compound concepts, and this possibility will be copied in the language too. ([ Letters ] (126) 140.20–141.3.) Taking this view, al-Fārābī makes a number of remarks that contain the first explicit formulations of the thesis of compositionality. [ 6 ]

Al-Fārābī clearly believes that mismatches between words and concepts are a bad thing, but it’s less clear why he believes this, or what he thinks should be done about it. The original matching was set up by an artless consensus of the community, presumably because it served some social purpose. Al-Fārābī never analyses in detail what this purpose might be, or, for example, how it would be damaged by using derived words for underived concepts. Does he really fear that a mismatch could lead to a breakdown in communication, even if the whole community adopts the mismatch? Germann (2015/6: 138f) has suggested that his fear is more specific: he worries that if mismatches develop, teachers—including philosophy teachers—may be unable to pass information reliably to their students.

Another possibility is that he is afraid that a mismatch will cause errors in logical reasoning, because the relationships between concepts that make an argument valid will not be visible in the corresponding words. In [ Expressions ] 102.8–15, after telling us that demonstrations and syllogisms take place in internal speech, not external, he comments that

most students don’t have the ability to imagine how concepts are ordered in the mind, so instead one takes expressions that signify the concepts, so as to enable the student’s mind to make a transition from them to the concepts.

Any mismatch between concepts and words could disrupt this process.

In any event, al-Fārābī is in no hurry to reform the language. He is content to continue using the word mawjūd for “is”.

There is one part of the regime of primary concepts that al-Fārābī never suggests that language should replicate. Some concepts are more inclusive than others; for example, “animal” is more inclusive than “human”. Following one reading of Aristotle, al-Fārābī believes that there are ten maximally inclusive simple primary concepts (ignoring “thing”, “concept”, “one”, and “being” which include all concepts). He refers to these ten concepts as “categories” ( maqūlāt , not to be confused with ma‘qūlāt above). But we will prefer to call them by their alternative name “supreme genera”, because al-Fārābī confusingly also applies the name “category” to all simple primary concepts. Languages do distinguish the minimally inclusive concepts, those that apply to just one thing, by using proper names for them. But it’s unrealistic to expect languages to copy the rest of this regime of inclusions, and we know of no place where al-Fārābī suggests that it should.

Some of the historical processes mentioned above will have the effect of making people think about the primary concepts and their regime. Al-Fārābī points out that as a result, people will now have concepts that classify concepts in the soul rather than identifiable objects in the external world. So these are a new kind of concept, and al-Fārābī calls them “secondary concepts” (often translated as “second intelligibles”). Thinking about secondary concepts will give us “tertiary concepts”, and so on to infinity. As examples of secondary concepts, al-Fārābī mentions “genus”, “species”, “more/less inclusive”, “known”, “concept”. (All this is in [ Letters ] (7,8) 64.9–65.8.) [ 7 ]

Although al-Fārābī doesn’t recommend any particular reforms of language, he does make some detailed recommendations for a philosopher who is seeking to translate philosophy from another language and needs to introduce technical terms for the purpose. ([ Letters ] (155) 157.19–158.21.) It would be interesting to compare al-Fārābī’s recommendations with his own practice, if we could be sure which of the technical terms used for translating Greek writers we can credit to him.

He does introduce some new names for notions that he himself pioneered. Three noteworthy examples are:

He introduces yufīdu “provides” as a term of art for saying that the answer to a question posed in a philosophical debate “provides” information (cf. Section 4 below). The root is rare in his writings except for this usage, and its use in a related sense in linguistic writers probably antedates his use of it (see Giolfo & Hodges 2018).
He borrows from the linguists the term istithnā’ (“exception”) as a name for the inference rules of his hypothetical logic (cf. Section 6 below ). The choice rests on a formal similarity between these rules and a property of the syntactic construction known as “exception”. [ 8 ]
His choice of the name “secondary concept” is based on an analogy with Porphyry’s theory of “second impositions”, i.e., words for talking about words. [ 9 ]

Al-Fārābī’s tale of the origins of language runs on into a tale of how language makes it possible to handle concepts in new ways. For al-Fārābī one key difference between language and concepts is that language is public and allows communication between people. Hence many of the new uses of concepts have to do with social interaction. In each case he is interested in the development of new skills for handling concepts. Skills involve instruments and rules for handling these instruments; so the appearance of a new skill involves an acceptance of the rules ( qawānīn , singular qānūn ) for handling its instruments. A bundle of associated skills and their rules is called an “art” ( ṣinā‘a ).

The first new art that he calls attention to is rhetoric ( khiṭāba ), the art of the orator, which uses concepts in order to persuade people to do or believe certain things. The main users of this skill are political and religious leaders, who employ it in order to assert their authority. Alongside rhetoric al-Fārābī mentions the art of poetry ( shi‘r ), which uses concepts in order to bring people to certain states of mind. He sees this art as most useful for religious leaders. He also mentions an art which he calls the art of sophistry. This art embodies the skill of producing bad arguments from false premises. It’s hard to see what could have led him to the conclusion that there is such an art, beyond the fact that the Alexandrian syllabus contained, wedged between a book on dialectical methods and one on rhetorical methods, Aristotle’s treatise Sophistical Refutations . Aristotle’s treatise is usually understood to be teaching the art of detecting and refuting bad arguments, not that of creating them!

One effect of the introduction of language is that people are able to learn the opinions of other people. They will inevitably discover that some people disagree with them, not least in speculations about the nature of the universe. So the art of dialectics or debate ( jadal ) is introduced in order to resolve differences of opinion between two people. ([ Letters ] (140,141) 150.2–151.7.) But a dialectical resolution of a disagreement is no guarantee of the truth of the agreed conclusion; one of the debaters might just be better at arguing ([ Debate ] 40.9–13).

A realization that dialectics doesn’t lead to certain truth will inspire some individuals to seek other methods that do. At this point the community discovers the art of “demonstration” ( burhān ), which establishes truths with certainty. Al-Fārābī believes that among the Greeks this art was achieved by Plato:

Plato was the first to be aware of the demonstrative methods and to distinguish them from the dialectical, sophistical, rhetorical, and poetical methods. But from his point of view they were distinguished in use and according to matter, and in terms of what guidance he received from his considerations at leisure and his superior natural intelligence. He didn’t prescribe universal rules for them. Afterwards Aristotle did prescribe such rules in his book Posterior Analytics . ([ Rhetoric ] 55.13–17)

It was a commonplace in the Neoplatonic schools that the high point of logic was Posterior Analytics with its treatment of knowledge with certainty. The Neoplatonists also considered that Aristotle had arranged his Organon so that the path up to this summit through Categories , De Interpretatione , and Prior Analytics assembled the tools of logic, and the downward slope from Posterior Analytics onwards allowed the student to apply these tools within demonstrative methods, dialectical methods, sophistical methods, rhetorical methods, and poetic methods in turn. Al-Fārābī inherited this view of Aristotle; see [ Aristotle ] pp. 82–93.

He also inherited the zeal of the Neoplatonic schools to catalogue the ingredients of logic. Thus in [ Letters ] he catalogued the logical arts according to the social needs that brought them into existence, while in [ Aristotle ] he catalogued them according to the books of the Organon that Aristotle devoted to them. These two principles of classification led to essentially the same divisions between logical arts. But sometimes he used principles that draw distinctions in different places. For example in [ Syllogism ] he classified kinds of logic by the syllogisms (i.e. two-premise inferences) that they used; we come to this classification in Section 6 below. Elsewhere he classified kinds of logic by the kinds of premise that they accepted in their syllogisms.

All the kinds of logic, even the less syllogistic kinds, must have rules about what to adopt as starting premises. In the case of rhetoric, practicality implies that the orator should choose premises that the audience will accept; likewise in dialectics it makes sense to start with premises that have some plausibility. Al-Fārābī believes that in practice the community will insist on restrictions that add a note of objectivity: for example, that experts agree to the premise, or that nobody positively disagrees with it. He formulates some conditions along these lines, including that the premises must be at least “standard” ( masshūr ) or “received” ( maqbūl ). (For discussion of such conditions and where they apply, see Aouad 1992 and Black 1990: Chapter 5A. Chatti 2017 reviews how al-Fārābī catalogues the starting points of inferences in hypothetical logic. Kleven 2023 studies the treatment of the starting points of reasoning in some of al-Fārābī’s introductory essays, and adds some interesting information about the manuscripts.)

Rhetorical reasoning might be the hardest to make sense of, particularly when [ Letters ] suggests that the rhetorician’s job is done when he or she has persuaded the audience. Surely that aim could be achieved by means that don’t involve logic at all? But recently it has come to be accepted that the Latin essay [ Didascalia ] published in [ Rhetoric ] is probably a translation of the prologue to al-Fārābī’s lost Long Commentary on Rhetoric . In fact the work goes way beyond vague remarks about methods of persuasion; see Woerther 2020. For example al-Fārābī observes that medical reasoning about what remedies to apply to this present invalid, and agricultural reasoning about how to increase the yield of this particular field, cannot be demonstrative since they apply only to this particular individual (invalid or field); so we have to take them as rhetorical reasoning (Woerther (2020 p. 346)). On this reckoning, much of the reasoning of our most respected experts must count as rhetoric.

In sections 23 and 24 towards the end of Prior Analytics ii, Aristotle discusses argument by induction and argument by analogy, with a view to showing that both of them are reducible to syllogism. Since [ Syllogism ] is an epitome of Prior Analytics , al-Fārābī closes the book with some sections in which he gives his own reductions of induction and analogy to syllogism. Some manuscripts of [ Syllogism ], and some manuscripts of the later work [ Short Syllogism ], [ 10 ] include a pair of essays which we will refer to as the Tailpiece; the first essay is on the logical device of “transfer”, and the second is on the application of this device to reduce arguments in Islamic jurisprudence ( fiqh ) to syllogisms. In the first of these two essays al-Farabi refers to a number of named argument forms (for example “transfer from the observed to the unobserved”), and it is clear that he is referring to earlier debates about these argument forms; but there is no agreement on whether the debates were in Roman Empire medical circles or in Islamic theology.

One particular strand in this complex is a distinction that al-Fārābī makes between two forms of analogy, which he describes as taḥlīl and tarkīb respectively. Some authors have read these words as “analysis” and “synthesis” respectively, and tried to read these as descriptions of two different kinds of formal proof. But this is certainly wrong, since the distinction that al-Fārābī himself draws between the two kinds of argument is not about the form of the resulting proof, but about the criteria for success in the search for a middle term. Al-Fārābī himself is a little conflicted at this point; in loyalty to Aristotle he wants to emphasise the reduction to syllogism, but the point he makes about search, which is central for his application to fiqh in the second essay, is not about the form of the final syllogistic proof at all. (See Chatti and Hodges 2020 for further details on the Tailpiece, and Hodges 2020 for the increasing interest in search algorithms in this period.) [ 11 ]

Further remarks comparing al-Fārābī’s dialectics with Islamic fiqh can be found in Gyekye (1989) and Young (2017: 539–543).

4. Requests and Questions

Al-Fārābī has explained that language grew out of a need to communicate requests. Requests and questions of various kinds are a central feature of his thinking. At [ Debate ] 43.2f he distinguishes two main kinds of request: those that are requests for a commitment, and those that are requests for knowledge or information. This division corresponds to the roles of questions in debate and in science respectively. We begin with debate.

Al-Fārābī cites Aristotle as saying that the primary aim in debate is to refute proposed views; reaching agreement is a secondary aim ([ Debate ] 14.7–9). Accordingly the rules of debate provide that one of the debaters, known as the “questioner” ( sā’il ), has the role of refuting the views offered by the other debater (the “responder”, mujīb ). It’s also the questioner’s task to elicit from the responder commitments to statements. (Committing is called “conceding” or “submitting”, taslīm .) The questioner must then try to refute these statements and the responder must try to defend them. The questioner elicits a commitment by presenting to the responder a pair of incompatible possibilities, and the responder must choose which possibility to defend. This pair of incompatible possibilities is referred to as “what was sought after” ( maṭlūb , in Latin quaesitum) , or the “question” ( mas’ala ).

The simplest case is where the questioner requires the responder to commit to a view on whether some primary concept is instantiated in the world. For example, “Is there or is there not a vacuum?” More complicated, because it combines two concepts, is a question like “Is the sky spherical or not?” More bizarre, “Stone and human, which of the two is animal?” ([ Debate ] 43.16–20) When the responder has made a commitment, the questioner must devise a syllogism whose conclusion contradicts the commitment, and then attempt to get the responder to commit to the premises of this syllogism and to its validity. The responder is allowed to challenge on any of these points, whereupon the two participants swap roles.

Al-Fārābī comments that the rules of debate have been found useful for other purposes besides resolving differences of opinion. For example, in demonstrative science debate trains the participants to be nimble and systematic thinkers; it clears out of the way sophistical nonsense, and gives prima facie conclusions that can then be checked by demonstrative methods. In fact it’s not humanly possible to reach philosophical truth without engaging in debate. ([ Debate ] 29.21–38.3.) The relationship between questioner and responder can serve as a template for the relationship of teacher to pupil, so far as this is not simply passing information from teacher to pupil. It can also be a basis for collaborative research. ([ Demonstration ] 77.1–83.9.)

