logic and critical thinking anu

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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PHIL102: Introduction to Critical Thinking and Logic

Course introduction.

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

The course touches upon a wide range of reasoning skills, from verbal argument analysis to formal logic, visual and statistical reasoning, scientific methodology, and creative thinking. Mastering these skills will help you become a more perceptive reader and listener, a more persuasive writer and presenter, and a more effective researcher and scientist.

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

Course Syllabus

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

Unit 1: Introduction and Meaning Analysis

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

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

Completing this unit should take you approximately 5 hours.

Unit 2: Argument Analysis

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

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

Completing this unit should take you approximately 7 hours.

Unit 3: Basic Sentential Logic

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

Completing this unit should take you approximately 13 hours.

Unit 4: Venn Diagrams

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

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

Completing this unit should take you approximately 6 hours.

Unit 5: Fallacies

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

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

Completing this unit should take you approximately 3 hours.

Unit 6: Scientific Reasoning

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

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

Completing this unit should take you approximately 4 hours.

Unit 7: Strategic Reasoning and Creativity

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

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

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1: Basic Concepts

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The most important thing we do as human beings is learn how to think. This is important in two senses of the word: it’s important to human beings because it is the most distinctively unique fact about our species—we think rationally and abstractly—but it’s also important because it the most wide reaching capacity we have—it touches virtually all aspects of our lives. Having a heart that pumps blood or a body capable of certain physical activities might be more fundamental meaning more crucial to simply surviving, but thinking underlies a broad range of activities without which we would be living less than full human lives.

The common title of this course is “Logic and Critical Thinking.” So, we can think about the course as having two main components: the study of formal logic and the study of the tools and strategies of critical thinking. This text is structured in a bit of a “sandwich”. Units on critical thinking and then formal logic, and then units on more critical thinking topics.

First, Logic. We’ll define logic more fully later, but for now: logic is a sort of reasoning that is mathematical in its precision and proofs. It’s like math with words and concepts, in a sense.

Oh no! Not math! I'm no good at math.

Don’t worry, dear student. Logic is more straightforward than a lot of the complex concepts that get discussed in math classes. Even better, all of logic can be broken down into simple, step-by-step processes that a computer can do. You just need to follow the steps carefully and you’ll be guaranteed the right answer every time. There’s no magic to it, no special skills or abilities needed. You just need to follow directions carefully and put a bit of work into it.

Next, let’s get a bit of a definition of critical thinking going. Critical thinking is primarily the ability to think carefully about thinking and reasoning—to have the ability to criticize your own reasoning. ‘Criticize’ here isn’t meant in the sense of being mean or talking down or making fun of. Instead, I mean the word in the sense of, for example, how a coach might take a critical stance toward her players’ skills—he throws high every time, she doesn’t lead with her foot, they ride too forward in the saddle, etc. ‘Critical’ here means something more like ‘reflective’ or ‘careful’ or ‘attention to potential errors’.

So to engage in critical thinking is to engage in self-critical, self-reflective, self-aware thinking and reasoning—thinking and reasoning aimed at self-improvement, at truth, and at careful, deliberate, proper patterns of reasoning.

There are many definitions of what critical thinking is, but here’re my thoughts:

As you can see, being a critical thinker involves training yourself to have a lot of good habits and dispositions. It involves developing rational virtues so that when the time comes to think about something complex, you are naturally disposed to think well. It doesn’t happen overnight and it certainly doesn’t come for free—no one is born with it. We all need to train ourselves and educate ourselves to stay guarded against errors in reasoning.

1.1: Vital Course Concepts
1.2: Kinds of Inferences
1.3: Chapter 1 - Key Terms
1.E: Chapter One (Exercises)

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Article Contents

Introduction, the central argument, where should non-western contributions to logic and critical thinking be taught, acknowledgements.

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Does Critical Thinking and Logic Education Have a Western Bias? The Case of the Nyāya School of Classical Indian Philosophy

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Anand Jayprakash Vaidya, Does Critical Thinking and Logic Education Have a Western Bias? The Case of the Nyāya School of Classical Indian Philosophy, Journal of Philosophy of Education , Volume 51, Issue 1, February 2017, Pages 132–160, https://doi.org/10.1111/1467-9752.12189

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In this paper I develop a cross-cultural critique of contemporary critical thinking education in the United States, the United Kingdom, and those educational systems that adopt critical thinking education from the standard model used in the US and UK. The cross-cultural critique rests on the idea that contemporary critical thinking textbooks completely ignore contributions from non-western sources, such as those found in the African, Arabic, Buddhist, Jain, Mohist and Nyāya philosophical traditions. The exclusion of these traditions leads to the conclusion that critical thinking educators, by using standard textbooks are implicitly sending the message to their students that there are no important contributions to the study of logic and argumentation that derive from non-western sources. As a case study I offer a sustained analysis of the so-called Hindu Syllogism that derives from the Nyāya School of classical Indian philosophy. I close with a discussion of why contributions from non-western sources, such as the Hindu Syllogism, belong in a Critical Thinking course as opposed to an area studies course, such as Asian Philosophy .

One question in the philosophy of education is the question concerning education for democracy , EDQ: How should public education enable the ethical implementation and proper functioning of democratic processes, such as voting on the basis of public and civic discourse? At least one plausible answer is that a public education should provide citizens of a political body with basic skills in public discourse, which is inclusive of critical thinking and civic debate. That is, education for democracy should have an element that enables ethical public discourse on topics of shared concern. This answer is grounded on two ideas. First, democratic processes, such as voting, take into account the will of the people through reflective deliberation and the exchange of ideas on matters of public concern, such as prison reform, marriage, taxation and gun control. Second, critical thinking through civic engagement allows for the expression of individual autonomy on a matter of public concern. Call this general answer to EDQ, the critical thinking and civic debate response , CTCD. Two important questions the CTCD response faces are the content question : What exactly are critical thinking, civic debate and ethical public discourse? And the normative question : What are the appropriate forms, norms and intellectual virtues by which we should engage in critical thinking, civic debate and ethical public discourse? 1

On March 24, 2014 at the Cross Examination Debate Association (CEDA) Championships at Indiana University, two Towson University students, Ameena Ruffin and Korey Johnson, became the first African-American women to win a national college debate tournament, for which the resolution asked whether the US president's war powers should be restricted. Rather than address the resolution straight on, Ruffin and Johnson, along with other teams of African-Americans, attacked its premise. The more pressing issue, they argued, is how the US government is at war with poor black communities. In the final round, Ruffin and Johnson squared off against Rashid Campbell and George Lee from the University of Oklahoma, two highly accomplished African-American debaters with distinctive dreadlocks and dashikis. Over four hours, the two teams engaged in a heated discussion of concepts like “nigga authenticity” and performed hip-hop and spoken-word poetry in the traditional timed format. At one point during Lee's rebuttal, the clock ran out but he refused to yield the floor. “Fuck the time!” he yelled. His partner Campbell, who won the top speaker award at the National Debate Tournament two weeks later, had been unfairly targeted by the police at the debate venue just days before, and cited this experience as evidence for his case against the government's treatment of poor African-Americans.

In the 2013 championship, two men from Emporia State University, Ryan Walsh and Elijah Smith, employed a similar style and became the first African-Americans to win two national debate tournaments. Many of their arguments, based on personal memoir and rap music, completely ignored the stated resolution, and instead asserted that the framework of collegiate debate has historically privileged straight, white, middle-class students . ( emphasis added ) 3

Although there are many important features that these cases bring to light, here I want to draw attention to three features that help us understand the importance of both the content question and the normative question. First, the kind of evidence that is appealed to does not just consist in objective facts, such as what the law states, and reasoning deductively or inductively from a set of premises, it also contains personal experience. Second, the mode of engagement used does not consist simply in rational argumentation through the use of the standard format of ethical theory, followed by premise, application and finally a conclusion. Rather, it includes poetry and hip-hop that takes both a reason-based approach and an emotional and musical element into play. Third, the norm of engagement used does not see deference to rules as trumping either the importance of what is talked about or the length of time one talks about it. We might summarise a caricature reaction to these students by a hypothetical critic as follows: how rude of these students to not debate the issue, to disregard the rules, and to fail to take into consideration the kinds of evidence required for public debate and discourse on matters of social and political concern. In light of these cases and the caricature, the critical thinking and civic debate community faces an important and unexamined question : does critical thinking and civic debate education rest on an uncritical examination of its very foundation? Is the foundation perhaps insensitive to race, class, gender and non-western traditions of critical thinking and debate? Call this question the meta-critical question about critical thinking.

The meta-critical question about critical thinking and civic debate education is extremely important to any education policy that embraces the CTCD response to EDQ. Furthermore, it is central to the project of coming to understand how public discourse is possible in a community that has diverse individuals with non-overlapping conceptions of the good life. In the next section, I present, explain, and defend the central argument leading to the conclusion that critical thinking education should include contributions from non-western sources. As a case study I present some material, well known in the classical Indian philosophical and comparative philosophy community, concerning contributions to logic and critical thinking deriving from the Nyāya tradition of orthodox Indian philosophy. My examination of these contributions aims to establish that there are things that critical thinking education can take on board from non-western traditions that are important and valuable to critical thinking and logic education. In the third section , I present and respond to the objection that contributions to critical thinking from non-western traditions should not be taught in a Critical Thinking course but rather in an area studies course, such as Asian Philosophy .

At present there is a social blindspot that critical thinking and debate education suffers from in the US, UK and those countries that use the standard model that originates from the US and UK. In short the blindspot is that critical thinking and debate education is insensitive to variation over what could count as critical thinking and civic debate based on an examination of non-western contributions to critical thinking and debate. The neglect of these traditions is largely due to the fact that those that work on critical thinking, logic and debate, such as members of the informal logic community are generally not historically informed about non-western contributions to critical thinking through engagement with those that work on Asian and comparative philosophy. Simply put, institutional separation has led to an impoverished educational package for critical thinking education for the past 100 years in which the modern university has developed. The central argument I will develop to expose the problem is as follows.

Critical thinking, and practice in ethical civic debate, is important to public discourse on social and political issues that citizens of a democratic body vote on when making policy decisions that concern all members of the public. The current model for critical thinking and civic debate education is dominated by a western account of informal logic, formal logic, debate rules and intellectual virtues. Critical thinking education should include contributions from non-western philosophers.∴ Critical thinking education should be revised so as to be inclusive of contributions from non-western thinkers.

