Topic Name Description
Course Syllabus Page Course Syllabus
1.1: Introduction to Critical Thinking Page Critical Thinking

Watch this video for a basic sense of what critical thinking is and why it is important.

Book Critical Thinking Skills

Read these four tutorials on critical thinking. As you read, compare the abilities that a person acquires after becoming a critical thinker with your own goals as a student, as well as with your future career and life goals.

1.2.1: The Elements of Meaning Book Meaning Analysis

While meaning may not seem like the sort of thing that needs explaining, the ways in which it is produced, both in speech and in writing, can lead to confusion and thus warrant close examination.

In this section, you will read about the nature of linguistic meaning, the different types of definitions, the difference between literal meaning and conversational implicature, and the difference between verbal and factual disputes.

Complete the exercises to enhance your critical thinking skills and your understanding of meaning.

1.2.2: Necessary and Sufficient Conditions Page Necessity and Sufficiency

Phenomena in the world are related to one another in all sorts of complicated ways. Sometimes we can say very generally whether one thing is necessary for something else or whether it is merely sufficient. The concepts of necessary and sufficient conditions help us understand and explain the different kinds of connections between concepts and how different states of affairs are related to each other.

1.2.3: Thinking Critically about Ordinary Language Book Meaning Analysis Continued

Thinking needs to be precise and clear, but the language we use to express our thoughts is often imprecise and misleading. In this section, you will read about identifying common ways language can lead us astray.

Complete all exercises and check your answers.

1.3: Assessing Sources Book Research Skills Tutorial

Read this tutorial, which discusses appropriate questions to ask to determine whether a source is credible and reliable. As you read, make a list of important questions to ask. Make notes under each question about why that question is important. Also, write down any tips to consider when answering each question.

Page Evaluating Sources and Peer Review

Watch these videos to learn about the basic principles of evaluating sources. The first video identifies characteristics of scholarly articles, and the second video explains the "peer review" editorial process.

Page Evaluating Internet Material

Read this article, which explains factors relevant to assessing the reliability of Internet sources. Many of the factors mentioned in this material are also relevant to assessing the reliability of other sources.

2.1.1: What Are Arguments? Book What is an Argument?

Read this section, which differentiates an argument in the logical sense from the ordinary language sense of a heated disagreement and introduces you to the basic structures of logical argument: statements, premises, and conclusions.

Complete Exercise 1, identifying which sentences are statements. Once you identify them, begin thinking about what premises might lead to those statements. When you finish, check your responses with the answer key.

If you would like to download the full textbook, it can be found here: Introduction to Logic and Critical Thinking.

Page More on Arguments

Read this tutorial, which explains how to identify an argument by picking out its components. Complete the exercises and check your answers.

2.1.2: How to Tell an Argument from a Non-Argument Book Identifying Arguments

Read this section, which will give you some tips on how to spot an argument. While the premise and conclusion indicators are not guarantees of an argument, they can assist you in identifying an argument.

Complete Exercise 2, distinguishing arguments from non-arguments and identifying the conclusion of argument sentences. Despite the name, the conclusion often precedes the premises when we present arguments in ordinary language. When you finish the exercise, check your answers against the answer key.

Page The Standard Format of an Argument

Read this tutorial, which explains how to put an argument in standard form. Be sure to complete the exercise.

2.2: Good Argument Form Book Validity and Soundness

These sections will introduce you to the concept of validity – the term for when the conclusion of an argument follows from its premises. Pay careful attention to the difference between validity and soundness. All sound arguments are valid, but not all valid arguments are sound. Remember that premises do not have to be true for an argument to be valid.

Complete Exercise 5, checking your answers against the key.

Book Validity, Soundness, and Valid Patterns

Validity and soundness are two of the most important concepts in the study of arguments, and they are often confused with one another. Read these three tutorials on the distinction between valid and sound arguments, their relationship to the truth of the statements that make them up, and the structural patterns that help us to recognize them.

Complete the exercises and check your answers.

Page Quiz on Truth, Validity, and Soundness

Complete this knowledge check, which tests your knowledge of the distinction between valid and sound arguments. Note that deductive arguments might be, but need not be, valid or sound; deductive arguments may be valid or invalid and sound or unsound.