Al-Fārābī’s treatment of information-seeking questions is strongly influenced by two contexts in which Aristotle’s Organon uses question words. The first of these is in Categories , where Aristotle (at least as al-Fārābī reads him) classifies primary concepts under the ten supreme genera. Aristotle explains his classification partly through question words: “how much” (Arabic kam ), “how” ( kayfa ), “where” ( ayna ), “when” ( matā ). Al-Fārābī takes note of most of these question words, and adds two more: “what” ( mā ) and “which” ( ayyu ) ([ Letters ] (166) 165.17, (183) 181.16.) In [ Expressions ] 47.5–12 he notes that the answers to some of these questions can be classified by the question word or a word derived from it: “quantity” ( kamiyya ), “quality” ( kayfiyya ), “quiddity” or “whatness” ( māhiyya ). (See the discussion of these questions in Diebler 2005.)

The second context is the second book of Posterior Analytics . In the opening lines of this book Aristotle lists the four “things that we seek”, namely that it is so ( annahu yūjadu ), why it is ( li-mādhā ), what it is ( mā ) and which it is ( ayyu ). In [ Letters ] (210) 200.16 al-Fārābī adds the question “is it the case that” ( hal ), which turns Aristotle’s “that it is” into a question.

Large parts of both [ Expressions ] and [ Letters ] are devoted to explaining how we can elicit philosophical information by asking these and similar questions. [ 12 ] Thus for each primary concept we can ask “What is it”? Al-Fārābī defines the genus ( jins ) of the concept to be the answer to this question. By asking “which thing” (in that genus), we get a more specific description that provides the species ( naw‘ ) below the genus. Al-Fārābī explains how further questions can elicit the differentiae and the definitions of concepts. The “essence” ( dhāt ) of a concept consists of the concepts included in the definition of the concept; these concepts in the essence are also described as “constitutive” ( muqawwim ) for the concept.

Al-Fārābī tries hard to convince us that the philosophers’ questions are a natural extension of everyday questions. (Diebler 2005 draws a plausible comparison with ordinary language philosophy.) But the effort hardly succeeds. In what everyday context would we ask, about a date-palm, “What is it?” and accept the answer “It’s a body”? ([ Letters ] (167) 166.16) The outcome is that al-Fārābī unintentionally raises problems that are still resonant in the philosophy of questions. Compare “It’s a body” with the answer “[He] is a person who is over three inches tall” discussed by Cross and Roelofsen 2018.

In his [ Demonstration ] (64.5–7) al-Fārābī tells us:

Two arts or sciences differ through having different subjects ( mawḍū‘ ). If their subjects are identical then the arts or sciences are identical; if their subjects are different then the arts or sciences are different. Their subjects can differ either by having different features ( aḥwāl , singular ḥāl ) or in themselves.

Thus an art or science—al-Fārābī is very little exercised about the difference between the two—studies some entities called its subjects, and it ascribes to these entities some features. Like other Aristotelians, al-Fārābī flips between saying (for example) that the subjects of arithmetic are numbers and that the subject of arithmetic is number; the two locutions mean the same.

In [ Letters ] sections 11–18 al-Fārābī undertakes to identify several arts or sciences in these terms, namely “the art of logic and the sciences of nature, politics, mathematics and metaphysics”. The first step is to identify their subjects. In all these cases, he says, the “primary subjects” are the primary concepts ([ Letters ] 66.20f). For example, in mathematics we study primary concepts from the point of view of quantity, abstracting from their other features ([ Letters ] (15) 67.19–68.5). (See Druart 2007 and Menn 2008 on the important question of how metaphysics fits into this picture.)

Al-Fārābī tells us what features of the primary concepts are studied in logic:

Insofar as [the primary concepts] are signified by expressions, and insofar as they are universals, and insofar as they are predicates or subjects, and insofar as they are defined in terms of each other, and insofar as they are asked about and taken in a question about them, they are logical. They are taken so as to investigate the compounds of them, one with another, where the aforementioned things attach to them, and the features of the compounds after they have been compounded. ([ Letters ] (12) 67.1–5). [ 13 ]

He gives no examples, but here is one. In his book [ Syllogism ] 27.6f he claims that the following argument is a valid syllogism:

No stone is an animal. Some body is an animal. This yields: Some body is not a stone.

We can paraphrase his claim:

This paraphrase (*) illustrates why “predicate” and “subject” are listed among the logical features, and also why logic has to consider compounds of primary concepts (since the three sentences express propositions, which are compounds of concepts). Al-Fārābī’s reference to being “asked about and taken in a question about them” could refer either to dialectical questions, or to the questions that extract information about concepts, or possibly to both.

The features listed as characterizing the art of logic are concepts that classify other concepts, and so they are secondary concepts. This distinguishes logic from mathematics and natural science. For example, natural science finds causes, but these causes are “not outside the categories” ([ Letters ] (16) 68.17).

By describing simple primary concepts as the “first” or “primary” subjects of logic, al-Fārābī suggests that there might be further subjects of logic. This makes sense; why shouldn’t the rules of logic apply to secondary concepts just as much as to primary concepts? In fact the way al-Fārābī has set things up would allow him to explain how this should go. Laws about secondary concepts will need tertiary concepts. But there is no need to restate the laws of logic using tertiary concepts, because “the features that attach to the primary concepts are exactly the same as those that attach to the secondary concepts”, and so on all the way up ([ Letters ] (9) 65.16f).

There is an obvious criticism of al-Fārābī’s definition of logic, namely that the features that he lists are too vague. For example, how could we use his list to determine whether the art of poetry is or is not a part of logic? The real problem is that for al-Fārābī himself with his Neoplatonic heritage, logic consists of whatever Aristotle said in the Organon , and al-Fārābī never comes near finding any abstract way of characterizing this body of material. [ 14 ]

Al-Fārābī gives an even vaguer characterization of the subjects of logic in his [ Catalogue ] (59.9–11):

As for the subjects of logic, about which it gives rules, they are concepts insofar as expressions signify them, and expressions insofar as they signify concepts.

This definition could have been copied from a text in the Neoplatonic tradition.

We return briefly to the question why al-Fārābī includes the subject of categories in a logic syllabus. Commentaries in the Alexandrian tradition normally started with a statement of the purpose of the material to be discussed. Al-Fārābī’s epitome [ Categories ] has no such statement, but the surviving fragments of the longer [ Commentary on Categories ] do address the question. They tell us (p. 196) that Aristotle’s Categories was intended to catalogue the simple universal primary concepts, but Aristotle found it sufficient to catalogue the ten supreme genera instead. Some people (p. 202) didn’t think Categories was specifically intended for logic; but “under the conditions we have mentioned, the contents of Categories turn out to be a specific part of logic”. But in fact no such conditions have been mentioned, at least in the surviving fragments. What needs to be shown is that the features (the aḥwāl ) of categories studied in the first book of the syllabus are ones that will serve some purpose in later books. But this issue is not addressed at all. Al-Fārābī does address it in [ Rhetoric ] 87.16–89.4, where he says that the terms of premises can be in any of the ten supreme genera, in any combination. This only confirms the suspicion that the supreme genera are irrelevant to logical reasoning.

6. Tools for Inference

In this section we run quickly through al-Fārābī’s formal systems of logic. We assume some knowledge of Aristotle’s syllogistics, as in Smith (2022). Al-Fārābī discusses four logical systems: 6.1 Categorical syllogisms, 6.2 hypothetical syllogisms, 6.3 modal syllogisms, 6.4 demonstrative syllogisms.

In [ Syllogism ] and [ Short Syllogism ] Al-Fārābī recognizes three figures of categorical syllogisms, following Aristotle. [ 15 ] In these three figures he recognizes respectively four, four, and six valid moods, as listed by Smith (2022) but not always in the same order. (For example in [ Syllogism ] he puts Darii before Celarent ). Following Aristotle again, he regards the first figure syllogisms as “perfect”, i.e., self-evident and not in need of justification. For the moods in second and third figures he gives justifications by reduction to first figure, following Aristotle in the main. (His chief departure from Aristotle in these justifications is that he never uses proof by reductio ad absurdum , though he does recognize such proofs as valid.) Aristotle’s justification of Darapti [ 16 ] relies on the conversion implication: from “Every B is an A ” infer “Some A is a B ” (cf. [ Syllogism ] 30.3). This implication fails to hold if we allow “Every B is an A ” to be true when there are no B s. Accordingly al-Fārābī declares that “Every B is an A ” is false unless there is at least one B ([ Categories ] 124.14). Though he sometimes seems to forget he said this, he is the earliest logician on record as having spelled out this implication of “Every B is an A ”.

Probably his main difference from Aristotle in categorical syllogisms is his treatment of the pairs of formal premises (i.e., with letters for terms) where Aristotle says “no syllogism occurs” in the sense that no syllogistic conclusion follows validly. Al-Fārābī calls these premise-pairs “nonproductive” ( ghayr muntij ). Aristotle had used the fact that valid inference rules preserve truth as a means to proving nonproductivity of a formal premise-pair; for any proposed conclusion, he found nouns that could be put for the letters, in such a way that the premises came out true and the conclusion false. During the Roman Empire period a tendency developed for logicians to skip these proofs and fall back instead on “laws of syllogism” that were supposed to give necessary and sufficient conditions for a premise-pair to be productive (cf. Lee 1984: 119f). This was generally a lapse from the rigor of Aristotle’s work, because the arguments given to justify the laws of syllogism were of a poor standard. Though al-Fārābī does once briefly mention Aristotle’s counterexample method ([ Syllogism ] 20.2–5), in practice he relies entirely on the laws of syllogism. By contrast the earlier logic texts of Paul the Persian and Ibn al-Muqaffa‘, both heirs of the Alexandrian view, copied Aristotle’s nonproductivity proofs in categorical logic with total formal rigor.

For further discussion of al-Fārābī’s categorical syllogisms, see Chatti and Hodges 2020 and Chatti 2019.

A hypothetical sentence consists of two shorter sentences joined together, as in the connected ( muttaṣil ) form “If p then q ” or the separated ( munfaṣil ) form “Either p or q ”. For the logic of these sentences, al-Fārābī confines his attention almost entirely to simple inferences like modus ponens:

If this visible thing is a human, then it is an animal; but it is a human. Therefore it is an animal.

or an inference with exclusive disjunction:

This number is either even or odd; but it is even. Therefore it is not odd.

His treatment is so similar to the contents of Boethius’ De Syllogismis Hypotheticis that they must have drawn on a common source now lost.

Al-Fārābī points out that hypothetical sentences can be chained so as to form “compound syllogisms”, as for example in

Either p or q . If p then not r . If not r then s . If s then t . Not t . Therefore q .

This formalizes an argument at his [ Short Syllogism ] 90.6–9. He also gives examples of categorical syllogisms chained together—though these can be found already in Aristotle.

There is almost no mention of modal syllogisms in any of al-Fārābī’s surviving works. He must have discussed modal syllogisms in his [ Commentary on Prior Analytics ]; but the relevant part of this work is lost and we have to rely on citations by Avicenna, Averroes, and Maimonides. These citations between them tell us of only one modal syllogistic mood that al-Fārābī either accepted or rejected. [ 17 ]

From [ Commentary on De Interpretatione ] 193.3–19 and quotations in Maimonides, we know that al-Fārābī claimed, against Galen, that logic with possibility statements is useful in practical arts where actual outcomes have to be predicted, such as medicine, agriculture, and navigation (Schacht & Meyerhof 1937: 67). This looks at first sight like a confusion between possibility and probability. But more likely al-Fārābī believed that the laws of modal logic could be tweaked so as to work with “Probably” in place of a modal operator. In fact al-Fārābī does say at [ Demonstration ] 44.20–22 that in many of the arts, “Necessarily every A is a B ” and “Most A s are B s” are treated as equivalent. (But wouldn’t this correlate “Probably” with “Necessarily” rather than “Possibly”? Al-Fārābī is not here to answer the question.)

There is further evidence of al-Fārābī experimenting with other sentence forms in modal logic. Both Avicenna (Street 2001) and Averroes (Ibn Rushd, Maqālāt 102.13f) cite al-Fārābī as considering syllogistic premises containing “insofar as”, for example, “Every A can be a B insofar as it is a B ”.

From Averroes (Ibn Rushd, Maqālāt 129.11–17) we also know that al-Fārābī observed that to get the syllogism

Every C is a possible B . Every B is a possible A . Therefore every C is a possible A .

(a form that Aristotle accepted as perfect) we need that “Every B ” in the second premise means “Every possible B ”; otherwise the C s might be possible B s but not actual B s, so that they would escape the quantifier of the second premise, and hence violate the dictum de omni . From this al-Fārābī inferred that at least in this modal syllogism, Aristotle intended ‘Every B ’ to be read as ‘Every possible B ’.

Exactly what al-Fārābī meant by the dictum de omni is hard to make out from Averroes’ account. But al-Fārābī’s use of it seems to contain an attempt to give a set-theoretic justification of Barbara [ 18 ] in modal contexts. Another quotation from Averroes (Ibn Rushd, Maqālāt 154.18f) shows al-Fārābī using the dictum de omni (again presumably a set-theoretic argument) to justify a syllogism where the major premise has a negative subject:

A sculpture is not an animal. What is not an animal is not a human. Therefore a sculpture is not a human.

This is Celarent [ 19 ] but with the middle term made negative.

We saw in Section 3 above that al-Fārābī believed Aristotle had prescribed universal rules for demonstrative reasoning in his Posterior Analytics . But apart from some discussion of techniques for finding definitions, the only rules that al-Fārābī offers us in [ Demonstration ] are categorical syllogisms in mood Barbara with extra pieces clamped on. (These are in the section [ Demonstration ] 33.1–39.4; they are quoted in Strobino 2019.)