Why should we accept the premises of this argument?

Premise 1: Critical thinking, and practice in ethical civic debate, is important to public discourse on social and political issues that citizens of a democratic body vote on when making policy decisions that concern all members of the public.

The main objection to Premise 1 derives from the work of Michael Huemer's (2005) paper: Is Critical Thinking Epistemically Responsible? In this work he provides an argument against the epistemic responsibility of critical thinking. The core idea is that if one is forming a belief on an issue of public concern one ought to do so responsibly. Given that one ought to form the belief in a responsible way, one might consider different strategies open to the person for how to form the belief. Consider the following belief forming strategies.

Credulity : In forming a belief a person is to canvass the opinions of a number of experts and adopt the belief held by most of them. In the best case, the person finds a poll of the experts; failing that, the person may look through several reputable sources, such as scholarly books and peer-reviewed journal articles, and identify the conclusions of the experts.

Skepticism : In forming a belief a person is to form no opinion on the matter; that is, the person is to withhold judgement about the issue.

Critical Thinking : In forming a belief a person is to gather arguments and evidence that are available on the issue, from all sides, and assess them. The person tries thereby to form some overall impression on the issue. If the person forms such an impression, then she bases her belief on it. Otherwise, the person suspends judgement.

Now, where P is a specific controversial and publicly debated issue, and C b P is the context of belief formation for P, the central argument against the epistemic responsibility of critical thinking is the following.

Adopting Critical Thinking about P in C b P is epistemically responsible only if Critically Thinking about P is the most reliable strategy from the available strategies in C b P. One ought to always use the most reliable strategy available in forming a belief about an issue of public concern. Critical Thinking about P is not the most reliable strategy from the available strategies in C b P.∴ It is not the case that Critical Thinking about P in C b P is epistemically responsible.

In Vaidya (2013) , I offered an extensive argument against Huemer's position. That argument depends on a development of a theory of what constitutes an autonomous critical identity, and why forming a critical identity is valuable for a person. As a consequence, I will not go into a sustained response to Huemer's argument here. Rather, I will note a simple set of points that can be used to assuage the initial force of what is being argued.

First, in so far as the claim is that critical thinking about an issue is not to be preferred over taking the view of an expert on an issue it is clear that choosing who the expert is on the issue is a matter of critical thinking. In order for one to identify someone as an expert one must understand how to track through sources for the appropriate identification of experts. So, in general, deference to experts actually depends on critical thinking , since deference is a choice one must make. The core idea is that one cannot outsource all cognition to an alternative source, since outsourcing is itself a decision that has to be made .

Secondly, it is important to distinguish between the different types of issues in which deference to experts can be made. For example, there is a difference between an argument that contains a scientific conclusion, with mathematical and scientific premises, and an argument that contains moral premises and has a moral conclusion. Given this difference, it is plausible to maintain that deference to experts in the scientific and mathematics case is not the same as deference in the moral case. While I can defer to a moral expert to tell me what a moral theory says, such as what the details of consequentialism, as opposed to deontology, are, I can't defer to a moral expert on the issue of what the correct moral conclusion is, independently of the adoption of a specific moral view. By contrast, I can defer to a scientist or a mathematician as to which conclusion to believe on the basis of the premises.

Premise 2: The current model for critical thinking and civic debate education is dominated by a western account of informal logic, formal logic, debate rules and intellectual virtues.

The key defence I will offer for Premise 2 relies on an examination of two of the most commonly used textbooks for critical thinking in the US and UK, Patrick Hurley's A Concise Introduction to Logic and Lewis Vaughn's The Power of Critical Thinking: Effective Reasoning about Ordinary and Extraordinary Claims . The guiding idea of the argument is that if our main textbooks for teaching critical thinking and logic at the introductory level do not engage non-western philosophy, we can reasonably infer that those that use the textbook are not teaching critical thinking and logic by way of engaging non-western sources. Of course there will be those that supplement the texts, perhaps even for the very reason I am presenting here—that they lack non-western ideas. But we can safely examine and entertain the claim that I am defending as being primarily about textbooks as opposed to variable classroom practice . More importantly, if the textbooks are widely used, which they are, we can ask: what do they represent about critical thinking and civic debate education?

I will focus my examination of non-western contributions to critical thinking on two places in critical thinking education where adjustments can be made. The point of this presentation is to show that our main textbooks can be altered to include non-western sources in specific ways. Although there are many contributions I could discuss, for simplicity I will focus on contributions from the Nyāya School of classical Indian philosophy concerning the nature of argumentation. In future work I will discuss other cases, such as those deriving from Africana, Arabic, Jaina, and Jewish philosophy. I begin my investigation of the Nyāya by answering a basic question: Is there a distinction in Indian philosophy between different kinds of discussions that allows us to isolate out critical discourse from non-critical discourse?

Is there any critical thinking in Indian philosophy?

Of course this question cannot be seriously entertained by anyone who works in Indology or Asian and Comparative Philosophy. However, for those who are not in the know, a presentation and defence of an affirmative answer must be made. For if one is to include non-western ideas about critical thinking in a textbook that is eventually used to teach the subject, one needs to show that non-western traditions are in fact engaging in critical thinking. In order to do that we need to look at competing views of what critical thinking is, the content question , in order to locate critical thinking outside of the west.

The Skill View holds that critical thinking is exhausted by the acquisition and proper deployment of critical thinking skills.

The Character View holds that critical thinking involves the acquisition and proper deployment of specific skills as well as the acquisition of specific character traits, dispositions, attitudes, and habits of mind. These components are aspects of the “critical spirit” ( Siegel, 1993 , 163–165).

Given this distinction, where does classical Indian philosophy fall? We have three options. Indian philosophical traditions take one or another of the views, or there is no discussion at all of either of these views. I will show that some Indian philosophical traditions make a distinction between various kinds of discussion, one of which is a critical discussion, and that there is evidence for the character view of critical thinking.

Discussion is the adoption of one of two opposing sides. What is adopted is analyzed in the form of the five members, and defended by the aid of any of the means of right knowledge, while its opposite is assailed by confutation, without deviation from the established tenets ( Sinha, 1990 , p. 19).

Wrangling , which aims at gaining victory, is the defense or attack of a proposition in the manner aforesaid, by quibbles, futilities, and other processes which deserve rebuke ( Sinha, 1990 , p. 20).

Cavil is a kind of wrangling, which consists in mere attacks on the opposite side ( Sinha, 1990 , p. 20).

Matilal maintains, on the basis of Akṣapāda's Nyāya Sūtras that there are three distinct kinds of discussions. Vāda is an honest debate where both sides, proponent and opponent, are seeking the truth, that is, wanting to establish the right view. Jalpa , by contrast, is a discussion/debate in which one tries to win by any means, fair or unfair. Vitaṇdā is a discussion in which one aims to destroy or demolish the opponent no matter how. One way to explain the distinctions is as follows: (i) vāda is an honest debate for the purposes of finding the truth, (ii) jalpa is a debate aimed at victory where one propounds a thesis; (ii) vitaṇdā is a debate aimed at victory, where no thesis is defended, one simply aims to demolish the view propounded by the proponent. 4 The distinction between these three kinds of discussions grounds the claim that classical Indian philosophers were aware of different kinds of discussions based on the purpose of the discussion, and that critical thinking, for the purposes of finding the truth on an issue, was not at all a foreign idea .

One who has acquired the knowledge (given by the authoritative text) based on various reasons and refuting the opponent's view in debates, does not get fastened by the pressure of the opponent's arguments nor does he get subdued by their arguments ( Van Loon, 2002 , p. 115).

Discussion with specialists: promotes pursuit and advancement of knowledge, provides dexterity, improves power of speaking, illumines fame, removes doubt in scriptures, if any, by repeating the topics, and it creates confidence in case there is any doubt, and brings forth new ideas. The ideas memorized in study from the teacher, will become firm when applied in (competitive) discussion ( Van Loon, 2002 , pp. 115–116).

Discussion with specialists is of two types— friendly discussion and hostile discussion. The friendly discussion is held with one who is endowed with learning, understanding and the power of expression and contradiction, devoid of irritability, having uncensored knowledge, without jealousy, able to be convinced and convince others, enduring and adept in the art of sweet conversation. While in discussion with such a person one should speak confidently, put questions unhesitatingly, reply to the sincere questioner with elaborateness, not be agitated with fear of defect, not be exhilarated on defeating the partner, nor boast before others, not hold fast to his solitary view due to attachment, not explain what is unknown to him, and convince the other party with politeness and be cautious in that. This is the method of friendly discussion ( Van Loon, 2002 , pp. 117–118, emphasis added ).

The passages from the Handbook of Ayurveda , especially the emphasised area, substantiate the idea that the character view is in play in one of the oldest recorded presentations of critical reasoning and how it is to be executed.

Furthermore, in his Indian Logic , Jonardon Ganeri (2004) presents a picture of argumentation and critical thinking in ancient India by turning to the classic dialogue of the Buddhist tradition: Milinda-pañha ( Questions for King Milinda ). Ganeri presents an important passage on discussion and critical thinking. 5

Milinda: Reverend Sir, will you discuss with me again?

Nāgasena: If your Majesty will discuss ( vāda ) as a scholar, well, but if you will discuss as a king, no.

Milinda: How is it that scholars discuss?

Nāgasena: When scholars talk a matter over one with another, then there is a winding up, an unraveling, one or other is convicted of error, and he then acknowledges his mistake; distinctions are drawn, and contra-distinctions; and yet thereby they are not angered. Thus do scholars, O King, discuss.

Milinda: And how do kings discuss?

Nāgasena: When a king, your Majesty, discusses a matter, and he advances a point, if any one differ from him on that point, he is apt to fine him, saying “Inflict such and such a punishment upon that fellow!” Thus, your Majesty, do kings discuss.

Milinda: Very well. It is as a scholar, not as a king, that I will discuss.( As quoted in Ganeri, 2004 , p. 17)

When scholars talk a matter over one with another, then is there a winding up, an unraveling, one or other is convicted of error, and he then acknowledges his mistake ; distinctions are drawn, and contra-distinctions; and yet thereby they are not angered ( as quoted in Ganeri, 2004 , p. 17, emphasis added ).

