the elements of arguments an introduction to critical thinking and logic

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The Elements of Arguments: An Introduction to Critical Thinking and Logic

The Elements of Arguments introduces such central critical thinking topics as informal fallacies, the difference between validity and truth, basic formal propositional logic, and how to extract arguments from texts. Turetzky aims to prevent common confusions by clearly explaining a number of important distinctions, including propositions vs. propositional attitudes, propositions vs. states of affairs, and logic vs. rhetoric vs. psychology. Exercises are provided throughout, including numerous informal arguments that can be assessed using the skills and strategies presented within the text.

ISBN-10 1554814073
ISBN-13 978-1554814077
Publisher Broadview Press
Publication date April 11, 2019
Language English
Dimensions 6.5 x 0.62 x 9 inches
Print length 336 pages
See all details

Editorial Reviews

“Compared to other books in this area I find The Elements of Arguments to be near the top in quality. In terms of teaching to a diverse group of students from varying backgrounds and with different abilities, I find it to be exceptional. The author is extremely sensitive to traditional problems and confusions that surround the subject making it a challenge to teach. He has given the higher education community a standard of the highest caliber with admirable benefit to the students we serve.” ― Dennis Brandon, California State University, Northridge

“In a crowded ﬁeld of introductory texts, The Elements of Arguments stands out. Turetzky has achieved in one volume an admirably clear presentation of both ‘critical thinking’ and ‘logic’ as distinct but overlapping disciplines. Instructors will beneﬁt greatly from the book’s lucid deﬁnitions, careful distinctions, and abundant exercises. Students will ﬁnd their reading rewarded with varied and accessible examples as well as insightful sections relating logic to other ﬁelds such as psychology, rhetoric, and the philosophy of language. Using this text, students will be well prepared to handle reasoning and arguments in any subject.” ― Tyler Will, Colorado State University

From the Back Cover

About the author.

Philip Turetzky taught philosophy at Colorado State University, the University of South Dakota, Ripon College, and other post-secondary institutions. He is the author of Time (Routledge, 1998) and numerous academic articles.

Product details

Publisher ‏ : ‎ Broadview Press (April 11, 2019)
Language ‏ : ‎ English
Paperback ‏ : ‎ 336 pages
ISBN-10 ‏ : ‎ 1554814073
ISBN-13 ‏ : ‎ 978-1554814077
Item Weight ‏ : ‎ 1.05 pounds
Dimensions ‏ : ‎ 6.5 x 0.62 x 9 inches
#142 in Logic (Books)
#861 in Philosophy of Logic & Language
#9,530 in Core

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The Elements of Arguments: An Introduction to Critical Thinking and Logic

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Pursuing Truth: A Guide to Critical Thinking

Chapter 2 arguments.

The fundamental tool of the critical thinker is the argument. For a good example of what we are not talking about, consider a bit from a famous sketch by Monty Python’s Flying Circus : 3

2.1 Identifying Arguments

People often use “argument” to refer to a dispute or quarrel between people. In critical thinking, an argument is defined as

A set of statements, one of which is the conclusion and the others are the premises.

There are three important things to remember here:

Arguments contain statements.
They have a conclusion.
They have at least one premise

Arguments contain statements, or declarative sentences. Statements, unlike questions or commands, have a truth value. Statements assert that the world is a particular way; questions do not. For example, if someone asked you what you did after dinner yesterday evening, you wouldn’t accuse them of lying. When the world is the way that the statement says that it is, we say that the statement is true. If the statement is not true, it is false.

One of the statements in the argument is called the conclusion. The conclusion is the statement that is intended to be proved. Consider the following argument:

Calculus II will be no harder than Calculus I. Susan did well in Calculus I. So, Susan should do well in Calculus II.

Here the conclusion is that Susan should do well in Calculus II. The other two sentences are premises. Premises are the reasons offered for believing that the conclusion is true.

2.1.1 Standard Form

Now, to make the argument easier to evaluate, we will put it into what is called “standard form.” To put an argument in standard form, write each premise on a separate, numbered line. Draw a line underneath the last premise, the write the conclusion underneath the line.