This is disappointing, but at least it’s clear where the extra pieces come from. Demonstrative reasoning gives knowledge with certainty, and in [ Certainty ] al-Fārābī writes down some necessary and sufficient conditions for certainty. (These “conditions of certainty” are listed by López-Farjeat 2020 and discussed by Black 2006.) The condition that is relevant here is the last one:

If the previous conditions hold, it is not accidental that they do.

([ Certainty ] 100.18.) In other words they hold by reason of essence. Also in a discussion of demonstration in [ Attainment ] 51.15–52.17 al-Fārābī tells us that demonstration must proceed from some primary concepts, and the concepts in question are those that are answers to the questions “what”, “by what”, “how”, “from what”, and “for what”. These are not exactly the questions listed in Section 4.2 above , but they are clearly in that territory. Again they indicate that a demonstration should follow from the constitutive properties of the subjects under discussion, i.e., from their essences.

Suppose we have constitutive properties of A and B which between them ensure that every A is a B , and likewise constitutive properties which ensure that every B is a C . Then by Barbara we know that every A is a C ; but for demonstrative certainty we want “Every A is a C ” to be ensured by the constitutive properties of A and C . Some of al-Fārābī’s syllogisms confirm that this is so, considering different kinds of constitutive property. [ 20 ] In some other cases the constitutive properties fail to yield the required sentences, and al-Fārābī comments that the syllogism gives fact but not cause.

Galston (1981) offers reasons for thinking that al-Fārābī may have considered demonstrative proofs a distant ideal, to be reached only after a substantial amount of work at the dialectical level. [ 21 ]

Al-Fārābī’s most sophisticated definition of syllogism is at [ Expressions ] 100.3–5: a syllogism is

things that are arranged in the mind in an order ( tartīb ) such that when the things have been put in this order, the mind as a result finds itself unavoidably looking down at something else of which it was ignorant before, so that it knows it now, and thus the mind is equipped to submit to the thing it looked down at, just as if it [already] knew that thing.

The reference to “order” must owe something to Aristotle’s remark at Topics 156a22–26 that in a debate, the questioner can sometimes hoodwink the responder by asking the questions in the wrong order. But by bringing the notion of order into the definition of syllogism itself, al-Fārābī opens up a new chapter in logic (see Hodges 2018 on this and Avicenna’s development of the theme).

For further illumination on al-Fārābī’s understanding of logical consequence, we need to explore what he says about logical rules. At [ Catalogue ] 53.5–9 he tells us:

The art of logic provides in general the rules whose nature is to constitute the intellect and to guide a person along the correct and true path in everything where there can be conceptual error, and the rules that protect and guard him against mistakes and slips and errors in concepts, and the rules through which one tests things in concepts where one can’t be trusted not to make an error.

But these are Neoplatonic commonplaces. [ 22 ] Elsewhere al-Fārābī says deeper things about the rules of logic, as follows.

Recall from Section 3 above that on al-Fārābī’s understanding, the correct methods of logic were known by the time of Plato, who had them “according to matter”, and it was Aristotle who reformulated them as “universal rules”. He very probably has the same thing in mind when he says that Aristotle in Prior Analytics considered declarative sentences “from the point of view of their composition ( ta’līf ) and not of their matter” ([ Commentary on De Interpretatione ] 53.3f). The point he is making here becomes clear if we go back to the example syllogism spelled out at (*) in Section 5 above . This is actually al-Fārābī’s second shot at this syllogistic mood. In his first shot ([ Syllogism ] 26.11f) he followed Aristotle’s preferred style and used letters A , B , C in place of the “matters” stone, animal, and body respectively. So a corresponding paraphrase will read

Here (**) is a universal rule in the sense that it is for all A , B , and C ; the premises and conclusion contain no matter and are bare compositions.

Mallet (1994: 329–335) calls attention to a passage in [ Analysis ] 95.5–8, where al-Fārābī says he will explain “how we define syllogism” and how it is used.

Firstly, it is through knowledge of the topics, which are the universal premises whose particulars ( juz’iyyāt ) are used as major premises in a syllogism and in each separate art.

If “particulars” means what it usually means in such a context, namely existentially quantified statements, then this is just wrong: existentially quantified statements are hardly ever major premises in syllogisms. But as Mallet points out, the passage makes sense if the “universal premises” are statements like (**) and their “particulars” are corresponding statements of the form (*) . Al-Fārābī is then saying that natural language syllogisms are validated through being instances of universal rules stating that all arguments of a certain form are valid. If this is a correct reading, it makes al-Fārābī a formal logician in a strong sense. And indeed some writers have written about al-Fārābī’s “formalism” (Zimmermann 1981: xl).

However, there are reasons for caution. As Mallet’s paper shows, al-Fārābī in his further discussion of topics, both in [ Analysis ] and in [ Debate ], heads off in completely different directions (which are too complex to pursue here, but see Hasnawi 2009 and Karimullah 2014). Moreover al-Fārābī has a habit of justifying inferences by reference to real-world information about their terms (i.e., their matter) that is not contained in the premises. He does this with the syllogistic mood Baroco ([ Syllogism ] 27.8–12, [ Short Syllogism ] 79.5–12), and there is a one-premise example at [ Commentary on De Interpretatione ] 136.10. [ 23 ] Elsewhere he plays fast and loose with the “forms” of arguments, for example reducing a many-premise version of induction to a two-premise categorical syllogism without giving any indication of how a string of premises are reduced to a single one ([ Syllogism ] 35.14–18).

Al-Fārābī often refers to “universal rules”. But they need not be laws that can be shown to hold without exceptions. Take for example his essay [ Canons ], which closes (272.16) with a statement that the work has presented “universal rules” of poetry. The work consists mostly of classifications of different types of poetry, together with definitions of terms used in analyzing poetry, and a broad comparison with decorative arts. These “rules” are at best things that a person who aspires to work on the theory of poetry ought to know.

In any case the only kind of justification that al-Fārābī offers for logical rules is that they have been found useful for certain purposes in the community that uses them (cf. Section 3 above ). All in all, al-Fārābī treats the formal rules of logic as heuristics rather than as laws of a scientific theory. A case can be made for viewing al-Fārābī as one of the creators of what is now known as “informal logic”, as in the texts of Hitchcock (2017) and Walton (1989). The pivotal role that he gives to dialogue places him in the same world as Walton’s book.

Al-Fārābī defines a concept to be “true” ( ṣādiq ) if it is the same ( bi-‘aynihi ) in the external world as it is in the soul ([ Letters ] (88) 116.3f) For this definition to make sense, the concept need not be propositional. For example ([ Letters ] 118.5f), the concept “vacuum” is not true, because it exists only in the mind and not in the external world (Abed (1991: 111–115) discusses the relationship between existence and truth in al-Fārābī).

Al-Fārābī quite often uses the derived causative noun taṣdīq , which has a range of meanings between “verification” (i.e., gaining certainty that a thing is true) and “assent” (i.e., treating a thing as true). Al-Fārābī expounds this distinction at [ Demonstration ] 20.4–21.12. He also points to the range of meanings of taṣdīq at [ Attainment ] 90.6f: it can occur “either through certain demonstration or through persuasion”. Presumably the certain demonstration brings about verification and the persuasion brings about assent.

At [ Expressions ] 86.17–87.4 al-Fārābī tells us that teaching has three steps: “conceptualization” ( taṣawwur ), where we understand what the concept is and what our teacher is telling us about it; taṣdīq ; and “committing to memory” ( hifẓ ). [ 24 ] [ Demonstration ] 80.22, in another passage on teaching, adds that “We can seek taṣdīq either of simple things or of compound”. For al-Fārābī a proposition is always compound, so he is telling us that non-propositional concepts can be assented to.

The view that both propositions and non-propositional concepts can be true runs fairly deep in al-Fārābī’s thinking, although he recognizes that not everybody agrees with it ([ Commentary on De Interpretatione ] 52.13f). For example, this view allows him to think of definition of non-propositional concepts and demonstration of propositions as overlapping procedures; there can be definitions that are identical with demonstrations except in the order of their parts ([ Demonstration ] 47.11). [ 25 ] Avicenna a hundred years later found it essential to distinguish between non-propositional and propositional concepts. Provocatively he used al-Fārābī’s own terminology of taṣawwur and taṣdīq to fix the distinction; for Avicenna any concept can be conceptualized, but only propositions can go on to be verified. [ 26 ]

A sentence can be switched between true and false by adding a negative particle, for example, “It is not the case that” ( laysa ). But it matters where the negative particle is put; al-Fārābī discusses a number of cases, ad hoc with no clear overall pattern. One case that he discusses in detail is where the negation is attached to a noun, as when we form the noun “not-just” from the noun “just”. (Adjectives are counted as nouns.) Following Theophrastus (Fortenbaugh et al. 1992: 148–153) he identifies this kind of negation as “metathetic” ( ‘udūlī ); he takes the resulting metathetic sentence to be an affirmation, not a denial. Nothing can be both just and not-just, but there are things that are neither, for example infants. So an infant is not just, but it is also not not-just. For a similar reason the infant is not unjust. Also it is false that the infant is just, and false that it is not-just. Likewise it is false (rather than meaningless) that every heat is curvilinear ([ Categories ] 125.8). (Thom 2008 steers a clear path through these notions.)

Before al-Fārābī, metathesis seems to have played little or no role in rules of inference. So an example in al-Fārābī with a metathetic subject term is worth noting:

If every human is an animal, then every non-animal is a non-human.

This appears in his ([ Analysis ] 114.11f), where he introduces it as a topic. (Fallahi 2019 discusses this example.)

Al-Fārābī holds that “Come here” is neither true nor false, but “You must come here”, which can be used in place of it ( yaqūmu maqāma(hu) ), is true or false ([ Short De Interpretatione ] 47.3–48.1). The reason is that the first sentence, unlike the second, has the wrong shape to be true or false. He could be read as saying that every command has the same meaning as some indicative sentence, but truth and falsehood depend on the form of words used, not just on the meaning. But closer inspection shows that he uses the phrase yaqūmu maqāma for some quite weak equivalences where the two sentences in question definitely mean different things. For example, he uses the phrase when a questioner in a debate asks a question with a metathetic affirmation in place of a denial ([ Commentary on De Interpretatione ] 136.6). His words for different kinds of equivalence (for example, bi-manzila , “in the same role as”, which will be familiar to readers of Classical Arabic linguistics) deserve closer study. Having written [ Expressions ] and [ Letters ], he certainly deserves to have his prepositional phrases taken seriously.

At [ Commentary on De Interpretatione ] 89.12–100.25 Al-Fārābī presents a distinctive view of statements about the future (cf. Adamson 2006, Knuuttila 2020). In connection with a future battle, the disjunction “The battle either will or will not take place” is a necessary proposition and hence true. But since the future is indeterminate, neither of the sentences “The battle will take place” and “The battle will not take place” is true; moreover the lapse of truth value is something intrinsic in the world, it is not just our ignorance. Granted, if Allah knows that Zayd will leave home tomorrow, then it is true now that Zayd will leave home tomorrow, and this implication is a necessary truth. But the necessary truth of this implication doesn’t entail the necessary truth of its conclusion, and hence Zayd still has the freedom to choose. Al-Fārābī doesn’t make clear whether he is doubting the modal inference

Necessarily if p then q . Necessarily p . Therefore necessarily q

or whether he is allowing that there may be restrictions on what Allah necessarily knows. (Hasnawi [1985: 28f] relates this passage to Muslim debates about Allah’s foreknowledge.)

In several works al-Fārābī analyses features of Arabic as a language. Some of these works contain comparisons between Arabic and other languages: Greek, Syriac, Persian, and Sogdian in [ Letters ], Greek and Persian in [ Commentary on De Interpretatione ], and Greek in [ Expressions ]. Al-Fārābī’s comments on Greek include several mistranslations and dubious grammatical remarks, making it clear that he didn’t read Greek (for al-Fārābī’s knowledge of languages see Zimmermann 1981: xlviif). Also al-Fārābī has a strong tendency to classify languages as (1) Arabic and (2) “other languages”. So these comparisons are far from being a serious contribution to comparative linguistics, and one asks why he includes them.

On reading the comparisons, a pattern emerges. Al-Fārābī starts from a theory of the regime of concepts (cf. Section 2 above), and his chief concern is how well Arabic reflects this regime. The role of “other languages” is always to illustrate how other languages reflect the regime of concepts where Arabic fails to do so. As Menn puts it, “in practice, his reconstructed Greek serves as an ideal logical language, i.e. a language in which grammatical form always tracks logical form” (2008: 68).

Al-Fārābī’s starting point is the concepts required for sentences that appear in categorical syllogisms, such as

Zayd is human. Every horse is animal. Some horse is not stone.

Here “Zayd” , “horse”, “animal”, “stone” signify simple primary concepts; the proper name “Zayd” signifies a particular ( juz’ ), and the other three words signify universals ( kullī ). “Every” and “some” are quantifiers ( sūr ), and “is” is a copula ( rābiṭ ) signifying the connection between two primary concepts so as to form an affirmation or a denial ([ Commentary on De Interpretatione ] 102.17) Al-Fārābī groups all these words into two classes: noun ( ism ) for those signifying primary concepts, and particle ( ḥarf ) for the remainder. (Adjectives count as nouns.) He makes clear that the particles are a disparate group and need further classification ([ Expressions ] 42.8–12).