One reading of this claim is that Nāgasena is pointing out that a good discussion requires not only that certain moves are made ‘a winding up’ and an ‘unraveling’, but that the persons involved in making those moves have a certain epistemic temper . Participants in a good debate moreover have the capacity, and exercise the capacity, to (i) acknowledge mistakes , and (ii) not become angered by the consequences of where the inquiry leads . Nāgasena's answer to King Milinda suggests that Buddhist accounts of critical thinking also adopt the character view as opposed to the skill view . It is not enough to simply know how to ‘make moves’, ‘destroy’ or ‘demolish’ an opponent by various techniques. What is central to an honest debate is that a participant must also have a certain attitude and character that exemplifies a specific epistemic temper .

If one agrees with the character view, then this simple passage from Milinda - pañha could be compared with other passages, such as from the Meno , to teach critical thinking students what critical thinking is about. 6

The tale of two syllogisms

But once we have introduced students to what critical thinking is we are often faced with having to show them how to present their ideas for the purposes of a critical discussion. This takes us to the normative question : what are the appropriate forms, norms and intellectual virtues by which we should engage in critical thinking and civic debate? Many contemporary introductory level textbooks, such as Hurley's Concise Introduction to Logic and Vaughn's The Power of Critical Thinking contain some section where they present and discuss how an argument should be put into, what is often called, standard form . The notion of a standard form is normative . It suggests that an argument has a way that it should be presented for the purposes of engaging someone in a dialectical inquiry. Often discussion of standard form takes place either in the context of the presentation of how to identify an argument, or in the area where Aristotelian Categorical Logic is presented. However, the presentation of what constitutes a good argument, in either Hurley or Vaughn, is not given comparatively by considering other traditions. For example, it is simply presupposed that there is no alternative way in which one could present an argument. In contrast to the Aristotelian picture, the Hindu Syllogism has a different structure. It was developed and debated in classical Hindu, Buddhist and Jain philosophy for centuries. What is the basic contrast between the Aristotelian Syllogism and the Hindu Syllogism?

Aristotle was the ancient Greek philosopher who first codified logic for the western tradition. Students of logic and critical thinking are often brought into the topic of the syllogism and the standard form of reasoning by the following example from Aristotle.

Major Premise: All men are mortal.

Minor Premise: Socrates is a man.

Conclusion: Socrates is mortal.

Akṣapāda Gautama was the founding father of the Nyāya School of philosophy. Like Aristotle he was also concerned with the proper form of how an argument should be displayed. The most commonly discussed argument in Indian philosophy deriving from his work, and perhaps even earlier, is the following:

Thesis: The hill has fire.

Reason/Mark: Because of smoke.

Rule/Examples: Wherever there is smoke, there is fire, as in a kitchen.

Application: This is such a case, i.e., the hill has smoke pervaded by fire.

Conclusion: Therefore it is so, i.e., the hill has fire. 7

There are many differences between the two examples. Two of the most important, highlighted by Matilal (1985 , pp. 6–7), are: (i) Aristotle's Syllogism is in subject-predicate form, Akṣapāda's Syllogism is in property-location form; (ii) Aristotle's study of syllogistic inference is primarily about universal and particular form propositions, Akṣapāda's study involves singular propositions in the thesis and conclusion. However, even though there are these differences, both examples have a similar normative force . They are both offered as a case of good reasoning , and they both are examples of what counts as how one should present their argument in a debate.

Given that neither Hurley nor Vaughn discuss the Hindu Syllogism, we might ask all of the following questions. Does it make sense as an argument form? Is there any benefit to teaching it? What do we gain by including it?

The western gaze on classical Indian logic

To answer these questions we need to look at the history of the reception of the Hindu Syllogism and how to correct the colonialist interpretation of it.

In the study of classical Indian logic from the Anglo-European point of view it is well known that the Hindu Syllogism received a great deal of criticism and was often presented as being inferior to the Aristotelian Syllogism. Jonardon Ganeri (2001) has compiled a list of some of these critiques in his work on Indian Logic:

[Western philosophy] looks outward and is concerned with Logic and with the presuppositions of scientific knowledge; [Indian philosophy] looks inward, into the ‘deep yet dazzling darkness’ of the mystical consciousness ( as quoted in Ganeri, 2001 , p. 1).

I have a great doubt of [Indian Logical] views becoming of any value whatever in the cause of general knowledge or science, or of ever having any fair claim to be admitted as an integral part of the Catholic philosophy of mankind. It is absurd to conceive that a logic can be of any value from a people who have not a single sound philosophical principle, nor any intellectual power whatever to work out a problem connected with human nature in a manner that is at all rational or intelligent. Reasoning at least in the higher forms of it among such semi-barbarous nations, must be at its lowest ebb; [and there] does [not] seem to be any intellectual stamina, in such races of men, to impart to it more vigour and rationality. ( as quoted in , brackets added, Ganeri, 2001 , p. 7).

One point alone appears certain, and that is, that they [the Nyāya] can lay but slight claims to accuracy of exposition. This is proved clearly enough by the form of their syllogism, which is made to consist of five instead of three parts. Two of these are manifestly superfluous, while by the introduction of an example in the third the universality of the conclusion is vitiated ( as quoted in Ganeri, 2001 , p. 9).

That Hindu philosophy will have any great influence on the development of European philosophy and mediately of European civilization must be denied. You are compelled to think by reading the works of the Greeks, they introduce you to the process of their thoughts, and by this force you to accompany them with your own thoughts, until you arrive as it were by your own mind at the principles of their systems … The Hindus, on the other hand, are dogmatical. They commence synthetically with a statement of their principles, yet do not condescend to unfold the train of thought which has led to them ( as quoted in Ganeri, 2001 , p. 14).

As a consequence, of these attitudes one can see how and why it may have been acceptable to exclude Indian contributions to logic for the purposes of teaching. The guiding idea is that if the Hindu Syllogism is actually confused and not a good form of reasoning, then we ought not to teach it in a critical thinking course . Thus, one needs to defend the plausibility of teaching the Hindu Syllogism through a partial defence of what is valuable in it. Below I offer an account of some of the criticisms of the Hindu Syllogism, based on the work of Ganeri (1996 , 2001 ). From there I proceed to a defence of the Hindu Syllogism through an examination of J. L. Shaw's (2010 , 2016a , 2016b ) work on the distinctions between inference for oneself and inference for another, and Ga n ˙ ngeśa's notion of relevance, and my own distinction between different models through which we can understand a piece of reasoning.

The criticisms of the so-called Hindu Syllogism come largely from having two important figures in western logic in mind when thinking about the Hindu Syllogism. The figures are Aristotle and Mill. The former is important for his work on the codification of deductive patterns of inference. The latter is important for his work on inductive inference. Here are some common criticisms of the Hindu Syllogism:

It is redundant, since the Thesis and Conclusion say the same thing. It is superfluous, since the Application step is unnecessary. It is a convoluted hybrid of two distinct types of reasoning: inductive and deductive. In particular the argument can be broken down as follows:Deductive component:

All locations where there is smoke are locations where there is fire. There is smoke on the hill. ∴ There is fire on the hill. Notice this has the same form as Aristotle's argument: All Men are Mortal. Socrates is a Man. ∴ Socrates is Mortal. Inductive component: In a kitchen a fire is followed by smoke. ∴ In all cases fire is followed by smoke.

Given that the argument can be broken down into two independent and distinct arguments it can be argued that: (i) the good part is simply the deductive version offered by Aristotle, and (ii) the bad part is offered by Akṣapāda when the inductive component is combined with the deductive component. The inductive component joined to the deductive component is bad because a single instance is never capable of proving a universal rule. On an available western interpretation the critical question is: why does Akṣapāda think that the observation of fire in the kitchen followed by smoke is enough to justify the claim that all locations where there is smoke are locations where there is fire ? This question can be amplified into an argument that suggests that we should not teach the Hindu Syllogism in critical thinking, since it would confuse students about the difference between inductive and deductive reasoning. Although that critique assumes that we have the right account of how to divide different kinds of reasoning, I will forgo challenging that claim and simply show how the Hindu Syllogism can be defended even with that account in place. Thus, it will be useful to decode the western gaze on the Hindu Syllogism by providing an interpretative lens that is available from within western philosophy and classical Indian philosophy. 8

A corrective lens for the western gaze on the Hindu Syllogism

Not all western philosophers saw classical Indian philosophy in a negative light. Some who were more careful readers of the tradition saw that something drastically different could be going on. These interpretations are largely in line with how several philosophers in the Nyāya tradition see the steps in the set up of the Hindu Syllogism. I will build a defence of the Hindu Syllogism based on some of these ideas in conjunction with the following idea. Tarka-vidyā is the science of debate. It is an open question whether we should think of the classical Indian tradition of engaging debate, logic and philosophy along the same lines as we find in Plato's presentation of philosophy as distinct from rhetoric, and Aristotle's codification of logic separately from rhetoric. In particular there is nothing in classical Indian philosophy that speaks to the issue of separating ‘philosophy’ from the art of persuasion. All traditions of Indian philosophy are steeped in debate, and have their own competing manuals of debate.

Following the work of J. L. Shaw (2016a) it is worth noting three points. First , the theory of inference in classical Indian philosophy is largely based on the idea of how to cause a specific cognition (the conclusion) to arise on the basis of steps leading to the conclusion. Second , a good argument is one that is free of specific kinds of defects that can block the conclusion from arising in the correct way. Third , it is central to understanding inference in classical Indian philosophy to pay attention to the distinction between inference for oneself vs. inference for another and the concept of relevance as it pertains to questions and answers. 9 Finally, as a helpful comparative guide, we can distinguish between three models of reasoning:

In the manipulation model reasoning is fundamentally about manipulating a person's mind so that they believe what you want them to believe—no matter how that is brought about through reasoning. In the veritic model reasoning is fundamentally about finding the truth. In the erotetic model reasoning is fundamentally about engaging questions that arise from natural doubts or through dialectical inquiry.

Given the different models of reasoning we might ask: what base model of reasoning is at play in the western interpretation of the Hindu Syllogism? If the answer comes from philosophers and logicians from the Anglo-European tradition, it is likely to be the case that the veritic model is used, since that model is what is associated with philosophy and with the science of logic. Logic is about what follows from what. For example, propositional logic is about what we can conclude about the truth of a compound formula, such as (P ∧ Q), on the basis of what the truth-value is of each of its components, such as that P is true and Q is true. However, we can look at the Hindu Syllogism from another perspective.

According to the Nyāya each of the sentences in an inference for others is an answer to a question and each of them, except the last one, will give rise to a question. Moreover, each of them is used to generate a cognition in the hearer ( Shaw, 2010 , p. 45).