Book Rounding Out Arguments

Read these sections to learn how to round out arguments conceptually. The first section will distinguish between two types of argument: deductive and inductive. Pay careful attention to the difference between these two, and think about which kind of argument you use more often. The second section will help you identify arguments with a missing premise and determine how and when to supply this missing premise. It will also introduce you to the principle of charity and the difference between normative and descriptive statements – three very important terms! The third section shows you three rhetorical devices to hint at further argument without actually going through the argument: assuring, guarding, and discounting.

Complete the exercises, then check your answers against the keys.

Book Hidden Assumptions, Inductive Reasoning, and Good Arguments

When arguments are stated verbally or in writing, their structure may not be completely explicit. The section on hidden assumptions provides clues about how to identify hidden assumptions. The section on inductive reasoning introduces the important concept of induction. Inductive arguments form a whole second class of arguments, alongside deductive ones, and will be important in our unit on scientific reasoning later on. The final section puts together a number of the ideas laid out so far to describe the characteristics of a good argument.

Complete the exercises and check your answer.

2.3: Visualizing How Arguments Work Book More Complex Argument Structures

Visualizing argument structure can help determine how directly or indirectly supporting evidence leads to a conclusion. This section gives examples of simple and more complex arguments using arrows to represent the structure of an argument. Complete the exercises and then check your answers. The answer key has the arguments in standard form, but there is no key for the diagramming.

Page Argument Mapping

Read this tutorial about how to construct an argument map. Argument maps are a way of visually representing the logical structure of an argument.

2.4: Analogical Arguments Book Analogical Arguments

Read this section about an inductive argument many people use quite frequently: arguments from analogy. As you read, think about the difference between relevant and irrelevant similarities when it comes to analogies, as well as relevant disanalogies. Being able to identify these will help you make stronger inductive arguments.

Complete the exercise and check your work against the answer key.

Page More on Analogical Arguments

Read this tutorial on analogical arguments. Arguments that are based on analogies have certain inherent weaknesses. This tutorial will help you find out how analogical arguments are structured and the most common ways they may be undermined.

2.5: Valid Argument Patterns Page Valid Argument Patterns

Read this tutorial on reducing valid arguments to their basic structure using argument patterns. This text previews the kind of analysis we will do much more of in Unit 4. This kind of strategy is sometimes useful in analyzing arguments in real-life situations. For example, you might see these types of questions and find identifying argument patterns useful for the Law School Admission Test (LSAT).

3.1: The Basics of Logic Page What is Logic?

Read this tutorial, which describes some basic logic concepts: validity, topic neutrality, necessity, and the difference between formal and informal reasoning. 

3.1.1: Logical Statements, Connectives, and Relations Page Formal Methods of Evaluation

Read this section for an introduction to formal logic. Formal logic gives us a framework for objective, logical evaluations of conclusions. It can help you make valid inferences for certain kinds of statements. This section will not go deeply into how to do this type of logic but rather explain why it is important and give some basic examples.

Book Statements, Logical Connectives, and Logical Relations

Statements are the fundamental units of arguments and proofs in logic. These tutorials explain how to identify statements and introduce some of the basic ways that statements may be related to one another.

Complete the exercises and check your answers.

3.1.2: Logic Puzzles Page Fun Logic Puzzles

Try your hand at some fun and tricky logic puzzles. Check your answers after you have solved them.

Page The World's Hardest Logic Puzzle Ever!

Complete this exercise, which will allow you to solve a difficult logic puzzle. Watch the video on this puzzle for a discussion of the solution.

3.2.1: How to Write Sentences in Sentential Logic Book Propositional Logic Functions

Read these four sections to learn how to identify and apply propositional (or sentential) logic functions. Using these symbols, you should be able to turn statements into symbolic formulas to more clearly see the logical connections taking place and determine when the conclusions are valid. It can look confusing at first, but moving slowly through these units will allow you to make valid logical proofs.

As you go, complete the exercises, then check your answers against the answer keys.

Note that the symbols used in some places can differ slightly from those used elsewhere. This is because there is not one standard set of symbols used for sentential logic, but a few. This table shows you the differences and helps translate between them.

In the resources in this course, the symbols for disjunction and negation are the same in both systems, but the symbols for conjunction, conditional, and biconditional are different.