Al-Fārābī introduces a distinction between concepts that apply to a thing permanently and those (called accident, ‘araḍ ) that apply only temporarily. As a result, concepts have a temporal regime, and language should reflect this. Al-Fārābī is at his most a priori here, claiming that the temporal regime of concepts should be represented by a system of three tenses: past, present, and future. We don’t know whether he simply failed to notice other ways in which time is represented in Arabic grammar (for example, continuous tenses and pluperfect constructions), or for some reason he dismissed these features as marginal.

Broadly following Aristotle, al-Fārābī adds to noun and particle a third class, namely verb ( kalima ). A verb simultaneously expresses three pieces of meaning: a simple primary concept, a copular linking, and a tense (and hence a time). Thus in “Zayd walked”, the verb “walked” expresses (i) the primary concept “walking”, (ii) a linking of this concept to the concept of Zayd, and (iii) a past tense.

In spite of his blind spot about tenses, al-Fārābī’s comments on verbs in Arabic contain some of his best linguistic insights. For example, he notes that since tenses are needed only for talking about accidents, one should not expect to find a verb whose primary concept is a permanent notion such as “human” ( insān ). He tests this by constructing a verb from “human”, namely ta’annasa . By the rules of Arabic, one would understand it to signify something with a temporal feature, namely “becoming a human” ([ Commentary on De Interpretatione ] 34.4–9). Al-Fārābī also uses a quite subtle linguistic argument to show that Arabic has a word that can express pure tense without copula or primary concept. This is the word kāna , as in “Zayd was walking”, zaydun kāna yamshī . We can see that there is no copula in kāna , he tells us, because “Zayd is walking”, zaydun yamshī , already contains a copula in the verb yamshī ([ Commentary on De Interpretatione ] 42.6–18). We even find the beginnings of an analysis of the structure of events in al-Fārābī’s discussion of how the present tense can signify either a point of time or an interval ([ Commentary on De Interpretatione ] 40.3–41.18).

For al-Fārābī, music theory sits on the very edge of being a syllogistic art along with rhetoric and poetry:

… it becomes clear that [the theoretical art of music] has much in common with that of the scholars in the linguistic arts from the people of each tongue, and has much in common with the art of rhetoric and the art of poetry, both of which are parts of the art of logic in many things. ([ Music ] 173)

The link to poetry is clear, he tells us, given that poetry is perfected by being set to music. Besides this there are formal similarities: poetry is formed by concatenating letters from a finite alphabet, and music is formed by concatenating sounds from a finite palette. Al-Fārābī grants that in the case of music the palette is dictated by nature, whereas the letters of a national alphabet are adopted by convention in that nation ([ Music ] 120f). But he notes that in some cultures the music accompanying a poem is counted as a part of the poem, and that this can be justified by the fact that sometimes the poetic metre is sustained by the music rather than the words ([ Poetry ] 91.15–17). [ 27 ]

Al-Fārābī never considers music on its own as a syllogistic art. There is an obvious reason for this, namely that music is not built of words, and syllogisms (by Aristotle’s definition which al-Fārābī cites at [ Syllogism ] 19.8) are a form of verbal discourse ( qawl ). But this requires only that the premises are verbal; the conclusion, on both Aristotle’s definition and al-Fārābī’s own quoted in Section 7 above, is simply a “thing”. Already in Aristotle the conclusion of a practical syllogism is an action, not a proposition. (Thus Aristotle, De Motu Animalium 7, 701a11: “The two propositions result in a conclusion which is an action”.)

In what sense is it true that poetry contains words that compel assent to something that one didn’t previously know? Al-Fārābī discusses this question in three essays: [ Canons ], [ Poetry ], and [ Proportion ]. In all of them, part of his answer is that poetry excites our imagination and thereby persuades us to adopt certain attitudes.

This takes “syllogism” in a very weak sense. But in all three works al-Fārābī also indicates that poetry contains text that is “potentially” a syllogism. His only examples, in [ Proportion ] 505.22f, yield invalid categorical syllogisms in second figure, as follows (see Aouad & Schoeler 2002):

The person is beautiful. The sun is beautiful. Therefore the person is a sun. [ 28 ]
Fire acts quickly. The sword acts quickly, viz. to kill. Therefore the sword is a fire.

His point can be teased out in several different ways; the reader may have better suggestions than ours. But here at least is a reading that matches al-Fārābī’s text. Consider the following line of Abū Tammām, in a poem written in 838 to celebrate a military victory:

Knowledge lies in the bright spears gleaming between two armies. (translated in Stetkevych 2002: 156)

Reading this in context, we realize that the poet is telling us that the weapons gave certainty through a decisive victory. Knowledge is what gives certainty. So we can expand the text by what it brings to mind:

The spears give certainty. Knowledge gives certainty. Therefore the spears are knowledge.

This is not deductive reasoning. It’s a verbalizing of thoughts that the poem brings to our minds. Spelling it out, we are drawn to appreciate the fact that the battle resolved the situation. The text is an invalid syllogism in just the same way as al-Fārābī’s two examples above, but the fact that it is in second figure is really neither here nor there.

Note that in this case the poem provides the conclusion, not the premises. So it fits Black’s (1990: 226) description that “What appears in the finished product is not a poetic syllogism … but only its conclusion”. Are the hearers supposed to reconstruct the poet’s premises by telepathy? Black leaves the problem open, but in fact it’s a problem we have met before. In [ Syllogism ] 19.10f al-Fārābī tells us that

A syllogism is just composed to reach a quaesitum which was previously defined; the quaesitum was assumed first and one seeks to verify it by a syllogism.

This applies in various contexts, for example, when the questioner in a debate has the task of finding a syllogism to refute the responder’s claim; “the enquiry is always about a quaesitum whose syllogism has not yet been found” ([ Debate ] 45.6). In the poetical case the hearers have the task of finding a middle term that generates a poetic syllogism; in our example the middle term is “giving certainty”. And again, the premises yield the conclusion by imaginative suggestion, not by deduction.

There remain some problems with al-Fārābī’s account of poetic syllogisms. First, he never says that only the conclusion appears in the poem. Black (1990: 235–8) suggests that the practical syllogism might be a key to understanding other cases.

Second, why does al-Fārābī say in [ Canons ] 268.15 that “poetic discourse is in all cases absolutely false”? This is a gross exaggeration, and it raises the question whether a poet can really expect the audience to assent to a pack of lies. It seems we can handle this problem. Al-Fārābī’s statement in [ Canons ] is a typical Neoplatonist soundbite, witness the Alexandrian Elias ( In Categorias Prooemium 117.2–5):

Either all the premises [of the syllogism] are true, making it demonstrative, or they are all false and they make it poetic and mythic, or some are true and some are false ….

Al-Fārābī’s own more mature view, in [ Proportion ] 506.3f, is that

Poetry doesn’t aim either to tell lies or not to tell them; its aim and purpose is to arouse the imagination and the passion of the soul.

And even if some blatant lies do occur, we would surely admit (though al-Fārābī himself never quite says it in the texts that we have) that a false statement may still contain poetic truth.

[ Analysis ] Kitāb al-taḥlīl ( Analysis ), in [ Logic ] 2: 95–129.
[ Aristotle ] “The philosophy of Aristotle, the parts of his philosophy, the ranks of order of its parts, the position from which he started and the one he reached.” Translated by Mohsin Mahdi from an Arabic manuscript in Istanbul. Mahdi’s translation is Part III of his book Mahdi 2001 (below).
[ Attainment ] Kitāb taḥṣīl al-saʻāda , Jaʻfar Āl Yāsīn (ed.), Beirut: Dār al-Andalus, 1981; translated as “The Attainment of Happiness” in Mahdi 2001: 13–50.
[ Canons ] “Fārābī’s Canons of Poetry”, A. J. Arberry (ed./trans.), 1938, Rivista degli Studi Orientali , 17(2): 266–278. (Arabic and translation.)
[ Catalogue ] Iḥṣā al-‘ulūm ( Catalogue of the sciences ), ‘Uthmān Amīn (ed.), Paris: Dar Bibliyun, 2005. Latin translations (1) by Gundisalvi in Jakob Schneider, De Scientiis: secundum versionem Dominici Gundisalvi , Herder, Freiburg 2006 (includes German translation); (2) by Gerard of Cremona in Alain Galonnier, Le De Scientiis Alfarabii de Gérard de Crémone: Contribution aux problèmes de l’acculturation au XIIe siècle (édition et traduction du texte) , Turnhout: Brepols, 2017 (includes English translation).
[ Categories ] Kitāb al-qāṭāghūrīyās ayy al-maqūlāt , in [ Logic ] 1: 89–131; translated in D. M. Dunlop, 1958/1959, in “Al-Fārābī’s paraphrase of the Categories of Aristotle”, Islamic Quarterly , 4: 168–197 and 5(1): 21–54.
[ Certainty ] Sharā’iṭ al-yaqīn ( Conditions of certainty ), in Kitāb al-burhān wa-kitāb al-sharā’iṭ al-yaqīn ( Book of demonstration and book of conditions of certainty ), Majid Fakhry (ed.), Beirut: Dar el-Machreq, 1986, pp. 97–104.
[ Commentary on Categories ] “Al-Fārābī’s Long Commentary on Aristotle’s Categoriae in Hebrew and Arabic: A critical edition and English translation of the newly found extant fragments”, Mauro Zonta (ed./trans.), Studies in Arabic and Islamic Culture II , Binyamin Abrahamov (ed.), Ramat-Gan: Bar-Ilan University Press, 2006, pp. 185–253.
[ Commentary on De Interpretatione ] Sharḥ ‘ibāra , W. Kutsch and S. Marrow (eds.), Beirut: Dar el-Machreq, 1986; translated in Zimmermann 1981: 1–219. We cite the page and line numbers in the Kutsch and Marrow edition; Zimmermann’s translation gives these too.
[ Commentary on Prior Analytics ] Kitāb sharḥ al-qiyās , surviving part in Almanṭiqīyāt lil-Fārābī ( The logical works of al-Fārābī ), M. T. Daneshpazhuh (ed.), Qum: Maktabat Ayat Allah, 1988, vol. 2, pp. 263–553.
[ Debate ] Kitāb al-jadal ( Debate ), in [ Logic ] 3: 13–107. A fuller text is translated in David M. DiPasquale, Alfarabi’s Book of Dialectic (Kitab al-Jadal): On the Starting Point of Islamic Philosophy , Cambridge: CUP, 2019. (DiPasquale’s references to the Arabic text are to an edition not generally available.)
[ Demonstration ] Kitāb al-burhān ( Demonstration ), in Kitāb al-burhān wa-kitāb al-sharā’iṭ al-yaqīn ( Book of demonstration and book of conditions of certainty ), Majid Fakhry (ed.), Beirut: Dar el-Machreq, 1986, pp. 19–96.
[ Eisagoge ] Kitāb al-īsāḡūjī , in [ Logic ] 1: 75–87; translated in D. M. Dunlop, 1956, “AlFārābī’s Eisagoge ”, Islamic Quarterly , 3(2): 117–138.
[ Expressions ] Kitāb al-alfāẓ al-musta‘mala fī al-manṭiq ( Expressions used in logic ), Muhsin Mahdi (ed.), Beirut: Dar el-Machreq, 1968.
[ Harmony ] Al-Fārābī(?), L’armonia delle opinioni dei due sapienti: il divino Platone e Aristotele ( Al-jam‘ bayna ra’yay al-ḥakīmayn aflaṭūn al-ilāhī wa-arisṭūṭālīs ), Cecilia Martini Bonadeo (ed.), Pisa: Plus, 2009; English translation in Charles E. Butterworth, Alfārābī, The Political Writings, ‘Selected Aphorisms’ and other texts , Ithaca, NY: Cornell University Press, 2001, pp. 117–167.
[ Indication ] Risālat al-tanbīh ‘alā sabīl al-sa‘āda ( Indication of the way to happiness ), S. Khālīfāt (ed.), Amman: Jami‘at al-urdunīya, 1987; translated in Jon McGinnis and David C. Reisman, Classical Arabic Philosophy: An Anthology of Sources , Indianapolis: Hackett, 2007, pp. 104–120.
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[ Introductory ] Al-tawṭi’a aw al-risāla ṣuddira bihā al-manṭiq ( Preparation, or essay introducing logic ), in [ Logic ] 1: 55–62; translated in D. M. Dunlop, 1957, “Al-Fārābī’s Introductory Risālah on logic”, Islamic Quarterly , 3: 224–235.
[ Letters ] Kitāb al-ḥurūf ( Book of letters ), Muhsin Mahdi (ed.), Beirut: Dar al-Machreq, 1990. Paragraphs (108) to (157) are translated in Khalidi 2005, pp. 1–26. A new edition with full translation by Charles E. Butterworth is near publication. We cite this work in the style ( m ) n . p , where m is the paragraph number, n the page number and p the line number, all as in Mahdi’s edition; Khalidi gives the paragraph numbers.
[ Logic ] Al-manṭiq ‘inda al-Fārābī ( The Logic of al-Fārābī ), Rafiq al-‘Ajam (ed.), Beirut: Dar al-Machreq, vol. 1 1985, vols. 2 and 3 1986.
[ Music ] Kitāb al-Mūsīqā al-kabīr ( Great Book of Music ), Ghattas ‘Abd-al-Malik Khashaba (ed.), Cairo: Dār al-Kātib al-‘arabī li-al-ṭibā‘a wa-al-nashr, 1967; French translation in Rudolphe D’Erlanger, 1930, La Musique Arabe , vols 1, 2 (of six), Paris: Librairie Orientaliste Paul Geuthner.
[ Poetry ] “Kitāb al-shi‘r”, M. Mahdi (ed.), Shi‘r , 1959: 90–95; English translation in Geert Jan van Gelder and Marlé Hammond, 2008, Takhyīl: The Imaginary in Classical Arabic Poetics , Warminster: Gibb Memorial Trust: 15–18; French translation in Benmakhlouf et al. 2007: 112–118.
[ Proportion ] Qawl al-Fārābī fī al-tanāsub wa-al-ta’līf ( About proportion and composition ), in M. T. Daneshpazhuh (ed.), Al-manṭiqīyāt lil-Fārābī ( The logical works of alFārābī ), Qum: Maktabat Ayat Allah, Qum, 1988, vol. 1, pp. 504.1–506.6; French translation in Benmakhlouf et al. 2007: 107–111.
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[ Sophistry ] Kitāb al-amkinati al-muḡliṭa ( Situations of sophistry ), in [ Logic ] 2: 131–164.
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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

Al-Fārābī at Islamic Philosophy Online, last update 2 September 2007.
“Fārābī ii. Logic” by Deborah L. Black, in Encyclopaedia Iranica , last update January 24 2012.
Mahadurot: Modular Hebrew Digitally Rendered Texts, editor-in-chief Yehuda Halper: retrieved 27 April 2023. The Hebrew texts online are critical editions of medieval texts. They include a translation of [ Debate ], and a translation of [ Sophistry ] is promised.