In an inference for others, all the five sentences are needed, because each of them is an answer to a different question and gives some new information. But in an inference for oneself all of them are not required and there is no need to use a sentence. Hence a deaf and a mute person can also have an inferential cognition ( Shaw, 2010 , p. 46).

According to Ga n ˙ ngeśa, a Navya-Nyāya philosopher, there are several types of relevance ( san n ˙ gati ). The three important kinds for inference are: (i) justification ( upodghāta ), (ii) causing-effect ( kāryatva ), and (iii) cessation of objectionable questions ( avasara ). These three concepts of relevance are tied to an epistemic account of inference in terms of answering certain questions that arise from doubt. The steps in an inference aim to provide justification that puts an end to questions, including questions about the sequence of steps. This conception is central for understanding the classical Indian conception of dialectical reasoning. This account of relevance deals with (erotetic ordering-effects). The core idea is that by sequencing statements in a certain way relative to certain intellects we can lead one to the conclusion we want and end questions that arise either from doubt or objections ( Shaw, 2016b , pp. 286–293).

Let us look at what happens when you reinterpret the Hindu Syllogism as an inference for others under the erotetic model bearing in mind the sequencing of statements:

According to Shaw ( 2016a , pp. 92–100), the correct account of the Hindu Syllogism is the following:

( pratijñā ): The hill has fire. (The thesis is an answer to a question that arises on the basis of doubt. The question is: what is to be established?)

( hetu) : Because of smoke. (The reason is an answer to the question: what signifies what is to be established? In this case smoke signifies what is to be established.)

( udāharaṇa ): Wherever there is smoke there is fire, like in a kitchen when one is cooking and observes fire followed by smoke. (The rule/example is an answer to the question: why should one consider a to be a signifier of b ? In this case: why is smoke a signifier of fire? The answer is given by stating a rule along with examples.)

( upanaya ): The case of smoke on the hill is like the case of smoke in the kitchen. (The application step answers the question: Is the hill characterised by the particular and relevant kind of smoke?)

( nigamana ): The hill has fire. (The conclusion is an answer to the question: Is the fire, which is the significate of this kind of smoke, present on the hill? This is how the conclusion removes the doubt expressed in the thesis.)

Under the erotetic/inference-for-others model nothing is redundant and nothing is superfluous, the steps follow naturally from a series of questions that one would ask their interlocutor for the purposes of understanding why they believe that there is a fire on the hill. And importantly, the erotetic model does not preclude the discovery of truth. Rather, it aims at it through the investigation of questions. The main point is that one is brought into critiquing the Hindu Syllogism as redundant and superfluous in virtue of not drawing a distinction between an inference for oneself vs . an inference for others as well as failing to distinguish between different models we can use to understand a representation of reasoning. Who or what is the representation for?

Furthermore, Shaw informs us that some theorists in classical Indian philosophy think of how many steps there should be in an inference for others relative to one person's understanding of another's intellect . 10 For example, some scholars point out that for a sharp intellect one might only use the third and fourth step, and for a middle intellect one might only use the third, fourth and fifth step; while for a soft intellect one should use all five steps. This kind of theory makes sense if we are focused on a causal account of how the conclusion is caused to be cognised in an individual. The core question being: what does it take to correctly cause someone to cognise the conclusion in a way in which they will understand it ?

Thus, a complete understanding of the theory of cognition and the context of how the theory of argument and debate developed in India is required for understanding why exactly the steps are given. Once that is in place the initial objections go away.

Consider the Inductive Veritic version:

I have observed fire followed by smoke in my kitchen. ∴ Wherever there is smoke there is fire.

By contrast, the Analogical Erotetic version looks good.

Asha: Why do you believe that wherever there is smoke there is fire?

Anu: I have observed fire followed by smoke in my kitchen. Have you observed that?

Anu: I think the case of fire followed by smoke in my kitchen is the same as what is going on over there where I see smoke on the hill.

Asha: Why do you think these cases are similar?

Anu: Well I have never seen fire without smoke nor have I ever seen smoke without fire. That is I have always observed the co-presence of smoke and fire and co-absence of smoke and fire.

In the dialogue the main point of offering the example is not to inductively offer support for the conclusion. Rather, the point is to offer an example that has the following properties:

The interlocutor is likely to have experienced the same thing. The example has the properties of the universal claim. One can move from the example to an understanding of why one would believe the universal claim.

We can see the force of the use of the example in the dialogue by paying attention to what would happen had the interlocutor, Asha, responded differently. Imagine the following alteration in the conversation.

Asha: No! I have never seen fire followed by smoke in my kitchen because I don't cook. So, I don't see any reason to think that there is smoke on the hill over there because there is fire on the hill in a way that is similar to what is observed in a kitchen when one is cooking.

We can interpret Anu as giving the example of the kitchen, as opposed to observing fire followed by smoke in another case, because there is a likelihood that Asha has experienced something similar that would allow her to see why Anu holds that wherever there is smoke there is fire. Now, when Asha answers in the negative, this puts Anu in the situation of having to produce another example, since the first example cannot be used to persuade or help Asha understand why one should or would believe that there is fire on the hill simply because there is smoke on the hill and wherever there is smoke there is fire.

Moreover, we should be sensitive to the difference between the following questions:

Argument : What is the argument?

Knowledge : How are the premises of the argument known?

Persuasion : How do I get someone to believe the conclusion?

A natural question to ask after we have identified an argument is: how are the premises known? While the tradition stemming from Aristotle forward tends to separate the identification of the argument from how the premises are known, and how we should go about convincing someone in a debate, the tradition stemming from Akṣapāda does not. The Hindu Syllogism binds the logical, epistemic and persuasive aspects of reasoning together. And in fact when we look at scientific reasoning, this is what we often see. In science we are always concerned with using induction and deduction together. The idea that an argument can be good in science independently of the knowability of the premises is anathema to scientific investigation. Thus, we can see that there are virtues to at least a comparative examination of what counts as a legitimate argument form, and that by introducing our students to what an argument is through a comparative examination we allow them to have an open mind about how discussion and argumentation can be conducted.

Premise 3: Critical thinking education should include contributions from non-western philosophers.

Even though I have argued that there are legitimate things we can teach from outside the western tradition of logic and critical thinking, it does not follow that we should include them in a course on critical thinking and logic. Thus, I will begin a defence of this premise by examining a change that has occurred in textbooks for critical thinking. I will use the change that has occurred as the basis for posing a critical question: how can we allow for one kind of change, and not another kind of change?

If we examine, for example, the 1 st –10 th editions of Hurley's Concise Introduction to Logic and compare it to the 12 th edition we will see some changes with respect to explanations and problem sets, but we will also note an additional stark contrast. While the earlier editions only discuss philosophical contributions from men, such as Aristotle, Boole, Venn, Frege, Quine and Kripke, the 12 th edition includes discussion of Ruth Barcan Marcus and Ada Byron Lovelace. 11 Why was the change made? One hypothesis is that there was external pressure on the author from either the public at large, the external reviewers, or from publishers to change the fact that they were representing critical thinking and logic as a place where only men contributed. There are two basic ideas here. First, it is wrong to present logic through the eyes of the contributions of men, if in fact women did make contributions. Second, there might be something like an upward identity trajectory for women in logic and critical thinking when we present it alongside the fact that women made important contributions to the field. Another way to see the second point is as follows: by not presenting the works of women in logic, teachers and the book itself reinforced, the already present idea, that logic and critical thinking is for men, and not for women (more on this in the third section). But now to the critical question: why include women and leave out non-western thinkers? One way to show that there is no good reason to draw a difference is simply to examine a number of responses to this question and show how each is ineffective. The responses to the question will come by way of objections to the idea of including non-western sources.

Objection 1: Non-western thinkers do not belong in a logic and critical thinking textbook because they have no ideas that pertain to logic and critical thinking .

Response 1: In the prior section I have defended the idea that the Nyāya School of classical Indian philosophy has important ideas that are contributions to logic and critical reasoning. So, at this point what is important to point out is that the Nyāya School is one of many traditions that could be appealed to. Contributions, to name a few, have also been made by Africana, Jain, Buddhist, Arabic and Mohist traditions.

Objection 2: Non-western thinkers contributed ideas to logic and critical thinking, but all of their contributions are false, irrelevant, or not important .

Response 2: In the prior section I argued that one can read the Hindu Syllogism as a confused bit of proto-logic that forms part of the general history of logic, but that this reading is not necessarily the only one available. Against the reading I offered a corrective lens internal to the western tradition, based on the distinction between veritic and erotetic models of reasoning, that can be used to show how the Hindu Syllogism makes sense. Thus, the main response is that some of our thoughts about contributions from non-western philosophers are themselves confused by imposing a singular western lens on them when we are interpreting them. More importantly, we have the following situation. In some cases we could be interpreting a contribution from a non-western thinker as being incoherent because we are using the wrong lens for interpreting what is going on. In another case, it may be that the contribution is wrong only because we assume that there is only one correct understanding of western logic, as if no one in western logic has debated what the correct account of logic is. For example, independently of the contributions of non-western thinkers there is a debate, internal to western philosophy, over whether the logical connectives should be given a classical, intuitionistic or paraconsistent interpretation. And that debate sits alongside the debate over whether logical monism or logical pluralism is correct, the debate about whether there is more than one correct account of the consequence relationship: B is a logical consequence of A. But perhaps it is too much to defend the claim that the contributions coming from non-western traditions are in fact correct or better than those found in a standard logic and critical thinking textbook. So, lets consider a stronger, and distinct objection.

Objection 3: Logic and critical thinking textbooks should only contain information that is to the best of our knowledge true .

Response 3: The core of the objection is that we should only include contributions from non-western thinkers once they have been defended at a higher level and shown to be superior to, or at least as good as, the ideas that are presently discussed in an introductory level book. One argument for this is by way of analogy. Just as we don't include discussion of intuitionistic logic in an introduction to logic and critical thinking course, but rather only classical logic, we need not include ideas from non-western logic. Only the best, and true ideas about logic and critical thinking should be in an introductory level book.

Of course, this objection would be powerful, if it were in fact true. That is, if it were true that logic and critical thinking textbooks only contain true theories about how to reason. Lets consider one issue found in many introductory level textbooks: the inference from a universal proposition to a particular, often discussed as existential import .