Calculus II will be no harder than Calculus I.
Susan did well in Calculus I.
Susan should do well in Calculus II.

Now that we have the argument in standard form, we can talk about premise 1, premise 2, and all clearly be referring to the same thing.

2.1.2 Indicator Words

Unfortunately, when people present arguments, they rarely put them in standard form. So, we have to decide which statement is intended to be the conclusion, and which are the premises. Don’t make the mistake of assuming that the conclusion comes at the end. The conclusion is often at the beginning of the passage, but could even be in the middle. A better way to identify premises and conclusions is to look for indicator words. Indicator words are words that signal that statement following the indicator is a premise or conclusion. The example above used a common indicator word for a conclusion, ‘so.’ The other common conclusion indicator, as you can probably guess, is ‘therefore.’ This table lists the indicator words you might encounter.


Therefore	Since
So	Because
Thus	For
Hence	Is implied by
Consequently	For the reason that
Implies that
It follows that

Each argument will likely use only one indicator word or phrase. When the conlusion is at the end, it will generally be preceded by a conclusion indicator. Everything else, then, is a premise. When the conclusion comes at the beginning, the next sentence will usually be introduced by a premise indicator. All of the following sentences will also be premises.

For example, here’s our previous argument rewritten to use a premise indicator:

Susan should do well in Calculus II, because Calculus II will be no harder than Calculus I, and Susan did well in Calculus I.

Sometimes, an argument will contain no indicator words at all. In that case, the best thing to do is to determine which of the premises would logically follow from the others. If there is one, then it is the conclusion. Here is an example:

Spot is a mammal. All dogs are mammals, and Spot is a dog.

The first sentence logically follows from the others, so it is the conclusion. When using this method, we are forced to assume that the person giving the argument is rational and logical, which might not be true.

2.1.3 Non-Arguments

One thing that complicates our task of identifying arguments is that there are many passages that, although they look like arguments, are not arguments. The most common types are:

Explanations
Mere asssertions
Conditional statements
Loosely connected statements

Explanations can be tricky, because they often use one of our indicator words. Consider this passage:

Abraham Lincoln died because he was shot.

If this were an argument, then the conclusion would be that Abraham Lincoln died, since the other statement is introduced by a premise indicator. If this is an argument, though, it’s a strange one. Do you really think that someone would be trying to prove that Abraham Lincoln died? Surely everyone knows that he is dead. On the other hand, there might be people who don’t know how he died. This passage does not attempt to prove that something is true, but instead attempts to explain why it is true. To determine if a passage is an explanation or an argument, first find the statement that looks like the conclusion. Next, ask yourself if everyone likely already believes that statement to be true. If the answer to that question is yes, then the passage is an explanation.

Mere assertions are obviously not arguments. If a professor tells you simply that you will not get an A in her course this semester, she has not given you an argument. This is because she hasn’t given you any reasons to believe that the statement is true. If there are no premises, then there is no argument.

Conditional statements are sentences that have the form “If…, then….” A conditional statement asserts that if something is true, then something else would be true also. For example, imagine you are told, “If you have the winning lottery ticket, then you will win ten million dollars.” What is being claimed to be true, that you have the winning lottery ticket, or that you will win ten million dollars? Neither. The only thing claimed is the entire conditional. Conditionals can be premises, and they can be conclusions. They can be parts of arguments, but that cannot, on their own, be arguments themselves.

Finally, consider this passage:

I woke up this morning, then took a shower and got dressed. After breakfast, I worked on chapter 2 of the critical thinking text. I then took a break and drank some more coffee….

This might be a description of my day, but it’s not an argument. There’s nothing in the passage that plays the role of a premise or a conclusion. The passage doesn’t attempt to prove anything. Remember that arguments need a conclusion, there must be something that is the statement to be proved. Lacking that, it simply isn’t an argument, no matter how much it looks like one.