Name Meaning Symbol 1 Symbol 2
Conjunction  and  &  •
Disjunction  or  v  v
Negation  not  ~  ~
Conditional  if/then  →  ⊃
Biconditional  if and only if  ↔  ≡
Page Sentential Logic and Well-Formed Formulas

In this section, you will read about how formal systems of logic work and what they are useful for. You will first be introduced to the elements of a simple system of logic called SL, and then you will learn how to construct statements called well-formed formulas (WFFs) in SL.

Complete the exercises and check your answers.

3.2.2: Connectives and Truth Tables Book Truth Tables

Read these sections to learn how to interpret, make, and apply truth tables to sentential logic formulas, note conditional statements in sentential logic, and translate the word "unless" into sentential logic. Be sure to note the difference between an antecedent and a consequent and between a necessary and sufficient condition.

Complete the exercises, checking your answers against the key.

Page Connectives

Read this tutorial, which will introduce you to truth tables. Truth tables are an objective way of determining the validity of an argument as a whole when the argument is expressed symbolically.

Complete the exercises for this tutorial and check your answers.

3.2.3: How to Draw Truth Tables for More Complicated Statements Page Complex Truth Tables

Read this tutorial to expand your knowledge of truth tables. The last tutorial showed you how to construct truth tables for the basic connectives in sentential logic (SL). This tutorial extends the same technique to more complex well-formed formulas, which approximate the kinds of statements that might be part of an argument in ordinary language.

Complete the exercises for this tutorial and check your answers.

3.2.4: Properties of Individual Well-Formed Formulas and Relations Between Them Book Relationships in Truth Statements

Read these sections to learn more about relationships among truth statements and using and constructing logical proofs.

These sections review materially equivalent propositions and three other relationships among statements: tautological, contradictory, and contingent relationships. They also review the eight valid forms of inference: modus ponens, modus tollens, hypothetical syllogism, simplification, conjunction, disjunctive syllogism, addition, and constructive dilemma. They show how to construct proofs, including strategies for working forward or backward, depending on which is easier according to your premises. Finally, they summarize everything you have learned about sentential and propositional logic.

Complete the exercises as you study, then check your answers against the key.

Page Properties and Relations

Read this tutorial, which presents the concepts of consistency, entailment, and equivalence introduced in subunit 4.1.2 but defines them now in terms of their truth tables in SL. These are all relations between WFFs. This tutorial introduces the concepts of tautology, contingency, and inconsistency as properties of individual WFFs that can also be defined by their truth tables.

Complete the exercises for this tutorial and check your answers.

3.2.5: Understanding Truth Tables Page Understanding Truth Tables

This page reviews the nature of truth tables, the definitions of basic logical connectives, the rules for constructing truth tables, and the methods for using truth tables to determine whether a well-formed formula is tautologous, inconsistent, self-consistent, or contingent.

The material also discusses methods for using truth tables to determine whether two well-formed formulas are logically equivalent, contradictory, or consistent. Finally, it covers methods for using truth tables to determine whether an argument is valid.

3.2.6: How to Translate Ordinary Statements into Symbolic Formulae Page Formalization

Read this tutorial on formalization, which means turning statements and arguments in ordinary language into their symbolic counterparts; we might just as well call it translation. Notice that ordinary language contains hint words, letting us know when we will likely need one of the logical connectives.

Complete the exercises for this tutorial and check your answers.

3.2.7: Formalization Practice Page Propositional Logic and Symbolization

Read this section, which reviews and elaborates upon procedures for translating ordinary statements into the language of symbolic logic, which the text calls propositional logic.

Complete the exercises to test your understanding.

3.2.8: Two Methods for Determining the Validity of an Argument Book Validity and the Indirect Method

Read these tutorials, which provide information on determining whether an argument – or sequent – is valid in SL. Because using truth tables to establish validity is time-consuming, the second tutorial presents a shortcut version of the method.

Complete the exercises for both tutorials and check your answers.

3.2.9: Why Sentential Logic Is Not Enough Page Material Conditional

Read this tutorial on limitations. Some statements cannot be captured in sentential logic, especially statements involving words like every and all (like "all men are mortal"). This tutorial explains why and introduces the idea of predicate logic.

Complete the exercises for this tutorial and check your answers.