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The Connection Of Language And Thinking

Thinking is one of the important forms of consciousness activity. Therefore, it cannot be adequately described and understood outside the language. Thinking as a conscious process can be understood as communication. And communication is impossible without language. The topic is still controversial in modern linguistics, which determines the relevance of our study. Language is the main, decisive, but not always only means of communication. People invent and create certain forms of speech and linguistic expression. The article compares the logical and linguistic features of language and thinking. Thoughts addressed to speech and language are called linguistic thinking. Thoughts are embodied in words consciously. In words, our thoughts become meaningful. In human speech, comprehension, awareness, sensation as a process of linguistic thinking develops, affecting the new system of language. Understanding speech is usually divided into speech recognition and speech understanding. An understanding of the meaning of what was said and how it is expressed. The close connection between language and thinking can be justified by the fact that structural and conceptual meanings are closely related. The purpose of the article is to show how thinking is associated with language and how thought is reflected in words, and how to analyse key points in this issue. Using a descriptive method, we tried to show the connections between language and thinking. Keywords: Thinking language word form category consciousness

Introduction

In the aspect of the connection between language and thinking, the term logic has a double meaning. Thinking reflects reality. Understanding logic is connected with the concept of dialectic logic, reflecting the objective dialectics of things. The external forms of logical thinking, the laws of development of all material things, are the doctrine of nature and spirituality, of the development and understanding of the specific content of the world.

The ancient Greek philosopher Aristotle (the 4 th century BC) suggested that grammar is based on thinking. For the ancient Greeks, the logos was used simultaneously with words, consciousness, thinking, and speech. His followers, the abbots of the Por-Royal Monastery, the French scholars Arnault and Lanslo (1660), in the “General Rational Grammar”, stated that the goal of linguistics is to study logical principles based on all languages, since the laws and categories of thinking are the same for all thinkers people, but one grammar. Thus, logical and language categories are similar. Based on logic, there is a form of thinking that denies or confirms what is. The subject of thinking consists of S (subject of thinking) and the predicate P (relation or singularity), binders and quantum (all A and some E). The subject is the called subject, and the predicate is the action of the called subject. S is the singular, and P is universal.

According to the grammar of Por-Royal, ideas coincide with sentences. For example, the sentence “Man runs” is based on a thought. So everything in language is connected with logic. The remnants of such ideas are also reflected in the modern grammatical terminology of European languages. For example, in logical terms related to subject (English subject, German Subjekt, fr. sujet) and predicate (English predicate, German Prädikat, fr. Prédicat).

The great German linguist Humboldt ( 1984 ), his comrades-in-arms Leo Weisberger and American ethnologists Edward Sepir and Benjamin Wharf put forward the theory of linguistic relativity. According to this theory, people who speak different languages look at the world differently, so each language has its own logical thinking. Proof of this should be considered in scientific literature.

Humboldt notes that “language is a unique world between people and the objective world that surrounds it” ( Humboldt, 1984, p. 94 ). Each language covers a certain circle of people, and then it can leave this circle to enter another circle. Imagination and activity of a person depend on his impressions, and his attitude to objects is fully reflected in the language.

Problem Statement

Imagination and activity of a person depend on his impressions, and his attitude to objects is fully reflected in the language. Thinking is usually dependent from language. In different languages the same subject is not a different sign, but a different appearance. More vivid examples are associated with words that define colors in different languages: sinii [blue] and goluboi [sky blue] in Russian, blue, Blau, bleu in English, German and French. Some African tribes have two words for colors: the word for “hot” (red, orange, yellow) and the word for “cold” (blue, purple, green). Tarasov ( 2004 ), specifying the basic functions of the language, highlights: 1) language as a means of organizing the process of using existing knowledge to form new knowledge in the perceptual perception of reality; 2) language as a means of describing cultural objects in communication to distribute them, as a result of which the translation of culture occurs. The function of semantic contents assigned to linguistic signs in the memory of native speakers is to activate images of consciousness in communication, as well as in perceptual perception of reality, where the language organizes knowledge to categorize sensory information entering the brain ( Kabaloeva, 2012 ).

Modern formal logic is far from the structure of natural thinking with axiomatic structures and does not accept the structure of theoretical thinking as its subject; the latter is an object of interest in logic ( Narsky, 1967 ). Einstein ( 1965 ) also states: “Pure logical thinking does not provide any knowledge about the world of facts; perception of the real world is born from experience and ends with it. A purely logical situation does not say anything about reality” (p. 74). “We comprehend thoughts of already framed language frameworks”. Thinking can freely specify its categories, introduce new ones, while the categories of the language, being part of the system that each native speaker receives and retains, “cannot be changed at the will of the speaker” ( Benvenist, 2002 ). The language expresses not only knowledge about the world, but our attitude to the external world, to other people and to ourselves, as well as our emotions and strong-willed motives ( Garipova, 2009 ).

Nowadays, the problem of logic has become urgent for the development of cybernetics and logic, and it is widely discussed at various symposia. In particular, the importance of synthesis logic is discussed. From this point of view, it is impossible to contrast mathematical logic of content with forms of logic.

Research Questions

In a broad sense, logical categories are mental categories that represent real objects. This understanding of the problem is proved on the basis of the theory of Espersen ( 1958 ). Espersen writes:

It should be borne in mind that, depending on the structure of each language, in addition to syntactic and derived categories, independent of random facts existing in language, there are intra-language categories. These categories are universal because they can be applied to all languages and rarely precisely spelled out in these languages. Some of them relate to the facts of the inner world as gender, and some to logical and intellectual activity. Due to the lack of a proper term, these categories will be called categories of understanding. The question of grammars is to examine the relationship between syntactic and conceptual categories in each case . ( as cited in Garipova, 2009, p. 1485 )

These categories are reflected in syntactic categories in a mediocre and complex way. Speaking of the narrow meaning of logic, Panfilov ( 1957 ) notes that logical categories belong to categories at the logical and grammatical level. He compares them with grammatical categories that have certain meanings, but are not directly related to thinking ( Panfilov, 1957 ).

The least stressed problem is the result, where logical forms of thinking and language forms of its expression are correlated. It is worth noting that among all these limited problems, an extraordinary variety of concepts and views should be noted.

The relationship of word and concept is also one of the most controversial issues in logic and linguistics. The basis of the discussion is the relationship of meaning and concept. Summarizing the above, two main points can be emphasized: 1) the meaning of a word is a synonym for a concept; 2) the meaning of the word is interpreted as the linguistic catechism of the content plan. The second view seems more correct. It is important to note that the concept of the relationship between the meaning of a word and a concept is accepted not only by linguists, but also by logicians and philosophers.

Purpose of the Study

The article aims at describing the close relationship between thinking and language in a new way and to analyze the reflection of judgment and thought in language categories.

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Sociolinguistics, linguistics, semantics, discourse analysis, translation, interpretation

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Alieva, N. (2020). The Connection Of Language And Thinking. In D. K. Bataev (Ed.), Social and Cultural Transformations in the Context of Modern Globalism» Dedicated to the 80th Anniversary of Turkayev Hassan Vakhitovich, vol 92. European Proceedings of Social and Behavioural Sciences (pp. 67-73). European Publisher. https://doi.org/10.15405/epsbs.2020.10.05.10

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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.

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what is the contribution of studying language 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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Module 5: Thinking and Analysis

Learning objectives.

Describe the role that logic plays in critical thinking

Critical Thinking and Logic

Critical thinking is fundamentally a process of questioning information and data. You may question the information you read in a textbook, or you may question what a politician or a professor or a classmate says. You can also question a commonly held belief or a new idea. With critical thinking, anything and everything is subject to question and examination for the purpose of logically constructing reasoned perspectives.

What Is Logic, and Why Is It Important in Critical Thinking?

The word logic comes from the ancient Greek word logike , referring to the science or art of reasoning. Using logic, a person evaluates arguments and reasoning and strives to distinguish between good and bad reasoning. Using logic, you can evaluate ideas or claims people make, make good decisions, and form sound beliefs about the world. [1]

Critical thinking involves reflective thinking, considering bias, and remaining open minded and curious. It also demands the intellectual rigor to deconstruct and evaluate claims made by others while also making sound and strong arguments, ourselves. Logic is the study and evaluation of arguments to distinguish good reasoning from bad. When using logic in critical thinking, you will consider the logical structure in order to evaluate its quality. In the next section, we will explore what logical structure is.

Logical Structure

Suppose I argue as follows: if it is raining, then the ground is wet; but since it is not raining, it follows that the ground is not wet. This is an argument whose conclusion is the statement “the ground is not wet.” The two premises of the argument are the conditional statement “if it is raining, then the ground is not wet” and the statement “it is not raining.” We can rewrite the argument to clearly show each of the statements—the two premises and the conclusion—like this:

If it is raining, then the ground is wet.
The ground is not wet.
Therefore, it is not raining.

This example is a valid argument. A valid argument is an argument whose premises guarantee the truth of the conclusion. In other words, a valid argument is one such that on the assumption of the truth of the premises, it is impossible for the conclusion to be false. Think about the previous argument. Can you see that if we accept the two premises (lines 1 and 2) as true, then we must logically accept the conclusion (line 3) to be true? Valid arguments are the gold standard of reasoning in logic—it is what all arguments aspire to be. When you have constructed a valid argument, no one can argue with your reasoning (although they can still disagree with you regarding whether your premises are true). What is interesting about the concept of logical validity is that an argument can be valid (i.e., the reasoning can be good) even if the premises are obviously false or absurd. For example, consider this (slightly altered) argument from a scene in Monty Python and the Holy Grail :

If this woman weighs the same as a duck, then she is is made of wood.
Everything made of wood is a witch.
This woman does weigh the same as a duck.
Therefore, this woman is a witch.

Clearly, the first two premises of this argument (lines 1 and 2) are false. However, if we hold them (and also the premise in line 3) true, then the conclusion follows logically. That is, this argument is a valid argument. Think about the logic of this argument for a second. If we assume that lines 1 and 3 are true, then it follows that the woman is made of wood. And if that is true then by line 2, it follows that she is a witch, which is the conclusion stated in line 4. This silly argument illustrates that logic is first and foremost about the relationship between premises and conclusion, not the actual truth of the premises. Whether or not the premises of an argument are true is often a matter that is outside logic. For example, if one of the premises of an argument were the statement “some mammals do not give live birth,” then logic alone cannot help you figure out whether that is true. For that you need another disciplines: biology.

Let’s return to the first argument for a second to illustrate what logical structure is. That argument has a certain structure that looks like this:

If A then B.
Therefore, not A.

What is interesting about logic is that once we can see the form of an argument, then we can automatically know that the argument is valid without even considering or thinking about the content of the argument. Any argument that has a valid structure is a valid argument. Logic is (in part) the study of these structures. The structure that I have just identified has a name: modus tollens (which in Latin means “way of denying,” since the second premise contains a negation, “not”). Lines 1 and 3 of the Monty Python argument above also contain a valid structure that looks like this:

Therefore, B.

That argument form is called modus ponens (which in Latin means “way of affirming”).

There are many different valid argument structures; however, this is not a logic course, so we will not consider them all. The important thing to understand is that logic concerns the strength of the relationship between the premises and the conclusion, and the goal in constructing arguments is to construct valid arguments. Again, valid arguments are such that the premises of the argument leave no possibility that the conclusion could be false. In contrast, invalid arguments are ones where the premises do leave open the possibility that the conclusion is false. In other words, the premises do not imply the truth of the conclusion. If an argument is invalid, then we should be able to give a counterexample that proves the argument is invalid. A counterexample is simply a description of a possible scenario where the premises are true and yet the conclusion is false. Let’s look at an example.

If the train is late, Shondra is angry.
Shondra is angry.
Therefore, the train is late.