2.2 Evaluating Arguments

The first step in evaluating an argument is to determine what kind of argument it is. We initially categorize arguments as either deductive or inductive, defined roughly in terms of their goals. In deductive arguments, the truth of the premises is intended to absolutely establish the truth of the conclusion. For inductive arguments, the truth of the premises is only intended to establish the probable truth of the conclusion. We’ll focus on deductive arguments first, then examine inductive arguments in later chapters.

Once we have established that an argument is deductive, we then ask if it is valid. To say that an argument is valid is to claim that there is a very special logical relationship between the premises and the conclusion, such that if the premises are true, then the conclusion must also be true. Another way to state this is

An argument is valid if and only if it is impossible for the premises to be true and the conclusion false.

An argument is invalid if and only if it is not valid.

Note that claiming that an argument is valid is not the same as claiming that it has a true conclusion, nor is it to claim that the argument has true premises. Claiming that an argument is valid is claiming nothing more that the premises, if they were true , would be enough to make the conclusion true. For example, is the following argument valid or not?

If pigs fly, then an increase in the minimum wage will be approved next term.
An increase in the minimum wage will be approved next term.

The argument is indeed valid. If the two premises were true, then the conclusion would have to be true also. What about this argument?

All dogs are mammals
Spot is a mammal.
Spot is a dog.

In this case, both of the premises are true and the conclusion is true. The question to ask, though, is whether the premises absolutely guarantee that the conclusion is true. The answer here is no. The two premises could be true and the conclusion false if Spot were a cat, whale, etc.

Neither of these arguments are good. The second fails because it is invalid. The two premises don’t prove that the conclusion is true. The first argument is valid, however. So, the premises would prove that the conclusion is true, if those premises were themselves true. Unfortunately, (or fortunately, I guess, considering what would be dropping from the sky) pigs don’t fly.

These examples give us two important ways that deductive arguments can fail. The can fail because they are invalid, or because they have at least one false premise. Of course, these are not mutually exclusive, an argument can be both invalid and have a false premise.

If the argument is valid, and has all true premises, then it is a sound argument. Sound arguments always have true conclusions.

A deductively valid argument with all true premises.

Inductive arguments are never valid, since the premises only establish the probable truth of the conclusion. So, we evaluate inductive arguments according to their strength. A strong inductive argument is one in which the truth of the premises really do make the conclusion probably true. An argument is weak if the truth of the premises fail to establish the probable truth of the conclusion.

There is a significant difference between valid/invalid and strong/weak. If an argument is not valid, then it is invalid. The two categories are mutually exclusive and exhaustive. There can be no such thing as an argument being more valid than another valid argument. Validity is all or nothing. Inductive strength, however, is on a continuum. A strong inductive argument can be made stronger with the addition of another premise. More evidence can raise the probability of the conclusion. A valid argument cannot be made more valid with an additional premise. Why not? If the argument is valid, then the premises were enough to absolutely guarantee the truth of the conclusion. Adding another premise won’t give any more guarantee of truth than was already there. If it could, then the guarantee wasn’t absolute before, and the original argument wasn’t valid in the first place.

2.3 Counterexamples

One way to prove an argument to be invalid is to use a counterexample. A counterexample is a consistent story in which the premises are true and the conclusion false. Consider the argument above:

By pointing out that Spot could have been a cat, I have told a story in which the premises are true, but the conclusion is false.

Here’s another one:

If it is raining, then the sidewalks are wet.
The sidewalks are wet.
It is raining.

The sprinklers might have been on. If so, then the sidewalks would be wet, even if it weren’t raining.

Counterexamples can be very useful for demonstrating invalidity. Keep in mind, though, that validity can never be proved with the counterexample method. If the argument is valid, then it will be impossible to give a counterexample to it. If you can’t come up with a counterexample, however, that does not prove the argument to be valid. It may only mean that you’re not creative enough.