1. All men are mortal ∴ 2. Some men are mortal.

Under Aristotle's interpretation the universal claim that All As are Bs entails the particular claim that Some As are Bs, because we can only be talking about categories that contain at least one instance. However, Boole disagrees, since some universal sentences articulate essential properties of entities, or definitions of entities, which are true, without there being anything that falls under one of the categories.

1. All unicorns are single-horned creatures. ∴ 2. Some unicorns are single-horned creatures.

On Boole's interpretation, universal claims, such as All As are Bs, need not imply particular claims, such as Some As are Bs, because there might not be any entities that fall under one or the other of the categories. The fact that we have a true statement about unicorns embedded in the sentence ‘All unicorns are single-horned creatures’ can be very useful even if there are no unicorns. For example, we may wonder whether there are any creatures of a certain kind, and then go search for them on the basis of the statement. Surely, we can discover that there are no creatures of the relevant kind. As a consequence, we would conclude that there are no unicorns.

Thus, Boole's interpretation and Aristotle's both make sense. So, it seems reasonable to teach them. But then what is the objection to teaching the Hindu Syllogism alongside Aristotle's syllogism? The fact is: logic and critical thinking textbooks do not teach: (i) only things that are true, and (ii) things that are uncontroversial truths. For the most part they teach that which has been canonised. There is no reason a comparative presentation of the Hindu Syllogism and Aristotle's Syllogism cannot be taught in much the same way that we currently teach Aristotle's Square of Opposition comparatively with Boole's interpretation of it, where existential import fails. The fact is: even if the Hindu Syllogism is inferior to Aristotle's ( which it isn't ) we can still teach them comparatively as we already do in the case of teaching universal to particular inferences.

Conclusion: Critical thinking education should be revised so as to be inclusive of contributions from non-western thinkers.

Let me conclude my presentation of the argument by clarifying the conclusion of it so as to block an immediate objection to it, as opposed to the premises. One might simply object to the conclusion by pointing to the fact that there are textbooks available to educators that focus on cross-cultural critical thinking, or at least there are texts that are sensitive to ideas that come from outside of the western canon. For example, Wanda Teays's (1996) ground breaking Second Thoughts: Critical Thinking from a Multicultural Perspective , and Maureen Linker's (2015) Intellectual Empathy: Critical Thinking for Social Justice , are two texts that include material from non-western traditions. However, this objection to the conclusion, based on pointing to texts like Teays's and Linker's rests on a confusion between two ways in which critical thinking can be cross-culturally sensitive.

The multicultural approach to critical thinking takes critical thinking tools that originated in the west and applies them to the multicultural world we live in. By contrast, the cross - cultural approach to critical thinking aims to include tools that originated from non-western traditions into the actual curriculum of critical thinking for the purposes of improving the set of tools available and being respectful of the idea of inclusion in critical thinking. While the two approaches are distinct, they are not mutually exclusive. One could write a text that is both cross-cultural and multicultural. For example, meditation is a tool of critical thinking that derives from Hindu and Buddhist philosophy. It aims to help us gain critical self-understanding of our own mental states. It can be included in a critical thinking textbook as an example of critical thinking from outside the western canon. It is, for the most part, a non-western contribution to critical thinking.

Moreover, it should be clear that the argument offered here aims at the cross-cultural inclusion approach.

Suppose now that the argument for inclusion of non-western ideas into critical thinking education is good. One critical question we can ask is the following: where should non-western ideas about critical thinking and logic be taught? One response is simply the following: of course non-western contributions to logic and critical thinking should be taught. However, they should be taught in an area studies course, such as Asian Philosophy . They do not belong in an introductory level course on logic and critical thinking, especially one that aims to help us understand how to critically think in the context of public policy and decision making through civic debate and public discourse.

The Character View holds that critical thinking involves the acquisition and proper deployment of specific skills as well as the acquisition of specific character traits, dispositions, attitudes, and habits of mind. These components are aspects of the ‘critical spirit’.

The Comprehensive View holds that critical thinking involves (i) the development of the appropriate skills that are constitutive of critical thinking, (ii) along with the appropriate character traits, dispositions, attitudes, and habits of mind, which are constitutive of the ‘critical spirit’. However, it also requires (iii) that the skills/tools and the nature of the ‘critical spirit’ be derived from all traditions that have contributed to critical discourse. Finally, the view requires that at some point a critical thinker engage the meta-critical question about critical thinking. That is, that a critical thinker acquire a proper understanding and appreciation of the sources of critical discourse for the purposes of bringing harmony to all that participate in the activity.

On the basis of this distinction, the following argument can be made. At the introductory level the primary goal of a course on critical thinking and logic is to teach students thinking skills, since the skills are essential for college success, life-long learning, civic engagement and public discourse. As a consequence, the historical source from which the skills derive is not important. Rather, the skill itself is important. One way to amplify the argument's force is to concede that it was a mistake to include references to western thinkers in the presentation of logic and critical thinking in the first place. The simple idea is that just as there is a difference between maths and the history of maths, there is a difference between logic and critical thinking, and the history of it.

This argument is powerful, since there is so much need for students to learn critical thinking skills as opposed to the mere history of the discipline. But as soon as this point is made, a key presumption is revealed: there are no skills that can be acquired through studying non-western contributions to logic and there is nothing to be gained critically by studying logic and critical thinking from a historically informed global perspective .

However, there is an interesting and substantial response that can be given to this point. The argument builds from the discussion in the prior section where I explored the relationship between the inclusion of women in critical thinking and logic textbooks in contrast to the absence of non-western thinkers. I will present the argument as an analogy:

Inclusion of women in critical thinking and logic textbooks along with women role models for critical thinking and logic education reduces stereotype threat . The problem that women face in critical thinking and logic education is sufficiently similar to the case of minorities.∴ Inclusion of minorities in critical thinking and logic textbooks with minority role models for critical thinking and logic education would reduce stereotype threat for minorities.

Stereotype threat occurs when a person believes they will be judged on the basis of some group-based stereotype. They do not need to believe the stereotype , and the stereotype need not even be prevalent in their environment . All that is necessary to activate this particular social identity threat is that a person believes that others will treat them negatively or evaluate them unfairly on the basis of one of their social identities. For example, a woman who thinks either that ‘women are not logical’ is true or that many other people believe this to be true may find that such a belief impacts her performance on logical tasks or enjoyment of these tasks ( Lehan, 2015 , pp. 3–4).

A female philosophy student will probably be in the minority as a woman in her department, and she'll almost certainly be in the minority as a woman if she takes classes in the more stereotypically male areas like (for example) logic, language and metaphysics. As she continues on to higher levels of study, the number of women will be steadily diminishing. In any class she takes other than feminist philosophy, she's likely to encounter a syllabus that consists overwhelmingly (often exclusively) of male authors . The people teaching most of the classes are also very likely to be male. All of these factors calling attention to low numbers of women are known to provoke stereotype threat. Since stereotype threat has its strongest effect on the most committed students, this means that the most committed women are likely to underperform ( Saul, 2013 , p. S. 2.1, emphasis added ).

Saul's point, in the emphasised text, is equally true of minority students and their upward trajectory in philosophy. The syllabi and the people teaching the courses will largely be white males.

[A] successful method for reducing stereotype threat is the introduction of counter-stereotype role models. One way to do this is to introduce students to members of the stereotyped group who have done well in the area. For example, “when female students are exposed to women that have performed successfully in mathematics and science related fields, they perform better than female students who do not have examples of women with such performance” … One study showed that reading essays about women who are successful in math can reduce the negative effects of stereotype threat … “Thus, direct and indirect exposure to women that have successfully navigated the field can be enough to reduce the negative impacts of stereotype threat for female students”… This suggests the importance of highlighting women in logic. “[T]he direction of [the] impact [of role model introduction] depends on the believed attainability of their success: Models of attainable success can be inspiring and self-enhancing, whereas models of unattainable success can be threatening and deflating”. In the interest of attainability, it is also extremely important to mention women currently working in logic such as Audrey Yap, Penelope Maddy, Dorothy Edgington, Susan Haack and many others conveniently listed on the Women in Logic list ( Lehan, 2015 , pp. 10–11).

Thus, given that the technique of including women in critical thinking textbooks, and as role models in the classroom, has successfully led to stereotype reduction for women, we can legitimately ask: would the same technique work for minorities? It seems that the relevant question to explore is: are the two cases similar enough? Are the stereotypes that women face the same as the stereotypes that minorities face? And interestingly: what about the intersectional case of minority women? Here are some important considerations.

Unlike the case of the category woman , the category minority is quite diverse with various stereotype alterations within the category. For example, do Asians face the same stereotype threat in a critical thinking and logic course that African Americans or Latin Americans face? Arguably they do not, given the model minority status that is often attributed to Asian Americans (Indians, Pakistani, Chinese, Koreans or Japanese). The difference is that teachers, in the US, don't typically look at Asian Americans thinking that they are going to do poorly in a critical thinking or logic course as much as they think that an African American or Latin American might. But this opens up the intersectionality question: given that everyone that has a race has a gender, could it be that the stereotype threat that women face applies without any thought to racial differences? More specifically, do teachers operate with different implicit biases about Asian women than African American women or Latin American women? And do these gender-race interactions alter the stereotype threat?

More research needs to be done on these questions. For the purposes of what I am arguing here, I cannot answer them. What is relevant to my argument is that we look closely at the fact that there are two distinct questions in the area, one concerning performance, the other concerning retention. Suppose that Asian Americans, either male or female, generally perform well on critical thinking and logic, so that they do not face a stereotype threat the way an African American male or a Latina female might. We might say something like the following. Because of the stereotype threats that the African American and the Latin American faces they perform poorly, and their poor performance is one factor that accounts for why they do not stay in the field of philosophy. However, this cannot be the explanation in the case of Asian Americans, since there is no relevantly similar stereotype threat. Many Asian women perform extremely well on first-year courses in logic and critical thinking.

Philosophy as a science could [not] originate among the Orientals, who, though susceptible of the elements of high culture, were content simply to retain them in a spirit of passive resignation ( as quoted in Ganeri, 2001 , p. 13).

The core idea is that showing interest in Asian philosophy is showing interest in something that is mystical, non-rational and not really philosophy or science. Asians are often pressured into performing well in the sciences as a sign of intelligence. Thus, studying Asian philosophy is studying Asian religion, and not studying science. Anglophone philosophy focuses on logic and reason, and the stereotype of, for example Chinese or Indian philosophy, is that it does not, but in some form is mystical –in a bad sense. Consequently, Asian students typically adopt the dominant interests of western philosophers. The idea is that to be a real philosopher one must adopt an interest in western philosophy, since that is where one finds the true origins of rationality and science. In fact one often finds that it is easier for non-Asians to show a genuine interest in Asian philosophy than it is for an Asian to show an interest, since Europeans do not face a stereotype threat when engaging Asian philosophy. Rather, they are seen as having an open-minded interest in other traditions.