4.1.1: Venn Diagrams as Illustrations of Sets or Classes Book Categorical Logic and The Venn Test of Validity for Immediate Categorical Inferences

Read these sections to learn and apply a visual method for determining the validity of categorical inferences: Venn diagrams. Note the four categorical forms and what they mean: universal affirmative, universal negative, particular affirmative, and particular negative. Get comfortable drawing Venn diagrams for categorical statements and shading in the area or drawing a star for the statements you are given.

Complete the exercises, checking your answers against the answer keys, translating the diagrams into statements, and using the Venn test of validity to determine the validity of the given categorical inferences.

Page Basic Notation

Read the introduction and tutorial for an introduction to Venn diagrams. In Venn diagrams, circles represent sets or classes. These tutorials demonstrate how to use shading and overlapping to illustrate empty sets and relations of all, every, and nothing.

4.1.2: More Complicated Venn Diagrams Page Venn Diagram Exercises

Working with Venn diagrams involving three circles is almost the same as working with two circles. The only difference is that there are now eight distinct regions, each with a specific logical meaning.

Complete these exercises and check your answers.

4.1.3: Illustrating Experience with Venn Diagrams Book Universal Statements and Existential Commitment

Read this section to learn about a potentially counter-intuitive relationship between universal and particular affirmatives – namely, one does not imply the other. This is because universal affirmatives do not contain an "existential commitment": a statement that there is anything in the category the universal affirmative references.

Complete the exercise, keeping in mind that universal affirmatives do not contain existential commitments. Check your validity answers against the key.

4.1.4: Review of Introduction to Venn Diagrams Page More Venn Diagram Exercises

Complete these exercises relating to two-circle Venn diagrams. For each question, you must choose the sentence that best represents what is shown in the given diagram.

4.2.1: Using Venn Diagrams to Evaluate Syllogisms Book Venn Validity for Categorical Syllogisms

Read this section on Venn diagrams, which will help you use Venn diagrams to test the validity of whole categorical syllogisms rather than only categorical inferences. Read the section and identify the categories in every statement of the syllogisms as you go, making your own Venn diagrams to test the validity, as directed.

Complete the exercise, checking your validity answers against the key.

Page Syllogism

Read this tutorial on how to use Venn diagrams to evaluate arguments. You will be introduced to the concept of a syllogism, a special type of argument that cannot be evaluated in SL. Venn diagrams are ideal for evaluating this type of argument. Remember that a Venn diagram can only tell us if an argument is valid, not whether it is sound.

4.2.2: Understanding the Logic of Venn Diagrams Page The Logic of Venn Diagrams

This page reviews how to set up Venn diagrams and the rules for using Venn diagrams in evaluating argument validity. It also introduces the notion of conditional validity and explains how to use Venn diagrams to evaluate the validity of categorical syllogisms.

4.2.3: The Limitations of Venn Diagrams Page Limitations of Venn Diagrams

Read this tutorial about the limitations of Venn diagrams. Although Venn diagrams are a powerful tool for representing some types of statements, there are many statements that they cannot handle.

Complete the exercises for this tutorial, then check your answers.

4.2.4: Review of Venn Diagrams and Arguments Page Even More Venn Diagram Exercises

Complete these exercises to determine whether these arguments are valid or not. Draw out the Venn diagrams with pencil and paper.

5.1: Introduction to Fallacies Page What is a Fallacy?

Read this tutorial, which introduces the notion of fallacious reasoning. Fallacies are arguments that are frequently accepted as valid but contain subtle reasoning errors. It is important to know how to catch fallacies.

5.2: Types of Fallacies Page Formal versus Informal Fallacies

Read this section to learn the difference between formal and informal fallacies and learn two key formal fallacies that look like good logic but are not: denying the antecedent and affirming the consequent. There is a popular joke among philosophers about Descartes (the French philosopher who famously wrote, "I think, therefore I am") walking into a bar and, when the bartender asks if he'd like a drink, replying "I think not" and vanishing in a puff. While delightful to share among your philosopher friends, this joke actually falls prey to one of these fallacies – see if you can tell why.

Page List of Fallacies

Read this tutorial, which defines the most common fallacies. This list narrows down some of the fallacies in the previous text and is enough to get us started. We will look at a wider sample of fallacies later in this course. For now, focus on defining each fallacy and identifying the differences between the fallacies on the list.