An argument is a set of statements; one is the conclusion, the rest are premises.
The conclusion is the statement that the argument is trying to prove.
The premises are the reasons offered for believing the conclusion to be true.
Explanations, conditional sentences, and mere assertions are not arguments.
Deductive reasoning attempts to absolutely guarantee the truth of the conclusion.
Inductive reasoning attempts to show that the conclusion is probably true.
In a valid argument, it is impossible for the premises to be true and the conclusion false.
In an invalid argument, it is possible for the premises to be true and the conclusion false.
A sound argument is valid and has all true premises.
An inductively strong argument is one in which the truth of the premises makes the the truth of the conclusion probable.
An inductively weak argument is one in which the truth of the premises do not make the conclusion probably true.
A counterexample is a consistent story in which the premises of an argument are true and the conclusion is false. Counterexamples can be used to prove that arguments are deductively invalid.

( Cleese and Chapman 1980 ) . ↩︎

Elements of Arguments: An Introduction to Crit Thinking and Logic

Author(s) Philip Turetzky
Publisher Broadview Press

Print ISBN 9781554814077, 1554814073

Etext isbn 9781460406465, 146040646x.

Copyright 2019
Available from $ 39.21 USD SKU: 9781460406465R180

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Elements of Arguments: An Introduction to Crit Thinking and Logic is written by Philip Turetzky and published by Broadview Press. The Digital and eTextbook ISBNs for Elements of Arguments: An Introduction to Crit Thinking and Logic are 9781460406465, 146040646X and the print ISBNs are 9781554814077, 1554814073. Save up to 80% versus print by going digital with VitalSource.

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The elements of arguments: an introduction to critical thinking and logic - softcover, turetzky, philip.

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“In a crowded field of introductory texts, The Elements of Arguments stands out. Turetzky has achieved in one volume an admirably clear presentation of both ‘critical thinking’ and ‘logic’ as distinct but overlapping disciplines. Instructors will benefit greatly from the book’s lucid definitions, careful distinctions, and abundant exercises. Students will find their reading rewarded with varied and accessible examples as well as insightful sections relating logic to other fields such as psychology, rhetoric, and the philosophy of language. Using this text, students will be well prepared to handle reasoning and arguments in any subject.” ― Tyler Will, Colorado State University

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Introduction to Logic and Critical Thinking

(10 reviews)

Matthew Van Cleave, Lansing Community College

Publisher: Matthew J. Van Cleave

Language: English

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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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The Elements of Arguments: An Introduction to Critical Thinking and Logic

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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:

Non-statements

Statements

What time is it?

Do your homework.

The time is 11:00 a.m.

My teacher wants me to do my homework.

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?


True	True
True	False
False	True
False	False

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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The elements of arguments : an introduction to critical thinking and logic

Philip Turetzky Published in 2019 in Peterborough Ontario Canada Tonawanda NY USA by Broadview Press

"The Elements of Arguments introduces such central critical thinking topics as informal fallacies, the difference between validity and truth, basic formal propositional logic, and how to extract ar... show more

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520			a "The Elements of Arguments introduces such central critical thinking topics as informal fallacies, the difference between validity and truth, basic formal propositional logic, and how to extract arguments from texts. Turetzky aims to prevent common confusions by clearly explaining a number of important distinctions, including: propositions vs. propositional attitudes, propositions vs. states of affairs, and logic vs. rhetoric vs. psychology. Exercises are provided throughout, including numerous informal arguments that can be assessed using the skills and strategies presented within the text."-- c Provided by publisher.
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Form : Its reasons and conclusion will be related in such a way that if the reasons are true, the conclusion will likely be true. Content : The reasons will make claims that are true, or have a high probability of being true. Context : The argument as a whole fits the circumstances in which it was intended to apply.

A thorough evaluation should subject an argument to scrutiny along each of these dimensions. In what follows, we present each in turn, commenting on strategies that one can use while evaluating arguments. At the end of this unit, you should be able to provide systematic, three-part evaluations of arguments that determine whether the conclusion should be believed.

If it's hot in Moscow, then it's unbearable in Lewiston. It's hot in Moscow. ---------------------- Therefore, it's unbearable in Lewiston.

While not the most interesting argument in the world, it is useful for our purposes because its structure is easy to observe. One good way of revealing the structure of an argument is to replace the sentences found in the reasons and conclusion with symbols---this takes your mind off of what the argument is about and forces you to attend to the structures of the sentences and the relationships among them. If we do that here, we get the following form (1):

If A, then B. A ---------------------- Therefore, B.