If we assume the premises (lines 1 and 2) are true, is it possible for the conclusion to be false? If so, then this would show the argument is invalid. Here’s a hint if you can’t already see the answer: might Shondra be angry for some other reason and yet the train still be on time? Suppose Shondra is angry because she spilled coffee on her favorite pants. If so, then it could still be the case that any time the train is late, Shondra is angry but on this occasion the train is actually on time. Given this scenario, let’s check line by line the argument. In this scenario are the premises true? Yes they are—premise 1 is true since Shondra would have been angry if the train were late even though the train wasn’t late and premise 2 is true since Shondra is angry because of the coffee spill. And yet the conclusion is false since the train is not late in this scenario. Thus, we have given a counterexample: we have specified a scenario where the premises are true and yet the conclusion false. And that means the argument is invalid.

Logical Validity

Answer the questions in the following interactive to test your knowledge of logical validity.

Deductive vs. Inductive Arguments

Whereas the gold standard of deductive arguments is validity (as discussed in the last section), the standard of inductive arguments is something less than validity. A strong inductive argument is typically called a cogent argument. It is important to understand the difference between deductive and inductive arguments because you need to understand what kind of argument you are trying to make or evaluate. The main difference between inductive and deductive arguments is that whereas deductive arguments seek to establish their conclusions with absolute certainty, inductive arguments only seek to establish their arguments with a high degree of probability. Here’s an example of a strong inductive argument:

All ravens that have ever been observed anywhere in the world have been black.
Therefore, all ravens are black.

Notice that this argument doesn’t quite obtain the standard of validity. It is possible that there is a non-black raven somewhere in the world that hasn’t been observed. But even if that is a possibility, it seems that the “all ravens are black” conclusion is still highly likely, given the amount of confirmation that claim possesses (i.e., the number of ravens that have been observed and that all of them have been black).

Unlike deductive arguments, there is no inductive form that is strong. Any inductive argument could be strong or weak depending on the details of the argument. In contrast, deductive arguments have valid logical structures such that any argument that possesses an inductive form is thereby a valid argument, regardless of the topic of the argument; meaning that to evaluate inductive arguments, we have to draw on our knowledge of how the world is. We can say a couple of things about strong inductive reasoning, but to further understand these concepts would require a course in logic and/or scientific reasoning. We will conclude this page with a few rules of thumb to keep in mind when it comes to inductive arguments:

When making inductive generalizations (such as the ravens argument), make sure that the instances in your premises are not susceptible to any kind of sampling bias. For example, even if I have observed many black ravens, if I have only observed them in one part of the world, there is a good chance that my sample of ravens is not representative of all the ravens in the world.
Many times inductive arguments depend on establishing correlations and we try to infer causation based on correlation. However, this inference must be done carefully. As the saying goes, correlation is not causation; a correlation is not sufficient to establish causation—just because A and B are strongly correlated, or tend to occur together, doesn’t mean that A caused B. To establish that causal claim would require both a plausible causal story we can tell and (ideally) further test to determine whether A really does cause B.
Another common inductive argument is an analogical argument. Analogical arguments attempt to compare two different things (A and B) and argue that since they are similar in relevant respects, if A has a certain property (x), then B must have that property as well. The thing to be on the lookout for here is whether A and B really are similar in relevant respects; because if they aren’t, the logic of the analogical argument breaks down.

deductive argument: one whose conclusions can be established with absolute certainty, often as a result of their form

inductive argument: one whose conclusions can only be established with a high degree of probability

logic: the study and evaluation of arguments to distinguish good reasoning from bad

valid argument: one whose premises guarantee the truth of the conclusion

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"logike." Wordnik, https://www.wordnik.com/words/logic. ↵
College Success. Authored by : Linda Bruce. Provided by : Lumen Learning. License : CC BY: Attribution
Logic. Authored by : Matthew Van Cleave. Provided by : Lumen Learning. License : CC BY: Attribution
Logical Validity. Authored by : Matthew Van Cleave. Provided by : Lumen Learning. License : CC BY: Attribution

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

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

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

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

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

Watch the video below to learn more about critical thinking.

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

illustration of the terms logic, reasoning, and creativity

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

The process

illustration of "thoughts" inside a human brain, with several being connected and "analyzed"

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

Improving your critical thinking

illustration of the questions "What do I currently know?" and "How do I know this?"

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

Real-world applications

illustration of a hand holding a smartphone displaying an article that reads, "Study: Cats are better than dogs"

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

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

illustration of "Super Cat Blog" and "According to survery of cat owners" being highlighted from an article on a smartphone

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

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

illustration of a lightbulb, a briefcase, and the world

/en/problem-solving-and-decision-making/why-is-it-so-hard-to-make-decisions/content/

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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Chapter 7: Critical and Creative Thinking

Learning Framework: Effective Strategies for College Success

Learning Objectives

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

Define critical thinking
Describe the role that logic plays in critical thinking
Describe how critical thinking skills can be used to evaluate information
Apply the CRAAP test to evaluate sources of information
Identify strategies for developing yourself as a critical thinker
Identify applications in education and one's career where creative thinking is relevant and beneficial
Explore key elements and stages in the creative process
Apply specific skills for stimulating creative perspectives and innovative options
Integrate critical and creative thinking in the process of problem-solving

Critical and Creative Thinking

Critical Thinking

As a college student, you are tasked with engaging and expanding your thinking skills. One of the most important of these skills is critical thinking because it relates to nearly all tasks, situations, topics, careers, environments, challenges, and opportunities. It is a “domain-general” thinking skill, not one that is specific to a particular subject area.

What Is Critical Thinking?

Critical thinking is clear, reasonable, reflective thinking focused on deciding what to believe or do (Robert Ennis.) It means asking probing questions like “How do we know?” or “Is this true in every case or just in this instance?” It involves being skeptical and challenging assumptions rather than simply memorizing facts or blindly accepting what you hear or read.

Imagine, for example, that you’re reading a history textbook. You wonder who wrote it and why, because you detect certain biases in the writing. You find that the author has a limited scope of research focused only on a particular group within a population. In this case, your critical thinking reveals that there are “other sides to the story.”

Who are critical thinkers, and what characteristics do they have in common? Critical thinkers are usually curious and reflective people. They like to explore and probe new areas and seek knowledge, clarification, and new solutions. They ask pertinent questions, evaluate statements and arguments, and they distinguish between facts and opinion. They are also willing to examine their own beliefs, possessing a manner of humility that allows them to admit lack of knowledge or understanding when needed. They are open to changing their mind. Perhaps most of all, they actively enjoy learning, and seeking new knowledge is a lifelong pursuit. This may well be you!

No matter where you are on the road to being a critical thinker, you can always more fully develop and finely tune your skills. Doing so will help you develop more balanced arguments, express yourself clearly, read critically, and glean important information efficiently. Critical thinking skills will help you in any profession or any circumstance of life, from science to art to business to teaching. With critical thinking, you become a clearer thinker and problem solver.

The following video, from Lawrence Bland, presents the major concepts and benefits of critical thinking.

Critical Thinking and Logic

Critical thinking is fundamentally a process of questioning information and data and then reflecting on and assessing what you discover to arrive at a reasonable conclusion. You may question the information you read in a textbook, or you may question what a politician or a professor or a classmate says.

You can also question a commonly held belief or a new idea. It is equally important (and even more challenging) to question your own thinking and beliefs! With critical thinking, anything and everything is subject to question and examination for the purpose of logically constructing reasoned perspectives.

What Is Logic?

The word logic comes from the Ancient Greek logike , referring to the science or art of reasoning. Using logic, a person evaluates arguments and reasoning and strives to distinguish between good and bad reasoning, or between truth and falsehood. Using logic, you can evaluate the ideas and claims of others, make good decisions, and form sound beliefs about the world.

Questions of Logic in Critical Thinking

Let’s use a simple example of applying logic to a critical-thinking situation. In this hypothetical scenario, a man has a Ph.D. in political science, and he works as a professor at a local college. His wife works at the college, too. They have three young children in the local school system, and their family is well known in the community. The man is now running for political office. Are his credentials and experience sufficient for entering public office? Will he be effective in the political office? Some voters might believe that his personal life and current job, on the surface, suggest he will do well in the position, and they will vote for him. In truth, the characteristics described don’t guarantee that the man will do a good job. The information is somewhat irrelevant. What else might you want to know? How about whether the man had already held a political office and done a good job? In this case, we want to think critically about how much information is adequate in order to make a decision based on logic instead of assumptions.

The following questions, presented in Figure 1, below, are ones you may apply to formulate a logical, reasoned perspective in the above scenario or any other situation:

What’s happening? Gather the basic information and begin to think of questions.
Why is it important? Ask yourself why it’s significant and whether or not you agree.
What don’t I see? Is there anything important missing?
How do I know? Ask yourself where the information came from and how it was constructed.
Who is saying it? What’s the position of the speaker and what is influencing them?
What else? What if? What other ideas exist and are there other possibilities?

Infographic titled "Questions a Critical Thinker Asks." From the top, text reads: What's Happening? Gather the basic information and begin to think of questions (image of two stick figures talking to each other). Why is it Important? Ask yourself why it's significant and whether or not you agree. (Image of bearded stick figure sitting on a rock.) What Don't I See? Is there anything important missing? (Image of stick figure wearing a blindfold, whistling, walking away from a sign labeled Answers.) How Do I Know? Ask yourself where the information came from and how it was constructed. (Image of stick figure in a lab coat, glasses, holding a beaker.) Who is Saying It? What's the position of the speaker and what is influencing them? (Image of stick figure reading a newspaper.) What Else? What If? What other ideas exist and are there other possibilities? (Stick figure version of Albert Einstein with a thought bubble saying "If only time were relative...".

Problem-Solving with Critical Thinking

For most people, a typical day is filled with critical thinking and problem-solving challenges. In fact, critical thinking and problem-solving go hand-in-hand. They both refer to using knowledge, facts, and data to solve problems effectively. But with problem-solving, you are specifically identifying, selecting, and defending your solution. Below are some examples of using critical thinking to problem-solve:

Your roommate was upset and said some unkind words to you, which put a crimp in the relationship. You try to see through the angry behaviors to determine how you might best support the roommate and help bring the relationship back to a comfortable spot.
Your campus club has been languishing due to a lack of participation and funds. The new club president, though, is a marketing major and has identified some strategies to interest students in joining and supporting the club. Implementation is forthcoming.
Your final art class project challenges you to conceptualize form in new ways. On the last day of class when students present their projects, you describe the techniques you used to fulfill the assignment. You explain why and how you selected that approach.
Your math teacher sees that the class is not quite grasping a concept. They use clever questioning to dispel anxiety and guide you to a new understanding of the concept.

You have a job interview for a position that you feel you are only partially qualified for, although you really want the job and are excited about the prospects. You analyze how you will explain your skills and experiences in a way to show that you are a good match for the prospective employer.

You are doing well in college, and most of your college and living expenses are covered. But there are some gaps between what you want and what you feel you can afford. You analyze your income, savings, and budget to better calculate what you will need to stay in college and maintain your desired level of spending.

Evaluating Information with Critical Thinking

Evaluating information can be one of the most complex tasks you will be faced with in college. But if you utilize the following four strategies, you will be well on your way to success:

Read for understanding
Examine arguments
Clarify thinking
Cultivate “habits of mind”

Read for Understanding

When you read, take notes or mark the text to track your thinking about what you are reading. As you make connections and ask questions in response to what you read, you monitor your comprehension and enhance your long-term understanding of the material. You will want to mark important arguments and key facts. Indicate where you agree and disagree or have further questions. You don’t necessarily need to read every word, but make sure you understand the concepts or the intentions behind what is written. See the chapter on Active Reading Strategies for additional tips.

Examine Arguments

When you examine arguments or claims that an author, speaker, or other source is making, your goal is to identify and examine the hard facts. You can use the spectrum of authority strategy for this purpose. The spectrum of authority strategy assists you in identifying the “hot” end of an argument—feelings, beliefs, cultural influences, and societal influences—and the “cold” end of an argument—scientific influences. The most compelling arguments balance elements from both ends of the spectrum. The following video explains this strategy in further detail:

Clarify Thinking

When you use critical thinking to evaluate information, you need to clarify your thinking to yourself and likely to others. Doing this well is mainly a process of asking and answering probing questions, such as the logic questions discussed earlier. Design your questions to fit your needs, but be sure to cover adequate ground. What is the purpose? What question are we trying to answer? What point of view is being expressed? What assumptions are we or others making? What are the facts and data we know, and how do we know them? What are the concepts we’re working with? What are the conclusions, and do they make sense? What are the implications?

Cultivate “Habits of Mind”

“Habits of mind” are the personal commitments, values, and standards you have about the principle of good thinking. Consider your intellectual commitments, values, and standards. Do you approach problems with an open mind, a respect for truth, and an inquiring attitude? Some good habits to have when thinking critically are being receptive to having your opinions changed, having respect for others, being independent and not accepting something is true until you’ve had the time to examine the available evidence, being fair-minded, having respect for a reason, having an inquiring mind, not making assumptions, and always, especially, questioning your own conclusions—in other words, developing an intellectual work ethic. Try to work these qualities into your daily life.

In 2010, a textbook being used in fourth-grade classrooms in Virginia became big news for all the wrong reasons. The book, Our Virginia by Joy Masoff, had caught the attention of a parent who was helping her child do her homework, according to an article in The Washington Post . Carol Sheriff was a historian for the College of William and Mary and as she worked with her daughter, she began to notice some glaring historical errors, not the least of which was a passage that described how thousands of African Americans fought for the South during the Civil War.