As a consequence, what can be seen is that the inclusion of non-western thinkers in critical thinking and logic education isn't just about informing others that non-western thinkers have contributed to critical thinking and logic in important ways. If it were about that, it could be solved by an area studies course. Rather, it is about altering perceptions, held by westerners and non-westerners about the content of Asian philosophy. By introducing it in the context of an introduction to critical thinking and logic course we do away with the idea that there is something called Buddhist logic or Chinese logic. We introduce students to critical thinking and logic through contributions from everyone that in fact did contribute. In short:

We can make clear that critical thinking doesn't just come from the Greco-Roman-European tradition. It is part of the human condition. Many cultures contributed in interesting and controversial ways to what falls under the semantic range of the English phrase ‘critical thinking’. By introducing critical thinking through a cross-cultural lens we can reduce stereotype threat revolving around the idea that non-western cultures did not contribute to critical thinking, which is often touted as the prized reason for studying the humanities. We can help minority students that are interested stay in philosophy. Help the dominant group come to a better understanding of the roots of critical thinking. We can point out that how one person debates and discusses an issue of importance to their lives doesn't always follow the way in which another person does. And that this kind of cross-cultural understanding is important for the possibility of meaningful public discourse, disagreement and the development of epistemic tolerance and temper—tolerance of other epistemic norms.

How should public education enable the ethical implementation and proper functioning of democratic processes, such as voting on the basis of public and civic discourse?

Public education should provide citizens of a political body with basic skills in critical thinking, civic debate and ethical public discourse,

We live in a multicultural world where it is no longer possible to say that the demographics of, for example the US and the UK, are not sufficiently diverse across Indian, Chinese, Arabic, African … persons of origin to leave out ideas about critical discourse and discussion emanating from these traditions. To present critical thinking as originating from the human condition, as opposed to the western condition, is to give proper place to each individual, in a diverse body of individuals, who participates in an ethical public exchange of ideas leading to an outcome that pertains to all.

I would like to thank Purushottama Bilimoria, Karin Brown, Janet Stemwedel, Rita Manning, Peter Hadreas, Tom Leddy, Krupa Patel, Jessica Kraft, Stephen Phillips, members of the Association for Informal Logic and Critical Thinking, The Society for Philosophy in the Contemporary World, San Jose State University's 2015 Buddhism Conference , and The Society for Asian and Comparative Philosophy for discussion of this piece. I would also like to thank two anonymous referees of JOPE for their generous and outstanding comments on this piece. The ideas in this paper were much improved by their suggestions and guidance. I also owe a special intellectual debt to B. K. Matilal's (1985 , 1998 ), and Jonardon Ganeri's (1996 , 2001 , 2004 , 2011 ) outstanding work on Indian Logic. I also owe a deep debt of gratitude to Jaysankar Lal Shaw for his patience in explaining the importance of the precise formulation of the Nyāya account of inference, relevance and the distinction between inference for oneself and inference for others. Finally, I would like to thank my wife Manjula Rajan for helping me to see, through actual engagement, how the Hindu Syllogism works. Her constant evaluation of examples and pressing me for examples has shown me how the method actually works. This paper is actually written in a form that mixes Aristotle's Syllogism and Akṣapāda's Syllogism.

It should be noted here that the distinction between the content question and the normative question is notional. One could argue that the content question either determines the answer to the normative question or it restricts the acceptable answers to it. I am notionally separating these so as to not presuppose a specific answer to the question: how is the content of critical thinking related to the norms of civic debate and public discourse?

I take this work here to be an instance of the public-to-philosophy direction of fit through the aid of Kraft's work on public debate in The Atlantic . Her work pushed me to examine the presuppositions of what is going on in critical thinking and logic education.

It should be clear that in pointing to the actions of these students I am in no way endorsing their behaviour. Rather, I am using their actions as a moment for reflection on what constitutes critical thinking and what should be the norms for engaging in public discourse. Furthermore, it is important to note that there is more than one interpretation of what the students are trying to do by not engaging with the standard rules of civic debate that they were informed of prior to the competition. For example, it is possible to interpret their acts not as an engagement with an alternative model of critical thinking, but rather as an act of civil disobedience. If their act is one of civil disobedience, then it is unlikely that we can claim that they are engaging in an alternative form of critical thinking. However, regardless of the multiple interpretations, it is possible to use an interpretation of their actions as a guide to the critical question: could they be engaging in critical thinking and civic debate albeit an alternative one that may have its own merits?

Stephen Phillips's Critical Thinking in Service of Knowledge: Nyāya according to the Nyāya school of Classical Indian Philosophy , a currently unpublished presentation, has a discussion of this way of drawing the distinction.

In this section and the next I borrow heavily from the work of Ganeri, 1996 , 2001 and 2004 . While there are many controversies surrounding what actually happens in classical Indian logic, for the purposes of this paper I have decided to present a picture that shows that there are important contributions from Indian logic that can be used to teach critical thinking and logic at the introductory level. I take it that just as one can teach first-order logic while recognising that there are controversies concerning it, one can also teach portions of classical Indian logic while recognising that there are controversies concerning how to interpret it.

See Matilal, 1985 , p. 11 for discussion of the comparative point about division between different kinds of debate in Nyāya vs. Meno .

The version I am offering of the standard example derives from the work of Jaysankar Lal Shaw in his Nyāya on the Sources of Knowledge ( Shaw, 2016a ) and conversation. In his work he has articulated a sustained analysis of how the standard example of inference is to be presented. Although there is a debate in Indian philosophy, historically and in contemporary commentary, on the nature of inference, this should be no barrier to teaching the inference, for if the existence of a debate were sufficient, then we would not be teaching Aristotle either.

It is important to note, as B K. Matilal, 1985 , pp. 2–3 does, that western Indologists and philosophers are not the only people to blame when it comes to confusions about the so-called ‘Hindu Syllogism’. Matilal critiques S.C. Vidyābhūṣaṇa's very own article Influence of Aristotle on the Development of the syllogism in Indian Logic, which appeared in the pioneering work History of Indian Logic published in 1920. In that article Vidyābhūṣaṇa attempts to show that there are some commonalities between ‘The Syllogism in Indian Logic’ and the ‘logical rules’ and syllogism as found in Aristotle.

For a sustained presentation of the core ideas see the Inference section in Shaw, 2016a , for an excellent discussion of the relevant points.

Shaw informs us that according to Srinivasa Dasa in his book Jyatīndramata-dīpikā we must think of how many steps there are in a syllogism for others relative to our understanding of their intellect.

For example, compare Chapters 1 & 6 of the 12th edition with Chapters 1 & 6 of the 8th edition. Both chapters are on propositional logic, but only the 12th edition contains the presentation of Ruth Barcan Marcus, p. 35, and Ada Byron Lovelace p. 353. The 8th edition does not contain either. Yet both editions contain a discussion note on the history of logic, see p. 5 in the 8th edition, and compare that to p. 5 in the 12th edition.

Ganeri , J. ( 1996 ) The Hindu Syllogism: Nineteenth-Century Perceptions of Indian Logical Thought , Philosophy East and West , 46 . 1 , pp. 1 – 16 .

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Ganeri , J. ( 2001 ) Indian Logic: A Reader ( New York , Routledge Publishing ).

Ganeri , J. ( 2004 ) Indian Logic , in: D. Gabbay and J. Woods (eds.) Handbook of the History of Logic Vol. 1 . ( Amsterdam, Netherlands , Elsevier B. V. Publishing) .

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Ganeri , J. ( 2011 ) The Lost Age of Reason: Philosophy in Early Modern India (1450 – 1700 ) ( Oxford , Oxford University Press ).

Huemer , M. ( 2005 ) Is Critical Thinking Epistemically Responsible? Metaphilosophy , 36 . 4 , pp. 522 – 531 .

Hurley , P. ( 2014 ) A Concise Introduction to Logic. 12 th edition ( Boston, MA , Cengage-Wadsworth Publishing ).

Kraft , J. ( 2014 ) Hacking Traditional College Debate's White Privilege Problem . The Atlantic , April 16, 2014. Available online at: http://www.theatlantic.com/education/archive/2014/04/traditional-college-debate-white-privilege/360746/ . (Last accessed: February 15, 2015).

Lehan , V. ( 2015 ) Reducing Stereotype Threat in First-Year Logic Classes , Feminist Philosophy Quarterly , 1 . 2.4 , pp. 1 – 13 .

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Shaw , J. ( 2016a ) The Nyāya on Sources of Knowledge , in: J. L. Shaw (ed.) The Collected Writings of Jaysankar Lal Shaw: Indian Analytic and Anglophone Philosophy ( London , Bloomsbury Publishing) .

Shaw , J. ( 2016b ) The Concept of Relevance ( Saṅgati ) in Gaṅgeśa , in: J. L Shaw (ed.) The Collected Writings of Jaysankar Lal Shaw: Indian Analytic and Anglophone Philosophy ( London , Bloomsbury Publishing) .

Siegel , H. ( 1993 ) Not by Skill Alone: The Centrality of Character to Critical Thinking , Informal Logic , 25 . 3 , pp. 163 – 175 .

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2 Logic and the Study of Arguments

If we want to study how we ought to reason (normative) we should start by looking at the primary way that we do reason (descriptive): through the use of arguments. In order to develop a theory of good reasoning, we will start with an account of what an argument is and then proceed to talk about what constitutes a “good” argument.

I. Arguments

Arguments are a set of statements (premises and conclusion).
The premises provide evidence, reasons, and grounds for the conclusion.
The conclusion is what is being argued for.
An argument attempts to draw some logical connection between the premises and the conclusion.
And in doing so, the argument expresses an inference: a process of reasoning from the truth of the premises to the truth of the conclusion.

Example : The world will end on August 6, 2045. I know this because my dad told me so and my dad is smart.

In this instance, the conclusion is the first sentence (“The world will end…”); the premises (however dubious) are revealed in the second sentence (“I know this because…”).

II. Statements

Conclusions and premises are articulated in the form of statements . Statements are sentences that can be determined to possess or lack truth. Some examples of true-or-false statements can be found below. (Notice that while some statements are categorically true or false, others may or may not be true depending on when they are made or who is making them.)