We replaced "It's hot in Moscow" with "A" and "It's unbearable in Lewiston" with "B". Now that we can see the form of the argument, though, we can use it to build other arguments with the same form. All we do is replace "A" and "B" in our symbolic form with other sentences. For more, see Expanded Notes on Argument Forms .

While the form of arguments isn't everything, it is an essential element nevertheless. As with buildings, if the structure of an argument is weak, the argument will be weak. If the structure is strong, then the argument could be a good one, depending on the other essential element, viz., content. If an argument's form is good, then the reasons will support the truth of the conclusion; otherwise, they will not. Given this, it is important to have a clear sense of argument form, as it is one aspect that you will want to evaluate. For our purposes, it will do to talk about two broad categories of argument forms, the certainty producing and the probability producing. Arguments within these categories conform to different standards, and we will describe these standards briefly. More detailed and systematic study of argument form can be found in courses in formal logic .

Certainty Producing Arguments (CPA). Also known as deductive arguments , these are intended to produce their conclusions with certainty. The rhetoric of the argument context can indicate the presence of CPAs, as can reliance on the mere form of sentences and the roles played by certain terms, e.g., "if ... then", "all", "or", etc. (See Expanded Notes on CPAs for more on this.) In addition, CPAs are often associated with the analysis of concepts, as opposed to the investigation of the world of our experience. Note, though, that these are mere rules of thumb for identifying CPAs.

To say that the conclusions are produced with certainty is to say that if the reasons are true in a CPA, then the conclusion must be true. A CPA that meets this standard is known as valid . Note, though, that the standard of validity is merely hypothetical---it says that IF the reasons are true, the conclusion me be true; thus, if the reasons are false, then all bets are off. This is just more evidence that form is only part of the story---you also need content, and it will be the content that determines truth and falsity of particular reasons, as we will see in the next section. In valid CPAs, we say that the conclusion follows from the reasons.

Good CPAs, then, are valid arguments in which the conclusion follows from the reasons. Bad CPAs do not guarantee their conclusions, and you can detect this through the use of counterexamples. A counterexample is a specific example, rooted in what is possible, that makes the reasons in a CPA true and the conclusion false. What this demonstrates is that the truth of the reasons does not force the conclusion to be true, and so the CPA in question fails to meet the standard of validity and is invalid . A very good technique for determining the quality of a CPA involves attempting to identify a counterexample; if you can, the argument is formally weak, but if you can't (and you've really looked), then the argument may well be quite good. Still, it would help to know a bit more about the details of CPAs, and in particular, what makes a good CPA good, aside from the fact that it doesn't make room for counterexample. For these details, see Expanded Notes on CPAs .

Probability Producing Arguments (PPA). Also known as non-deductive arguments , these are intended to increase the probability that their conclusions are true. That is, if the reasons are true in a PPA, then there will be a high probability that the conclusion is true, if the argument is a good one. Signs that indicate the presence of a PPA include (a) the conclusion speaks of things that go beyond the reasons, (b) the conclusion is more tentative and is not presented as certain, given the reasons, and (c) the argument presents a conclusion supported by scientific reasons. As before, these should be regarded as rules of thumb.

If the the truth of the reasons in a PPA raise to a high probability the truth of the conclusion, we will call the argument strong . Note that the standard of "high probability" is vague---there is no clear way of specifying this in general. What counts as "strong" will vary, then, from argument to argument and context to context. (So if you evaluate an argument as strong, it would be a good idea to have an argument ready to back up your evaluation!) To reflect the difference between CPAs and PPAs, we do not say that the conclusion of a PPA follows from its reasons; rather, we say that the reasons support the conclusion.