Page False Dichotomy, Causal Slippery Slope, and Appeal to Authority

Read these sections to review three important fallacies you probably come across without realizing it: false dichotomy, causal slippery slope fallacy, and appeal to authority.

All three of these fallacies can be disguised as something that looks logical, but these readings will help you identify when that is not the case.

Book Inconsistency, Irrelevance, Insufficiency, and Inappropriate Presumption

Read these tutorials, which introduce four major classifications of fallacies. Although there are many possible ways of categorizing fallacies, the four major groups discussed in these tutorials are fairly standard.

Page Exercises on Fallacies

Complete this quiz, which will help you identify common fallacies.

5.3.1: Straw Man Fallacy Page Straw Man Argument

You may have heard criticisms of a "straw man" argument before and not known what that meant. This section walks you through a straw man argument and gives examples. After reading this section, try to come up with a few examples of straw man arguments, and look for straw man fallacies in your own life.

Page The Straw Man Fallacy

Watch this video, which explains a fallacy commonly known as the straw man fallacy. After watching this video, you should be able to define the fallacy and identify examples of the fallacy.

5.3.2: Gambler's Fallacy Page The Gambler's Fallacy

Watch this video, which explains a fallacy commonly known as the gambler's fallacy. After watching this video, you should be able to define the fallacy and identify examples of the fallacy.

Page More on the Gambler's Fallacy

Read this introduction to the gambler's fallacy and the example of how it works.

5.3.3: Begging the Question Page Begging the Question

Read this section on the fallacy of "begging the question". When we formalize the examples in the premise, they are not substantively different from the conclusion. Look out for "question begging" arguments in your life.

5.3.4: Red Herring Page The Red Herring Fallacy

Read this article to learn about the red herring fallacy. If you think bringing up colorful fish sounds out of place when discussing logic, then you're right! The red herring fallacy operates by bringing up irrelevant information. Often when we have arguments in our lives, though, people throw in "red herrings".

5.3.5: Ad Hominem (Against the Person) Page Ad Hominem

You have doubtless heard ad hominem attacks before – though you may not have known they were an informal fallacy. Read this section on the ad hominem fallacy for a definition and examples of these attacks. After reading, you should be able to identify ad hominem attacks when you encounter them.

5.3.6: Ad Ignorantium (Appeal to Ignorance) Page Appeal to Ignorance

Read this brief description of the "ad ignorantium" (or "appeal to ignorance") fallacy. This common fallacy insists on placing the burden of proof on whatever side opposes it.

5.3.7: Ad Populum (Appeal to the People) Page Appeal to the People

Read this article for a quick explanation and examples of the logical fallacy ad populum, or "appeal to the people". This fallacy relies on our social inclinations and is popularly seen in advertising. Despite the effectiveness of these kinds of appeals, they nonetheless are not logical arguments.

5.3.8: Complex Question (Double-Barreled Question) Page Double-Barreled Question

Read this article, which defines the double-barreled question fallacy and identifies examples of it.

5.3.9: Loaded Question Page Loaded Question

Read this article, which defines the loaded question fallacy and identifies examples of it.

5.3.10: Non Sequitur (It Does Not Follow) Page Formal Fallacy (Non Sequitur)

Read this article, which defines the non sequitur fallacy and identifies examples of it.

5.4: Cognitive Biases Page Cognitive Biases

Read this tutorial, which describes some examples of cognitive biases. These biases are ways of thinking that lead us to make poor inferences. Being able to identify cognitive biases helps us to improve our reasoning and helps us to assess other people's reasoning.

Page Cognitive Biases Explained

Watch this video to learn about availability, representativeness, and confirmation biases. Note that there are many other cognitive biases, including anchoring bias, availability heuristic bias, bandwagon bias, choice supportive bias, ostrich bias, outcome bias, overconfidence, placebo bias, survivorship bias, selective perception bias, and blind spot bias. Try to identify some examples of cognitive biases in your life.

6.1: The Basic Principles of Scientific Reasoning Page The Hypothetical-Deductive Method

Read these tutorials on scientific reasoning. Science is almost infinitely varied, but its basic method is surprisingly simple. These tutorials will introduce the four components of the hypothetical-deductive method and the difference between truth and confirmation.