Further investigation into the book revealed that, although the author had written textbooks on a variety of subjects, she was not a trained historian. The research she had done to write Our Virginia, and in particular the information she included about Black Confederate soldiers, was done through the Internet and included sources created by groups like the Sons of Confederate Veterans, an organization that promotes views of history that de-emphasize the role of slavery in the Civil War.

How did a book with errors like these come to be used as part of the curriculum and who was at fault? Was it Masoff for using untrustworthy sources for her research? Was it the editors who allowed the book to be published with these errors intact? Was it the school board for approving the book without more closely reviewing its accuracy?

There are a number of issues at play in the case of Our Virginia , but there’s no question that evaluating sources is an important part of the research process and doesn’t just apply to Internet sources. Using inaccurate, irrelevant, or poorly researched sources can affect the quality of your own work. Being able to understand and apply the concepts that follow is crucial to becoming a more savvy user and creator of information.

When you begin evaluating sources, what should you consider? The CRAAP test is a series of common evaluative elements you can use to evaluate the C urrency, R elevance, A uthority, A ccuracy, and P urpose of your sources. The CRAAP test was developed by librarians at California State University at Chico and it gives you a good, overall set of elements to look for when evaluating a resource. Let’s consider what each of these evaluative elements means.

One of the most important and interesting steps to take as you begin researching a subject is selecting the resources that will help you build your thesis and support your assertions. Certain topics require you to pay special attention to how current your resource is—because they are time sensitive, because they have evolved so much over the years, or because new research comes out on the topic so frequently. When evaluating the currency of an article, consider the following:

When was the item written, and how frequently does the publication come out?
Is there evidence of newly added or updated information in the item?
If the information is dated, is it still suitable for your topic?
How frequently does information change about your topic?

Understanding what resources are most applicable to your subject and why they are applicable can help you focus and refine your thesis. Many topics are broad and searching for information on them produces a wide range of resources. Narrowing your topic and focusing on resources specific to your needs can help reduce the piles of information and help you focus in on what is truly important to read and reference. When determining relevance consider the following:

Does the item contain information relevant to your argument or thesis?
Read the article’s introduction, thesis, and conclusion.
Scan main headings and identify article keywords.
For book resources, start with the index or table of contents—how wide a scope does the item have? Will you use part or all of this resource?
Does the information presented support or refute your ideas?
If the information refutes your ideas, how will this change your argument?
Does the material provide you with current information?
What is the material’s intended audience?

Understanding more about your information’s source helps you determine when, how, and where to use that information. Is your author an expert on the subject? Do they have some personal stake in the argument they are making? What is the author or information producer’s background? When determining the authority of your source, consider the following:

What are the author’s credentials?
What is the author’s level of education, experience, and/or occupation?
What qualifies the author to write about this topic?
What affiliations does the author have? Could these affiliations affect their position?
What organization or body published the information? Is it authoritative? Does it have an explicit position or bias?

Determining where information comes from, if the evidence supports the information, and if the information has been reviewed or refereed can help you decide how and whether to use a source. When determining the accuracy of a source, consider the following:

Is the source well-documented? Does it include footnotes, citations, or a bibliography?
Is information in the source presented as fact, opinion, or propaganda? Are biases clear?
Can you verify information from the references cited in the source?
Is the information written clearly and free of typographical and grammatical mistakes? Does the source look to be edited before publication? A clean, well-presented paper does not always indicate accuracy, but usually at least means more eyes have been on the information.

Knowing why the information was created is a key to evaluation. Understanding the reason or purpose of the information, if the information has clear intentions, or if the information is fact, opinion, or propaganda will help you decide how and why to use information:

Is the author’s purpose to inform, sell, persuade, or entertain?
Does the source have an obvious bias or prejudice?
Is the article presented from multiple points of view?
Does the author omit important facts or data that might disprove their argument?
Is the author’s language informal, joking, emotional, or impassioned?
Is the information clearly supported by evidence?

When you feel overwhelmed by the information you are finding, the CRAAP test can help you determine which information is the most useful to your research topic. How you respond to what you find out using the CRAAP test will depend on your topic. Maybe you want to use two overtly biased resources to inform an overview of typical arguments in a particular field. Perhaps your topic is historical and currency means the past hundred years rather than the past one or two years. Use the CRAAP test, be knowledgeable about your topic, and you will be on your way to evaluating information efficiently and well!

Next, visit the ACC Library’s Website for a tutorial and quiz on using the CRAAP test to evaluate sources.

Developing Yourself As a Critical Thinker

Dark-framed reading glasses laid down on top of a printed page

Critical thinking is a fundamental skill for college students, but it should also be a lifelong pursuit. Below are additional strategies to develop yourself as a critical thinker in college and in everyday life:

Reflect and practice : Always reflect on what you’ve learned. Is it true all the time? How did you arrive at your conclusions?
Use wasted time : It’s certainly important to make time for relaxing, but if you find you are indulging in too much of a good thing, think about using your time more constructively. Determine when you do your best thinking and try to learn something new during that part of the day.
Redefine the way you see things : It can be very uninteresting to always think the same way. Challenge yourself to see familiar things in new ways. Put yourself in someone else’s shoes and consider things from a different angle or perspective. If you’re trying to solve a problem, list all your concerns: what you need in order to solve it, who can help, what some possible barriers might be, etc. It’s often possible to reframe a problem as an opportunity. Try to find a solution where there seems to be none.
Analyze the influences on your thinking and in your life : Why do you think or feel the way you do? Analyze your influences. Think about who in your life influences you. Do you feel or react a certain way because of social convention, or because you believe it is what is expected of you? Try to break out of any molds that may be constricting you.
Express yourself : Critical thinking also involves being able to express yourself clearly. Most important in expressing yourself clearly is stating one point at a time. You might be inclined to argue every thought, but you might have greater impact if you focus just on your main arguments. This will help others to follow your thinking clearly. For more abstract ideas, assume that your audience may not understand. Provide examples, analogies, or metaphors where you can.
Enhance your wellness : It’s easier to think critically when you take care of your mental and physical health. Try taking activity breaks throughout the day to reach 30 to 60 minutes of physical activity each day. Scheduling physical activity into your day can help lower stress and increase mental alertness. Also, do your most difficult work when you have the most energy . Think about the time of day you are most effective and have the most energy. Plan to do your most difficult work during these times. And be sure to reach out for help i f you feel you need assistance with your mental or physical health (see Maintaining Your Mental (and Physical) Health for more information).

Complete ACTIVITY 1: REFLECT ON CRITICAL THINKING at the end of the chapter to deepen your understanding of critical thinking in action.

Creative thinking.

Creative thinking is an invaluable skill for college students because it helps you look at problems and situations from a fresh perspective. Creative thinking is a way to develop novel or unorthodox solutions that do not depend wholly on past or current solutions. It’s a way of employing strategies to clear your mind so that your thoughts and ideas can transcend what appears to be the limitations of a problem. Creative thinking is a way of moving beyond barriers and it can be understood as a skill —as opposed to an inborn talent or natural “gift”—that can be taught as well as learned.

However, the ability to think and act in creative ways is a natural ability that we all exhibited as children. The curiosity, wonder, imagination, playfulness, and persistence in obtaining new skills are what transformed us into the powerful learners that we became well before we entered school. As a creative thinker now, you are curious, optimistic, and imaginative. You see problems as interesting opportunities, and you challenge assumptions and suspend judgment. You don’t give up easily. You work hard. Is this you? Even if you don’t yet see yourself as a competent creative thinker or problem-solver yet, you can learn solid skills and techniques to help you become one.

Creative Thinking in Education

College is a great ground for enhancing creative thinking skills. The following are some examples of college activities that can stimulate creative thinking. Are any familiar to you? What are some aspects of your own college experience that require you to think creatively?

Design sample exam questions to test your knowledge as you study for a final.
Devise a social media strategy for a club on campus.
Propose an education plan for a major you are designing for yourself.
Prepare a speech that you will give in a debate in your course.
Arrange audience seats in your classroom to maximize attention during your presentation.
Participate in a brainstorming session with your classmates on how you will collaborate on a group project.
Draft a script for a video production that will be shown to several college administrators.
Compose a set of requests and recommendations for a campus office to improve its services for students.
Develop a marketing pitch for a mock business you are developing.
Develop a plan to reduce energy consumption in your home, apartment, or dorm.

How to Stimulate Creative Thinking

The following video, How to Stimulate the Creative Process , identifies six strategies to stimulate your creative thinking.

Sleep on it . Over the years, researchers have found that the REM sleep cycle boosts our creativity and problem-solving abilities, providing us with innovative ideas or answers to vexing dilemmas when we awaken. Keep a pen and paper by the bed so you can write down your nocturnal insights if they wake you up.
Go for a run or hit the gym . Studies indicate that exercise stimulates creative thinking, and the brainpower boost lasts for a few hours.
Allow your mind to wander a few times every day. Far from being a waste of time, daydreaming has been found to be an essential part of generating new ideas. If you’re stuck on a problem or creatively blocked, think about something else for a while.
Keep learning . Studying something far removed from your area of expertise is especially effective in helping you think in new ways.
Put yourself in nerve-racking situations once in a while to fire up your brain. Fear and frustration can trigger innovative thinking.
Keep a notebook with you, or create a file for ideas on your smartphone or laptop, so you always have a place to record fleeting thoughts. They’re sometimes the best ideas of all.

The following video, Where Good Ideas Come From by Steven Johnson, reinforces the idea that time allows creativity to flourish.

Watch this supplemental video by PBS Digital Studies: How To Be Creative | Off Book | PBS Digital Studio for a more in-depth look on how to become a “powerful creative person.”

Below is an article by Professor Tobin Quereau, called In Search of Creativity . Perhaps the article can help you think about some simple principles that can enhance your own creative thinking.

In Search of Creativity Tobin Quereau As I was searching through my files the other day for materials on creativity, I ran across some crumpled, yellowed notes which had no clear identification as to their source. Though I cannot remember exactly where they came from, I pass them along to you as an example of the absurd lengths to which some authors will go to get people’s attention. The notes contained five principles or practices with accompanying commentary which supposedly enhance creativity. I reprint them here as I found them and leave you to make your own judgment on the matter.... 1. Do It Poorly! One has to start somewhere and hardly anyone I know starts perfectly at anything. As a result, hardly anyone seems to start very much at all. Often times the quest for excellence quashes any attempt at writing, thinking, doing, saying, etc., since we all start rather poorly in the beginning. Therefore, I advocate more mediocrity as a means to success. Whatever you want, need, or have to do, start doing it! (Apologies to Nike, but this was written long before they stole the concept....) Do it poorly at first with pleasure, take a look or listen to what you’ve done, and then do it again. If you can turn out four good, honest, poor quality examples, the fifth time you should have enough information and experience to turn out something others will admire. And if you do the first four tries in private, only you need to know how you got there. 2. Waste Time! Don’t spend it all doing things. Give yourself time and permission to daydream, mull over, muse about your task or goal without leaping into unending action. “But what,” you say, “if I find myself musing more about the grocery shopping than the gross receipts?” Fine, just see what relationships you can come up with between groceries and gross receipts. (How about increasing the volume and lowering mark-ups? Or providing comfortable seating in the local superstore so that people can relax while shopping and thus have more energy with which to spend their money??) Whatever you do, just pay attention to what comes and get it down in writing somewhere somehow before it goes again. No need to waste ideas.... 3. Be Messy! (Not hard for some of us.) Don’t go for clarity before confusion has had time to teach you something new. In fact, I advocate starting with a large sheet of blank paper–anything up to 2 feet by 4 feet in size–and then filling it up as quickly and randomly as possible with everything that is, might be, or ought to be related to the task at hand. Then start drawing arrows, underlining, scratching through, highlighting, etc., to make a real mess that no one but you can decipher. (If you can’t figure it out either, that’s O.K., too–it doesn’t have to make sense in the beginning.) Then go back to Principle #1 and start doing something. 4. Make Mistakes! Search out your stumbling blocks. Celebrate your errors. Rejoice in your “wrongs” for in them lie riches. Consider your faux pas as feedback not failure and you’ll learn (and possibly even earn!) a lot more. Be like a research scientist and get something publishable out of whatever the data indicates. As one creative consultant, Sidney X. Shore, suggests, always ask, “What’s Good About It?” Some of our most precious inventions have resulted from clumsy hands and creative insight. 5. Forget Everything You Have Learned! (Except, perhaps, these principles!) Give yourself a chance to be a neophyte, return to innocence, start with “beginner’s mind”. In the Zen tradition of Japan, there is a saying in support of this approach because in the beginner’s mind all things are possible, in the expert’s mind only one or two. What would a five-year-old do with your task, goal, project, or problem? Take a risk and be naive again. Many major advances in math and science have come from young, wet-behind-the-ears upstarts who don’t know enough to get stuck like everyone else. Even Picasso worked hard at forgetting how to draw.... But I must stop! There was more to this unusual manuscript, but it would be a poor idea to prolong this further. As a responsible author, I don’t want to waste any more of your time on such ramblings. You know as well as I that such ideas would quickly make a mess of things. I am sure that the original author, whoever that was, has by now repudiated these mistaken notions which could be quite dangerous in the hands of untrained beginners. I even recall a reference to these principles being advocated for groups and teams as well as for individual practice—if you can imagine such a thing! It is a pity that the author or authors did not have more to offer, however, “In Search of Creativity” could have made a catchy title for a book....

Problem Solving with Creative Thinking

Creative problem-solving is a type of problem-solving that involves searching for new and novel solutions to problems. It’s a way to think “outside of the box.” Unlike critical thinking, which scrutinizes assumptions and uses reasoning, creative thinking is about generating alternative ideas— practices and solutions that are unique and effective. It’s about facing sometimes muddy and unclear problems and seeing how things can be done differently.