PPAs come in a greater variety than CPAs, so it is more difficult to provide a general characterization of what makes one good or bad. But there are standards that apply to these arguments, and it is important to familiarize yourself with them. There are several types of PPAs, and in the Expanded Notes on PPAs , we detail these types, describing them and commenting on the standards that apply to each. However, we can make a couple of general observations at this point. First, a PPA will typically be stronger if it is more detailed; the more vague a PPA is, the less compelling it will be. Second, a good PPA will typically have a conclusion that does not depend on a single, specific type of observation or data point, even if there are a lot of them; the broader the types of observations that support the conclusion, the stronger it generally is. (Think of a table---if it only has one leg, it won't be as stable as if it has several legs in different places.) Third, the stronger the conclusion of a PPA, the weaker the argument. If the conclusion is weak, it will not take as much to support it, and other things being equal, this will mean a stronger argument overall.

Form is very important, but it is hardly the only aspect of an argument that can be evaluated. In fact, form is not typically the obvious thing to evaluate---it is hidden beneath the surface and often difficult to ascertain. The more obvious aspect is that of content , i.e., what the argument is about. After completing Exercise One, continue on to the next section, where we discuss how to evaluate the content that fills in an argument's skeletal form.

If Idaho is larger than California, then it is larger than Alaska. Idaho is larger than California. ---------------------- Therefore, Idaho is larger than Alaska.

Evaluated in terms of its form, this is a good argument---it is a valid CPA of form (1) detailed above. But it is nevertheless a bad argument. After all, each of the sentences is false. Sentences (2) and (3) are clearly false, but so too is (1), since if Idaho were larger than California, it could still be smaller than Alaska, given that Alaska is bigger than California. What this demonstrates is that when it comes to argument quality, form isn't everything. Content matters, and here the content is in bad shape.

The content of an argument is what the argument is about , and this is based on what the sentences that constitute the argument are about. The primary measure of content quality is truth value. If any of the sentences are false, then the argument will be weak. If the sentences are true, then the argument will typically be strong, so long as it has good form. Consider argument (III):

Idaho is south of Canada. Nevada is south of Idaho. ---------------------- Therefore, Texas is south of Oklahoma.

All of the sentences in (III) are true, but it is still a bad argument. The truth values of (1) and (2) don't force (3) to be true because (1) and (2) have nothing to do with (3). Thus, the reasons and conclusion should have content that is related. This is often guaranteed by the form of the argument---in the case of (III), the argument has bad form, and this undermines the connection between the reasons and conclusion. (However, in certain unusual cases, an argument can have good form (logically speaking) and have true sentences and still be a bad argument, as is explained in the Expanded Notes on Content Evaluation .)

Thus, the evaluation of content is a two-part job. First, you need to determine the truth values of the reasons. Assuming that the form is in order, assessment of the reasons as true will generally imply that the argument is a good one. (Although don't judge before evaluating the context , as we will do in the next section.) There is little that can be said here about how you do this, as it depends on the discipline within which you're working. You might be able to tell by looking whether the reasons or true, or it might be a lot tougher than this. [INSTRUCTOR: You might wish to introduce at this point some specific detail about how one inspects substantive claims in your discipline for truth or falsity.] Second, you need to determine the overall thematic coherence of the argument. If the conclusion addresses a topic not mentioned in the reasons, or it goes beyond the reasons in a way that seems like a stretch, then that is a sign that the argument content might not be as coherent as it should be for the argument to be strong.

After finishing Exercise Two, proceed to the final section of this unit, Evaluating the Context .

Review the arguments in Grendel , Chapter 5, one last time and proceed to the Final Exercise. In the preceding sections, you should have identified and reconstructed an argument from that chapter. It is now time to bring your critical thinking about it to a close.

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Logic in Argumentative Writing

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This handout is designed to help writers develop and use logical arguments in writing. This handout helps writers analyze the arguments of others and generate their own arguments. However, it is important to remember that logic is only one aspect of a successful argument. Non-logical arguments , statements that cannot be logically proven or disproved, are important in argumentative writing—such as appeals to emotions or values. Illogical arguments , on the other hand, are false and must be avoided.