Examples of sentences that are statements:

It is below 40°F outside.
Oklahoma is north of Texas.
The Denver Broncos will make it to the Super Bowl.
Russell Westbrook is the best point guard in the league.
I like broccoli.
I shouldn’t eat French fries.
Time travel is possible.
If time travel is possible, then you can be your own father or mother.

However, there are many sentences that cannot so easily be determined to be true or false. For this reason, these sentences identified below are not considered statements.

Questions: “What time is it?”
Commands: “Do your homework.”
Requests: “Please clean the kitchen.”
Proposals: “Let’s go to the museum tomorrow.”

Question: Why are arguments only made up of statements?

First, we only believe statements . It doesn’t make sense to talk about believing questions, commands, requests or proposals. Contrast sentences on the left that are not statements with sentences on the right that are statements:

It would be non-sensical to say that we believe the non-statements (e.g. “I believe what time is it?”). But it makes perfect sense to say that we believe the statements (e.g. “I believe the time is 11 a.m.”). If conclusions are the statements being argued for, then they are also ideas we are being persuaded to believe. Therefore, only statements can be conclusions.

Second, only statements can provide reasons to believe.

Q: Why should I believe that it is 11:00 a.m.? A: Because the clock says it is 11a.m.
Q: Why should I believe that we are going to the museum tomorrow? A: Because today we are making plans to go.

Sentences that cannot be true or false cannot provide reasons to believe. So, if premises are meant to provide reasons to believe, then only statements can be premises.

III. Representing Arguments

As we concern ourselves with arguments, we will want to represent our arguments in some way, indicating which statements are the premises and which statement is the conclusion. We shall represent arguments in two ways. For both ways, we will number the premises.

In order to identify the conclusion, we will either label the conclusion with a (c) or (conclusion). Or we will mark the conclusion with the ∴ symbol

Example Argument:

There will be a war in the next year. I know this because there has been a massive buildup in weapons. And every time there is a massive buildup in weapons, there is a war. My guru said the world will end on August 6, 2045.

There has been a massive buildup in weapons.
Every time there has been a massive buildup in weapons, there is a war.

∴ There will be a war in the next year.

Of course, arguments do not come labeled as such. And so we must be able to look at a passage and identify whether the passage contains an argument and if it does, we should also be identify which statements are the premises and which statement is the conclusion. This is harder than you might think!

There is no argument here. There is no statement being argued for. There are no statements being used as reasons to believe. This is simply a report of information.

The following are also not arguments:

Advice: Be good to your friends; your friends will be good to you.

Warnings: No lifeguard on duty. Be careful.

Associated claims: Fear leads to anger. Anger leads to the dark side.

When you have an argument, the passage will express some process of reasoning. There will be statements presented that serve to help the speaker building a case for the conclusion.

IV. How to L ook for A rguments [1]

How do we identify arguments in real life? There are no easy, mechanical rules, and we usually have to rely on the context in order to determine which are the premises and the conclusions. But sometimes the job can be made easier by the presence of certain premise or conclusion indicators. For example, if a person makes a statement, and then adds “this is because …,” then it is quite likely that the first statement is presented as a conclusion, supported by the statements that come afterward. Other words in English that might be used to indicate the premises to follow include:

firstly, secondly, …
for, as, after all
assuming that, in view of the fact that
follows from, as shown / indicated by
may be inferred / deduced / derived from

Of course whether such words are used to indicate premises or not depends on the context. For example, “since” has a very different function in a statement like “I have been here since noon,” unlike “X is an even number since X is divisible by 4.” In the first instance (“since noon”) “since” means “from.” In the second instance, “since” means “because.”

Conclusions, on the other hand, are often preceded by words like:

therefore, so, it follows that
hence, consequently
suggests / proves / demonstrates that
entails, implies

Here are some examples of passages that do not contain arguments.

1. When people sweat a lot they tend to drink more water. [Just a single statement, not enough to make an argument.]

2. Once upon a time there was a prince and a princess. They lived happily together and one day they decided to have a baby. But the baby grew up to be a nasty and cruel person and they regret it very much. [A chronological description of facts composed of statements but no premise or conclusion.]

3. Can you come to the meeting tomorrow? [A question that does not contain an argument.]

Do these passages contain arguments? If so, what are their conclusions?

Cutting the interest rate will have no effect on the stock market this time around, as people have been expecting a rate cut all along. This factor has already been reflected in the market.
So it is raining heavily and this building might collapse. But I don’t really care.
Virgin would then dominate the rail system. Is that something the government should worry about? Not necessarily. The industry is regulated, and one powerful company might at least offer a more coherent schedule of services than the present arrangement has produced. The reason the industry was broken up into more than 100 companies at privatization was not operational, but political: the Conservative government thought it would thus be harder to renationalize (The Economist 12/16/2000).
Bill will pay the ransom. After all, he loves his wife and children and would do everything to save them.
All of Russia’s problems of human rights and democracy come back to three things: the legislature, the executive and the judiciary. None works as well as it should. Parliament passes laws in a hurry, and has neither the ability nor the will to call high officials to account. State officials abuse human rights (either on their own, or on orders from on high) and work with remarkable slowness and disorganization. The courts almost completely fail in their role as the ultimate safeguard of freedom and order (The Economist 11/25/2000).
Most mornings, Park Chang Woo arrives at a train station in central Seoul, South Korea’s capital. But he is not commuter. He is unemployed and goes there to kill time. Around him, dozens of jobless people pass their days drinking soju, a local version of vodka. For the moment, middle-aged Mr. Park would rather read a newspaper. He used to be a bricklayer for a small construction company in Pusan, a southern port city. But three years ago the country’s financial crisis cost him that job, so he came to Seoul, leaving his wife and two children behind. Still looking for work, he has little hope of going home any time soon (The Economist 11/25/2000).
For a long time, astronomers suspected that Europa, one of Jupiter’s many moons, might harbour a watery ocean beneath its ice-covered surface. They were right. Now the technique used earlier this year to demonstrate the existence of the Europan ocean has been employed to detect an ocean on another Jovian satellite, Ganymede, according to work announced at the recent American Geo-physical Union meeting in San Francisco (The Economist 12/16/2000).
There are no hard numbers, but the evidence from Asia’s expatriate community is unequivocal. Three years after its handover from Britain to China, Hong Kong is unlearning English. The city’s gweilos (Cantonese for “ghost men”) must go to ever greater lengths to catch the oldest taxi driver available to maximize their chances of comprehension. Hotel managers are complaining that they can no longer find enough English-speakers to act as receptionists. Departing tourists, polled at the airport, voice growing frustration at not being understood (The Economist 1/20/2001).

V. Evaluating Arguments

Q: What does it mean for an argument to be good? What are the different ways in which arguments can be good? Good arguments:

Are persuasive.
Have premises that provide good evidence for the conclusion.
Contain premises that are true.
Reach a true conclusion.
Provide the audience good reasons for accepting the conclusion.

The focus of logic is primarily about one type of goodness: The logical relationship between premises and conclusion.

An argument is good in this sense if the premises provide good evidence for the conclusion. But what does it mean for premises to provide good evidence? We need some new concepts to capture this idea of premises providing good logical support. In order to do so, we will first need to distinguish between two types of argument.

VI. Two Types of Arguments

The two main types of arguments are called deductive and inductive arguments. We differentiate them in terms of the type of support that the premises are meant to provide for the conclusion.

Deductive Arguments are arguments in which the premises are meant to provide conclusive logical support for the conclusion.

1. All humans are mortal

2. Socrates is a human.

∴ Therefore, Socrates is mortal.

1. No student in this class will fail.

2. Mary is a student in this class.

∴ Therefore, Mary will not fail.

1. A intersects lines B and C.

2. Lines A and B form a 90-degree angle

3. Lines A and C form a 90-degree angle.

∴ B and C are parallel lines.

Inductive arguments are, by their very nature, risky arguments.

Arguments in which premises provide probable support for the conclusion.

Statistical Examples:

1. Ten percent of all customers in this restaurant order soda.

2. John is a customer.

∴ John will not order Soda..

1. Some students work on campus.

2. Bill is a student.

∴ Bill works on campus.

1. Vegas has the Carolina Panthers as a six-point favorite for the super bowl.

∴ Carolina will win the Super Bowl.

VII. Good Deductive Arguments

The First Type of Goodness: Premises play their function – they provide conclusive logical support.

Deductive and inductive arguments have different aims. Deductive argument attempt to provide conclusive support or reasons; inductive argument attempt to provide probable reasons or support. So we must evaluate these two types of arguments.

Deductive arguments attempt to be valid.

To put validity in another way: if the premises are true, then the conclusion must be true.

It is very important to note that validity has nothing to do with whether or not the premises are, in fact, true and whether or not the conclusion is in fact true; it merely has to do with a certain conditional claim. If the premises are true, then the conclusion must be true.

Q: What does this mean?

The validity of an argument does not depend upon the actual world. Rather, it depends upon the world described by the premises.
First, consider the world described by the premises. In this world, is it logically possible for the conclusion to be false? That is, can you even imagine a world in which the conclusion is false?

Reflection Questions:

If you cannot, then why not?
If you can, then provide an example of a valid argument.

You should convince yourself that validity is not just about the actual truth or falsity of the premises and conclusion. Rather, validity only has to do with a certain logical relationship between the truth of the premise and the truth of the conclusion. So the only possible combination that is ruled out by a valid argument is a set of true premises and false conclusion.

Let’s go back to example #1. Here are the premises:

1. All humans are mortal.

If both of these premises are true, then every human that we find must be a mortal. And this means, that it must be the case that if Socrates is a human, that Socrates is mortal.

Reflection Questions about Invalid Arguments:

Can you have an invalid argument with a true premise?
Can you have an invalid argument with true premises and a true conclusion?

The s econd type of goodness for deductive arguments: The premises provide us the right reasons to accept the conclusion.

Soundness V ersus V alidity:

Our original argument is a sound one:

∴ Socrates is mortal.

Question: Can a sound argument have a false conclusion?

VIII. From Deductive Arguments to Inductive Arguments

Question: What happens if we mix around the premises and conclusion?

2. Socrates is mortal.

∴ Socrates is a human.

1. Socrates is mortal

∴ All humans are mortal.

Are these valid deductive arguments?

NO, but they are common inductive arguments.