Complete ACTIVITY 2: ASSESS YOUR CREATIVE-PROBLEM SOLVING SKILLS at the end of the chapter to see what skills you currently have and which new ones you can develop further.

As you continue to develop your creative thinking skills, be alert to perceptions about creative thinking that could slow down progress. Remember that creative thinking and problem-solving are ways to transcend the limitations of a problem and see past barriers.

Critical and creative thinking complement each other when it comes to problem-solving. The process of alternatively focusing and expanding your thinking can generate more creative, innovative, and effective outcomes. The following words, by Dr. Andrew Robert Baker, are excerpted from his “Thinking Critically and Creatively ” essay. Dr. Baker illuminates some of the many ways that college students will be exposed to critical and creative thinking and how it can enrich their learning experiences.

THINKING CRITICALLY AND CREATIVELY Critical thinking skills are perhaps the most fundamental skills involved in making judgments and solving problems. You use them every day, and you can continue improving them. The ability to think critically about a matter—to analyze a question, situation, or problem down to its most basic parts—is what helps us evaluate the accuracy and truthfulness of statements, claims, and information we read and hear. It is the sharp knife that, when honed, separates fact from fiction, honesty from lies, and the accurate from the misleading. We all use this skill to one degree or another almost every day. For example, we use critical thinking every day as we consider the latest consumer products and why one particular product is the best among its peers. Is it a quality product because a celebrity endorses it? Because a lot of other people may have used it? Because it is made by one company versus another? Or perhaps because it is made in one country or another? These are questions representative of critical thinking. The academic setting demands more of us in terms of critical thinking than everyday life. It demands that we evaluate information and analyze myriad issues. It is the environment where our critical thinking skills can be the difference between success and failure. In this environment we must consider information in an analytical, critical manner. We must ask questions—What is the source of this information? Is this source an expert one and what makes it so? Are there multiple perspectives to consider on an issue? Do multiple sources agree or disagree on an issue? Does quality research substantiate information or opinion? Do I have any personal biases that may affect my consideration of this information? It is only through purposeful, frequent, intentional questioning such as this that we can sharpen our critical thinking skills and improve as students, learners and researchers. While critical thinking analyzes information and roots out the true nature and facets of problems, it is creative thinking that drives progress forward when it comes to solving these problems. Exceptional creative thinkers are people that invent new solutions to existing problems that do not rely on past or current solutions. They are the ones who invent solution C when everyone else is still arguing between A and B. Creative thinking skills involve using strategies to clear the mind so that our thoughts and ideas can transcend the current limitations of a problem and allow us to see beyond barriers that prevent new solutions from being found. Brainstorming is the simplest example of intentional creative thinking that most people have tried at least once. With the quick generation of many ideas at once, we can block-out our brain’s natural tendency to limit our solution-generating abilities so we can access and combine many possible solutions/thoughts and invent new ones. It is sort of like sprinting through a race’s finish line only to find there is new track on the other side and we can keep going, if we choose. As with critical thinking, higher education both demands creative thinking from us and is the perfect place to practice and develop the skill. Everything from word problems in a math class, to opinion or persuasive speeches and papers, call upon our creative thinking skills to generate new solutions and perspectives in response to our professor’s demands. Creative thinking skills ask questions such as—What if? Why not? What else is out there? Can I combine perspectives/solutions? What is something no one else has brought-up? What is being forgotten/ignored? What about ______? It is the opening of doors and options that follows problem-identification. Consider an assignment that required you to compare two different authors on the topic of education and select and defend one as better. Now add to this scenario that your professor clearly prefers one author over the other. While critical thinking can get you as far as identifying the similarities and differences between these authors and evaluating their merits, it is creative thinking that you must use if you wish to challenge your professor’s opinion and invent new perspectives on the authors that have not previously been considered. So, what can we do to develop our critical and creative thinking skills? Although many students may dislike it, group work is an excellent way to develop our thinking skills. Many times I have heard from students their disdain for working in groups based on scheduling, varied levels of commitment to the group or project, and personality conflicts too, of course. True—it’s not always easy, but that is why it is so effective. When we work collaboratively on a project or problem we bring many brains to bear on a subject. These different brains will naturally develop varied ways of solving or explaining problems and examining information. To the observant individual we see that this places us in a constant state of back and forth critical/creative thinking modes. For example, in group work we are simultaneously analyzing information and generating solutions on our own, while challenging other’s analyses/ideas and responding to challenges to our own analyses/ideas. This is part of why students tend to avoid group work—it challenges us as thinkers and forces us to analyze others while defending ourselves, which is not something we are used to or comfortable with as most of our educational experiences involve solo work. Your professors know this—that’s why we assign it—to help you grow as students, learners, and thinkers! —Dr. Andrew Robert Baker, Foundations of Academic Success: Words of Wisdom

Problem-Solving Action Checklist

Problem-solving can be an efficient and rewarding process, especially if you are organized and mindful of critical steps and strategies. Remember to assume the attributes of a good critical thinker: if you are curious, reflective, knowledge-seeking, open to change, probing, organized, and ethical, your challenge or problem will be less of a hurdle, and you’ll be in a good position to find intelligent solutions. The steps outlined in this checklist will help you adhere to these qualities in your approach to any problem:

KEY TAKEAWAYS

Critical thinking is logical and reflective thinking focused on deciding what to believe or do.
Critical thinking involves questioning and evaluating information.
Evaluating information is a complex, but essential, process. You can use the CRAAP test to help determine if sources and information are reliable.
Creative thinking is both a natural aspect of childhood and a re-learnable skill as an adult.
Creative thinking is as essential a skill as critical thinking and integrating them can contribute to innovative and rewarding experiences in life.
Critical and creative thinking both contribute to our ability to solve problems in a variety of contexts.
You can take specific actions to develop and strengthen your critical and creative thinking skills.

ACTIVITY 1: REFLECT ON CRITICAL THINKING

Apply critical thinking strategies to your life

Directions:

Think about someone you consider to be a critical thinker (friend, professor, historical figure, etc). What qualities does he/she have?
Review some of the critical thinking strategies discussed on this page. Pick one strategy that makes sense to you. How can you apply this critical thinking technique to your academic work?
Habits of mind are attitudes and beliefs that influence how you approach the world (i.e., inquiring attitude, open mind, respect for truth, etc). What is one habit of mind you would like to actively develop over the next year? How will you develop a daily practice to cultivate this habit?
Write your responses in journal form, and submit according to your instructor’s guidelines.

ACTIVITY 2: ASSESS YOUR CREATIVE PROBLEM-SOLVING SKILLS

Access Psychology Today ’s Creative Problem-Solving Test at the Psychology Today Web site.
Read the introductory text, which explains how creativity is linked to fundamental qualities of thinking, such as flexibility and tolerance of ambiguity.
Then advance to the questions by clicking on the “Take The Test” button. The test has 20 questions and will take roughly 10 minutes.
After finishing the test, you will receive a Snapshot Report with an introduction, a graph, and a personalized interpretation for one of your test scores.

Complete any further steps by following your instructor’s directions.

LICENSES AND ATTRIBUTIONS

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Critical and Creative Thinking Authored by : Laura Lucas, Tobin Quereau, and Heather Syrett. Provided by : Austin Community College. License : CC BY-NC-SA-4.0

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Chapter cover image. Authored by : Hans-Peter Gauster. Provided by : Unsplash. Located at : https://unsplash.com/photos/3y1zF4hIPCg . License : CC0: No Rights Reserved
Creative Thinking Skills in College Success. Authored by : Linda Bruce. Provided by : Lumen Learning. Located at : https://courses.lumenlearning.com/collegesuccess-lumen/chapter/creative-thinking-skills/ . License : CC BY 4.0
Critical Thinking in Educational Psychology. Authored by : Kelvin Seifert and Rosemary Sutton. Provided by : Lumen Learning. Located at: https://courses.lumenlearning.com/educationalpsychology/chapter/critical-thinking/ . License : CC BY 4.0
Critical Thinking Skills in College Success. Authored by : Linda Bruce. Provided by : Lumen Learning. Located at : https://courses.lumenlearning.com/collegesuccess-lumen/chapter/critical-thinking-skills/ . License : CC BY 4.0
Critical Thinking 101: Spectrum of Authority. Provided by: UCB Learn. Located at : https://youtu.be/9G5xooMN2_c . License : CC BY 4.0
Evaluate: Assessing Your Research Process and Findings in Information Literacy. Authored by : Bernnard, Bobish, Hecker, Holden, Hosier, Jacobsen, Loney, Bullis. Provided by : Lumen Learning. Located at : https://courses.lumenlearning.com/informationliteracy/chapter/evaluate-assessing-your-research-process-and-findings/ . License : CC BY-NC-SA-4.0
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Where Good Ideas Come From. Authored by : Steven Johnson. Provided by: Riverhead Books. Located at : https://www.youtube.com/watch?v=NugRZGDbPFU . License : All Rights Reserved . License Terms : Standard YouTube License

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International Congress on Tools for Teaching Logic

TICTTL 2011: Tools for Teaching Logic pp 38–45 Cite as

Teaching Logic in Philosophy

Begoña Carrascal 23
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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6680))

Logic considered as a general model of reasoning is equated in most cases with argumentation. The symbolic component of logic is the main component of the teaching of the subject, even in a first course in Philosophy, but for students with poor technical skills, formal logic is not the best way to enhance their thinking and their initiation to the inquiry. To improve their reasoning, it would be better to begin with different problem solving tasks in natural language and only after their resolution should we try to symbolize them. Moreover, argumentation and reasoning are related but they aren’t the same thing. In argumentation the linguistic and social components can’t be forgotten. Training in argumentation is left to logic or never taught. Students’ argumentative skills should be developed in parallel both in oral discussions and by writing.

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Carrascal, B. (2011). Teaching Logic in Philosophy. In: Blackburn, P., van Ditmarsch, H., Manzano, M., Soler-Toscano, F. (eds) Tools for Teaching Logic. TICTTL 2011. Lecture Notes in Computer Science(), vol 6680. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21350-2_5

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Critical Thinking and Decision-Making
Simply put, critical thinking is the act of deliberately analyzing information so that you can make better judgements and decisions. It involves using things like logic, reasoning, and creativity, to draw conclusions and generally understand things better. This may sound like a pretty broad definition, and that's because critical thinking is a ...
(PDF) Critical Thinking for Language Learning and ...
The problem of development of student's critical and creative thinking skills in the process of teaching and learning a foreign language is reflected in numerous studies on enhancing the cognitive ...
How to apply critical thinking in learning
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.
Critical Thinking: An Approach that Synthesizes Analytic Philosophy
Critical Thinking: An Approach that Synthesizes Analytic Philosophy,' Indian Philosophical Quarterly, University of Pune, Vol 44, No 1, December, 2017, 67-78, ISSN: 0376-415X. 4 Natural language can suit with logical analysis. Logic ripostes language to understand the world. Wittgenstein writes, 'Logic is not a body of doctrine, but a mirror-image of the world.
Chapter 7: Critical and Creative Thinking
Critical Thinking Critical Thinking and Logic. Critical thinking is fundamentally a process of questioning information and data and then reflecting on and assessing what you discover to arrive at a reasonable conclusion. You may question the information you read in a textbook, or you may question what a politician or a professor or a classmate ...
Enhancing Critical Thinking In Foreign Language Learners
Critical thinking refers to the individuals' ability to think and make correct decisions independently. Nowadays enhancing critical thinking in learners is considered one of the foreign language teachers' tasks due to its high position in foreign language classrooms. There are various factors affecting language learners' critical thinking ...
Teaching Logic in Philosophy
Logic considered as a general model of reasoning is equated in most cases with argumentation. The symbolic component of logic is the main component of the teaching of the subject, even in a first course in Philosophy, but for students with poor technical skills, formal logic is not the best way to enhance their thinking and their initiation to the inquiry.

Introduction to Logic and Critical Thinking

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The Importance of Logic and Critical Thinking

2: Language, Meaning, and Definition

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al-Farabi’s Philosophy of Logic and Language

1. Al-Fārābī’s Writings and Their Background

4. Requests and Questions

6. Tools for Inference

Acknowledgments

Support SEP

The Connection Of Language And Thinking

Introduction

Problem Statement

Research Questions

Purpose of the Study

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What Is Critical Thinking? | Definition & Examples

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Module 5: Thinking and Analysis

Critical Thinking and Logic

What Is Logic, and Why Is It Important in Critical Thinking?

Logical Structure

Logical Validity

Deductive vs. Inductive Arguments

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

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

The process

Improving your critical thinking

Real-world applications

Why do we need critical thinking?

What is the process of critical thinking?

2. Analyze

3. Evaluate

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

2. Writing essays and theses

3. Attending lectures

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Learning Objectives

Critical Thinking

What Is Critical Thinking?

Critical Thinking and Logic

What Is Logic?

Questions of Logic in Critical Thinking

Problem-Solving with Critical Thinking

Evaluating Information with Critical Thinking

Read for Understanding

Examine Arguments

Clarify Thinking

Cultivate “Habits of Mind”

Developing Yourself As a Critical Thinker

Complete ACTIVITY 1: REFLECT ON CRITICAL THINKING at the end of the chapter to deepen your understanding of critical thinking in action.

Creative Thinking in Education

How to Stimulate Creative Thinking

Problem Solving with Creative Thinking