Logic is a formal system of analysis that helps writers invent, demonstrate, and prove arguments. It works by testing propositions against one another to determine their accuracy. People often think they are using logic when they avoid emotion or make arguments based on their common sense, such as "Everyone should look out for their own self-interests" or "People have the right to be free." However, unemotional or common sense statements are not always equivalent to logical statements. To be logical, a proposition must be tested within a logical sequence.

The most famous logical sequence, called the syllogism , was developed by the Greek philosopher Aristotle. His most famous syllogism is:

Premise 1: All men are mortal. Premise 2: Socrates is a man. Conclusion: Therefore, Socrates is mortal.

In this sequence, premise 2 is tested against premise 1 to reach the logical conclusion. Within this system, if both premises are considered valid, there is no other logical conclusion than determining that Socrates is a mortal.

This guide provides some vocabulary and strategies for determining logical conclusions.

The Development of Vygotsky’s Thought: An Introduction

Cite this chapter.

Norris Minick

Part of the book series: Cognition and Language ((CALS))

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The first part of this volume contains Vygotsky’s classic monograph Thinking and Speech , a work which was first published in Russian in 1934. The second contains a series of lectures that Vygotsky delivered in Leningrad in 1932. In addition to differences in subject matter and style, these two works are separated by an important conceptual shift in Vygotsky’s thinking which occurred in 1932 and 1933. Indeed, since several chapters of Thinking and Speech were written prior to 1933, the papers which constitute that volume also span this conceptual shift in the development of Vygotsky’s thought. As a consequence, if we are to understand these works, their relationship to one another, or their significance as part of the broader Vygotskian corpus, it is critical to consider the major changes that emerged in Vygotsky’s thinking as his perspectives developed between 1924 and 1934. 1

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Vygotsky’s Legacy: Understanding and Beyond

Thinking with the Rain. The Trajectory of a Metaphor in Vygotsky’s Theoretical Development

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Minick, N. (1987). The Development of Vygotsky’s Thought: An Introduction. In: Rieber, R.W., Carton, A.S. (eds) The Collected Works of L. S. Vygotsky. Cognition and Language. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1655-8_2