Other examples :

Suppose that there are two opaque glass jars with different color marbles in them.

1. All the marbles in jar #1 are blue.

2. This marble is blue.

∴ This marble came from jar #1.

1. This marble came from jar #2.

2. This marble is red.

∴ All the marbles in jar #2 are red.

While this is a very risky argument, what if we drew 100 marbles from jar #2 and found that they were all red? Would this affect the second argument’s validity?

IX. Inductive Arguments:

The aim of an inductive argument is different from the aim of deductive argument because the type of reasons we are trying to provide are different. Therefore, the function of the premises is different in deductive and inductive arguments. And again, we can split up goodness into two types when considering inductive arguments:

The premises provide the right logical support.
The premises provide the right type of reason.

Logical S upport:

Remember that for inductive arguments, the premises are intended to provide probable support for the conclusion. Thus, we shall begin by discussing a fairly rough, coarse-grained way of talking about probable support by introducing the notions of strong and weak inductive arguments.

A strong inductive argument:

The vast majority of Europeans speak at least two languages.
Sam is a European.

∴ Sam speaks two languages.

Weak inductive argument:

This quarter is a fair coin.

∴ Therefore, the next coin flip will land heads.

At least one dog in this town has rabies.
Fido is a dog that lives in this town.

∴ Fido has rabies.

The R ight T ype of R easons. As we noted above, the right type of reasons are true statements. So what happens when we get an inductive argument that is good in the first sense (right type of logical support) and good in the second sense (the right type of reasons)? Corresponding to the notion of soundness for deductive arguments, we call inductive arguments that are good in both senses cogent arguments.

With which of the following types of premises and conclusions can you have a strong inductive argument?
With which of the following types of premises and conclusions can you have a cogent inductive argument?

X. Steps for Evaluating Arguments:

Read a passage and assess whether or not it contains an argument.
If it does contain an argument, then identify the conclusion and premises.
If yes, then assess it for soundness.
If not, then treat it as an inductive argument (step 3).
If the inductive argument is strong, then is it cogent?

XI. Evaluating Real – World Arguments

An important part of evaluating arguments is not to represent the arguments of others in a deliberately weak way.

For example, suppose that I state the following:

All humans are mortal, so Socrates is mortal.

Is this valid? Not as it stands. But clearly, I believe that Socrates is a human being. Or I thought that was assumed in the conversation. That premise was clearly an implicit one.

So one of the things we can do in the evaluation of argument is to take an argument as it is stated, and represent it in a way such that it is a valid deductive argument or a strong inductive one. In doing so, we are making explicit what one would have to assume to provide a good argument (in the sense that the premises provide good – conclusive or probable – reason to accept the conclusion).

The teacher’s policy on extra credit was unfair because Sally was the only person to have a chance at receiving extra credit.

Sally was the only person to have a chance at receiving extra credit.
The teacher’s policy on extra credit is fair only if everyone gets a chance to receive extra credit.

Therefore, the teacher’s policy on extra credit was unfair.

Valid argument

Sally didn’t train very hard so she didn’t win the race.

Sally didn’t train very hard.
If you don’t train hard, you won’t win the race.

Therefore, Sally didn’t win the race.

Strong (not valid):

If you won the race, you trained hard.
Those who don’t train hard are likely not to win.

Therefore, Sally didn’t win.

Ordinary workers receive worker’s compensation benefits if they suffer an on-the-job injury. However, universities have no obligations to pay similar compensation to student athletes if they are hurt while playing sports. So, universities are not doing what they should.

Ordinary workers receive worker’s compensation benefits if they suffer an on-the-job injury that prevents them working.
Student athletes are just like ordinary workers except that their job is to play sports.
So if student athletes are injured while playing sports, they should also be provided worker’s compensation benefits.
Universities have no obligations to provide injured student athletes compensation.

Therefore, universities are not doing what they should.

Deductively valid argument

If Obama couldn’t implement a single-payer healthcare system in his first term as president, then the next president will not be able to implement a single-payer healthcare system.

Obama couldn’t implement a single-payer healthcare system.
In Obama’s first term as president, both the House and Senate were under Democratic control.
The next president will either be dealing with the Republican-controlled house and senate or at best, a split legislature.
Obama’s first term as president will be much easier than the next president’s term in terms of passing legislation.

Therefore, the next president will not be able to implement a single-payer healthcare system.

Strong inductive argument

Sam is weaker than John. Sam is slower than John. So Sam’s time on the obstacle will be slower than John’s.

Sam is weaker than John.
Sam is slower than John.
A person’s strength and speed inversely correlate with their time on the obstacle course.

Therefore, Sam’s time will be slower than John’s.

XII. Diagramming Arguments

All the arguments we’ve dealt with – except for the last two – have been fairly simple in that the premises always provided direct support for the conclusion. But in many arguments, such as the last one, there are often arguments within arguments.

Obama example :

The next president will either be dealing with the Republican controlled house and senate or at best, a split legislature.

∴ The next president will not be able to implement a single-payer healthcare system.

It’s clear that premises #2 and #3 are used in support of #4. And #1 in combination with #4 provides support for the conclusion.

When we diagram arguments, the aim is to represent the logical relationships between premises and conclusion. More specifically, we want to identify what each premise supports and how.

This represents that 2+3 together provide support for 4

This represents that 4+1 together provide support for 5

When we say that 2+3 together or 4+1 together support some statement, we mean that the logical support of these statements are dependent upon each other. Without the other, these statements would not provide evidence for the conclusion. In order to identify when statements are dependent upon one another, we simply underline the set that are logically dependent upon one another for their evidential support. Every argument has a single conclusion, which the premises support; therefore, every argument diagram should point to the conclusion (c).

Sam Example:

Sam is less flexible than John.
A person’s strength and flexibility inversely correlate with their time on the obstacle course.

∴ Therefore, Sam’s time will be slower than John’s.

In some cases, different sets of premises provide evidence for the conclusion independently of one another. In the argument above, there are two logically independent arguments for the conclusion that Sam’s time will be slower than John’s. That Sam is weaker than John and that being weaker correlates with a slower time provide evidence for the conclusion that Sam will be slower than John. Completely independent of this argument is the fact that Sam is less flexible and that being less flexible corresponds with a slower time. The diagram above represent these logical relations by showing that #1 and #3 dependently provide support for #4. Independent of that argument, #2 and #3 also dependently provide support for #4. Therefore, there are two logically independent sets of premises that provide support for the conclusion.

Try diagramming the following argument for yourself. The structure of the argument has been provided below:

All humans are mortal
Socrates is human
So Socrates is mortal.
If you feed a mortal person poison, he will die.

∴ Therefore, Socrates has been fed poison, so he will die.

This section is taken from http://philosophy.hku.hk/think/ and is in use under creative commons license. Some modifications have been made to the original content. ↵

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Introduction

Learning Outcomes

Indicative assessment, inherent requirements, requisite and incompatibility, prescribed texts, other information.

Offerings and Dates

This course aims to introduce students to practices of argumentation, critical analysis, and evaluation. Such skills in critical thinking are integral to the discipline of philosophy. They are also tremendously useful in other academic domains, in the workplace, and in everyday life. The course aims to help students to understand and develop the skills required for critical thinking, and to encourage them to explore the ways in which these skills can further the pursuit of both their academic and nonacademic projects. Topics covered may include: inductive and deductive reasoning, common fallacies, the use of rhetoric, and elementary logic.

Upon successful completion, students will have the knowledge and skills to:

Critically analyse one’s opinions to identify underlying assumptions and unforeseen consequences (especially assumptions or consequences that are open to objections).
Analyse one’s and others’ arguments and examine whether they are successful.
Analyse one’s and others’ unsuccessful arguments by identifying (1) where they have committed fallacies and (2) where their arguments are vulnerable to any criticisms.
Formulate and communicate arguments whose conclusions are supported by given reasons.

Course Contact: Dr Rebecca Cross

T: 02 61250982

E: [email protected]

Take-home Examination (1000 words) (20%) — Learning outcomes 1, 2, 3 (20) [LO null]
Essay (30%, 1500 words) — Learning outcomes 1, 2, 3, 4 (30) [LO null]
Final Examination (2 hours) (40%) — Learning outcomes 1, 2, 3, 4 (40) [LO null]
Lecture and tutorial participation (10%) — Learning outcomes 1, 2, 3, 4 (10) [LO null]

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

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Tuition fees are for the academic year indicated at the top of the page.

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees .

If you are an undergraduate student and have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). You can find your student contribution amount for each course at Fees . Where there is a unit range displayed for this course, not all unit options below may be available.

Course fees

Offerings, dates and class summary links.

ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage .

Second Semester

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Non-Fiction

Replete with exercises and suggestive material for the classroom, this volumes serves as the standard Humanities textbook and reference guide for today's student.

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COMMENTS

Logic and Critical Thinking
The course aims to help students to understand and develop the skills required for critical thinking, and to encourage them to explore the ways in which these skills can further their academic and non-academic pursuits. Topics covered may include: various forms of reasoning, common fallacies, the use of rhetoric, elementary logic, and decision ...
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PHIL1005; logic and critical thinking weekly lecture notes; Download. Save Share. PHIL1005 Notes. University: Australian National University. Course: Logic And Critical Thinking (PHIL1005) 36 Documents. Students shared 36 documents in this course. Info More info. Download. Save. PHIL1005 NOTES FOR FINAL EXAM.
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ANU; Logic And Critical Thinking; Logic And Critical Thinking (PHIL1005) 48 48 documents. 0 0 questions 72 72 students. Follow this course Chat. Lecture notes. Date Rating. year. Ratings. PHIL1005; logic and critical thinking weekly lecture notes. 30 pages 2020/2021 100% (3) 2020/2021 100% (3) Save. PHIL1005 Logic and critical thinking. 46 ...
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Introduction to Logic and Critical Thinking pg 139-146 Clear and Present Thinking pg 63-66 (plus exercises on pg 69-70) An Introduction to Reasoning pg 2-5 (plus exercises on pg 17) Chapter 6 is derived from Fundamental Methods of Logic pg 163-175 Introduction to Logic and Critical Thinking pg 158-169 Chapter 7 is derived from
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This course aims to introduce students to practices of argumentation, critical analysis, and evaluation. Such skills in critical thinking are integral to the discipline of philosophy. They are also tremendously useful in other academic domains, in the workplace, and in everyday life. The course aims to help students to understand and develop the skills required for critical thinking, and to ...
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