Page The Scientific Method Explained by a Scientist

Watch these videos. Pay attention to the discussion of the difference between the terms theory and evidence and the discussion of the reasoning method called Ockham's Razor (also sometimes called Occam's Razor).

Page What Makes One Scientific Theory Better than Another?

Read this tutorial on theory choice. In scientific practice, multiple theories will frequently be put forward to explain the same phenomena. When this happens, scientists sometimes use five criteria to guide their decisions among alternative theories.

6.2.1: The Basics of Causality Book Causal Reasoning

Read this section to investigate the complications of causality, particularly as it relates to correlation. Sometimes, two correlated events share a common cause, and sometimes, correlation is accidental. Complete the exercises to practice determining sufficient evidence for causation and determining accidental correlation. Check your answers against the key.

Page Causation

Read this tutorial, which outlines some important terminological distinctions for causation. Causation is an ideal topic to address in a course on critical thinking because it is something we feel we understand well in our everyday lives. Once we begin trying to think scientifically about causes, however, we find that fixing the causes of some events requires precision and subtlety.

Page Mill's Methods

Read this tutorial about Mill’s five methods for identifying causes. John Stuart Mill (1806-1873), the 19th-century English philosopher, proposed five distinct ways to identify a cause through observation. While these methods may appear to be common sense, it is important to see that they represent distinct modes of inference.

6.2.2: Causality is More Than Just Cause and Effect Page Causal Inferences

Read this tutorial on causality, which identifies seven different types of causal relations. Each type of relation is followed by a set of defining criteria. Although each type of relation is a cause-and-effect relationship between A and B, information about the context of the interaction and the relation of A and B to one another in time affects what we can say about the causal relation between them.

Page Correlation and Causation

Read this example-rich tutorial, which explains the difference between the two relationships of correlation and causation. Scientists looking for cause-and-effect relationships in the natural world need to be careful not to misconstrue causality with mere correlation.

Page Causal Diagrams

Read this tutorial, which illustrates two ways of diagramming cause and effect. They allow for the description of multiple causes and effects from a single event and for distinguishing between levels of causation. 

When multiple relations of cause and effect are involved in the behavior of some phenomenon, representing these relations visually is often the best way to get a handle on them and to assist in quantitative analysis of the system in question.

7.1: Strategic Reasoning Page Classifying Problems

Read this tutorial about what to consider when defining a problem and the three major classifications that problems usually fall under. Problem-solving is an activity that combines skills of critical and creative thinking. The first task in any problem-solving scenario is to identify the type of problem one is dealing with.

Complete the exercises for this tutorial, and check your answers.

Page Solving Problems

Read this tutorial, which outlines the mathematician George Pólya’s four-step problem-solving procedure.

Page Complex Systems

Read this tutorial, which introduces the technique of process analysis. This course has focused primarily on problems that are relatively simple in structure. You should be aware that many problems encountered will be highly complex, involving multiple variables and a mixture of problem types. You will read about flowcharts next.

Page Charts and Diagrams

Read this section on flowcharts. It may also be helpful to review subunit 6.2.5 on cause-and-effect diagrams. There are several useful visual techniques to facilitate solving complex problems.

Page Making Good Decisions

Read this tutorial about basic decision-making rules. Decision theory provides tools for evaluating the best course of action in scenarios involving risk and uncertainty.

7.2: Creative Thinking Page Three Basic Principles of Creative Thinking

Read this tutorial on principles of creative thinking. Creativity is a ubiquitous human activity, not just the province of artists and inventors. Human beings solve problems creatively every day. The nature of creativity thus incorporates both spectacular creative acts and more modest instances of creative reasoning. This tutorial explains what all forms of creativity have in common.

Page The Creativity Cycle

Read this tutorial on the creativity cycle. Although something remains mysterious about what occurs during a flash of creative inspiration, there are nonetheless certain procedures that encourage creative thinking. This tutorial outlines a repeatable four-step creative process based on what is known objectively about producing novel ideas and solutions.

Page Creative Heuristics and Group Creativity

Read these tutorials, which offer procedures for initiating creative thinking based on our existing factual knowledge. The quotations in the second tutorial demonstrate how these procedures form part of the creative process of some of the most famous minds in art, science, and philosophy.

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