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The Elements of Arguments: An Introduction to Critical Thinking and Logic
The Elements of Arguments introduces such central critical thinking topics as informal fallacies, the difference between validity and truth, basic formal propositional logic, and how to extract arguments from texts. Turetzky aims to prevent common confusions by clearly explaining a number of important distinctions, including propositions vs. propositional attitudes, propositions vs. states of ...
The Elements of Arguments: An Introduction to Critical Thinking and Logic
The Elements of Arguments: An Introduction to Critical Thinking and Logic - Ebook written by Philip Turetzky. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read The Elements of Arguments: An Introduction to Critical Thinking and Logic.
The Elements of Arguments: An Introduction to Critical Thinking and Logic
The Elements of Arguments introduces such central critical thinking topics as informal fallacies, the difference between validity and truth, basic formal propositional logic, and how to extract arguments from texts.
The Elements of Arguments: An Introduction to Critical Thinking and Logic
_The Elements of Arguments_ introduces such central critical thinking topics as informal fallacies, the difference between validity and truth, basic formal propositional logic, and how to extract arguments from texts. ... Introduction to logic and critical thinking. Merrilee H. Salmon - 2013 - Australia: Wadsworth. The voice of reason ...
Chapter 2 Arguments
Chapter 2 Arguments. Chapter 2. Arguments. The fundamental tool of the critical thinker is the argument. For a good example of what we are not talking about, consider a bit from a famous sketch by Monty Python's Flying Circus: 3. Man: (Knock) Mr. Vibrating: Come in.
Elements of Arguments: An Introduction to Crit Thinking and Logic
Elements of Arguments: An Introduction to Crit Thinking and Logic is written by Philip Turetzky and published by Broadview Press. The Digital and eTextbook ISBNs for Elements of Arguments: An Introduction to Crit Thinking and Logic are 9781460406465, 146040646X and the print ISBNs are 9781554814077, 1554814073. Save up to 80% versus print by going digital with VitalSource.
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The Elements of Arguments: An Introduction to Critical Thinking and Logic by Turetzky, Philip - ISBN 10: 1554814073 - ISBN 13: 9781554814077 - Broadview Press - 2019 - Softcover
The Elements of Arguments: An Introduction to Critical Thinking and Logic
"In a crowded ﬁeld of introductory texts, The Elements of Arguments stands out. Turetzky has achieved in one volume an admirably clear presentation of both 'critical thinking' and 'logic' as distinct but overlapping disciplines. Instructors will beneﬁt greatly from the book's lucid deﬁnitions, careful distinctions, and abundant exercises.
Introduction to Logic and Critical Thinking
This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a ...
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1.1: What is an Argument?
Both logic and critical thinking centrally involve the analysis and assessment of arguments. "Argument" is a word that has multiple distinct meanings, so it is important to be clear from the start about the sense of the word that is relevant to the study of logic. In one sense of the word, an argument is a heated exchange of differing views ...
1: Introduction to Critical Thinking, Reasoning, and Logic
It may seem strange to begin a logic textbook with this question. 'Thinking' is perhaps the most intimate and personal thing that people do. Yet the more you 'think' about thinking, the more mysterious it can appear. It is the sort of thing that one intuitively or naturally understands, and yet cannot describe to others without great ...
PDF Argument Critical Thinking Logic And The Fallacies
The Elements of Arguments: An Introduction to Critical Thinking and Logic Philip Turetzky,2019-04-11 The Elements of Arguments introduces such central critical thinking topics as informal fallacies, the difference between validity
Introduction to Critical Thinking
Critical thinking is the ability to think clearly and rationally about what to do or what to believe. It includes the ability to engage in reflective and independent thinking. Someone with critical thinking skills is able to do the following: Understand the logical connections between ideas. Identify, construct, and evaluate arguments.
Logic and the Study of Arguments
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 ...
The Elements of Arguments: An Introduction to Critical Thinking and Logic
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The elements of arguments : an introduction to critical thinking and logic
"The Elements of Arguments introduces such central critical thinking topics as informal fallacies, the difference between validity and truth, basic formal propositional logic, and how to extract arguments from texts. Turetzky aims to prevent common confusions by clearly explaining a number of important distinctions, including: propositions vs. propositional attitudes, propositions vs. states ...
Critical Thinking Worksite: Argument Evaluation
In the following exercise, you will have the chance to test your context evaluation skills on a few argument/context pairs. When you have completed this exercise, you have finished the Critical Thinking Worksite. The only thing left to do is the final project, which is described in the next section. Exercise Three.
Logic
Non-logical arguments, statements that cannot be logically proven or disproved, are important in argumentative writing—such as appeals to emotions or values. Illogical arguments, on the other hand, are false and must be avoided. Logic is a formal system of analysis that helps writers invent, demonstrate, and prove arguments.
PDF Introductory Logic
statements; how to construct an argument and how to detect fallacies in argument." Terms, statements, arguments, fallacies—these are concepts that will become familiar to your stu - dents in this study of Introductory Logic: The Fundamentals of Thinking Well. James B. Nance April 2014 A NOTE to the TEACHER for the FIFTH EDITION
The Development of Vygotsky's Thought: An Introduction
The first part of this volume contains Vygotsky's classic monograph Thinking and Speech, a work which was first published in Russian in 1934. The second contains a series of lectures that Vygotsky delivered in Leningrad in 1932. In addition to differences in subject matter and style, these two works are separated by an important conceptual ...

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Pursuing Truth: A Guide to Critical Thinking

2.1 Identifying Arguments

2.1.1 Standard Form

2.1.2 Indicator Words

2.1.3 Non-Arguments

2.2 Evaluating Arguments

2.3 Counterexamples

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2 Logic and the Study of Arguments

I. Arguments

II. Statements

III. Representing Arguments

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

V. Evaluating Arguments

VI. Two Types of Arguments

VII. Good Deductive Arguments

VIII. From Deductive Arguments to Inductive Arguments

IX. Inductive Arguments:

X. Steps for Evaluating Arguments:

XI. Evaluating Real – World Arguments

XII. Diagramming Arguments

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