Topic Name Description
Course Introduction 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.

URL Discussion: The Importance of Critical Thinking

Consider the following questions below from a variety of angles. Then, share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Make sure to review and respond to one or two other students’ posts before logging off. 

1. Is critical thinking important? Why, or why not?

2. How will the understanding and use of critical thinking benefit you in your life now and in the future?

3. How do emotions affect one’s ability to think critically?

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 the 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.

URL Discussion: Definitions

Evaluate the definitions presented below. If you find a definition to be inadequate or flawed, try to provide a better definition. Share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Review comments and alternative definitions that other students have posted, and respond to at least one or two other students’ posts. 

1. Discuss Mark Twain’s definition of love: Love is the irresistible desire to be irresistibly desired. 

2. Discuss this definition of cloud: A cloud is a large, semi-transparent mass with fleecy texture suspended in the atmosphere whose shape is subject to continual change.

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 in which language can lead us astray.

Complete all exercises and check your answers.

1.3: Assessing Sources Book Research Skills Tutorial

Read all five sections of this tutorial from "Credible Sources" through "Validity". This tutorial discusses appropriate questions to ask in order to determine whether a source is credible and reliable. As you read through the tutorial, make a list of important questions to ask. Leave plenty of space between each question. As you proceed, make notes under each question about why that question is important. Also, write down any tips to consider when attempting to answer each question.

Page Evaluating Sources and Peer Review

Watch these videos to learn about basic principles of evaluating sources. The first video identifies characteristics of scholarly articles, and the second video offers an explanation of 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.

URL Discussion: Finding and Assessing Sources

Consider your experiences with finding and assessing sources. In particular, using a personal experience as an example, discuss whether, and to what extent, one of the strategies in this section for evaluating sources has been or would have been helpful. Share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Review and respond to at least one or two other students’ posts.

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

Read section 1.1 (p. 1-3) of this textbook, 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 at the end of the subsection, identifying which sentences are statements, and once you identify them, begin thinking about what premises might lead to those statements. When you finish, check your responses with the answer key on p. 207.

The entire text book can be found here: Introduction to Logic and Critical Thinking

Page More on Arguments

Read this tutorial, which explains how to identify and 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 File Identifying Arguments

Read section 1.2 (p. 4-7) of this textbook, which will give you some tips for how to spot an argument. While the premise indicators and conclusion indicators are not guarantees of an argument, they can assist you to identify an argument.

Complete Exercise 2, at the end, 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 on p. 207.

The entire text book can be found here: Introduction to Logic and Critical Thinking

Page The Standard Format of an Argument

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

2.2: Good Argument Form File Validity and Soundness

Section 1.6 (p. 17-23) 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, the concept introduced in section 1.7. 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 on pages 209-210.

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, starting with A03 and clicking through to A05, 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 true/false 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 they may be sound or unsound.

File Rounding Out Arguments

Read sections 1.8 through 1.10 (p. 23-36) to learn how to round out arguments, conceptually. Section 1.8 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. Section 1.9 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! Section 1.10 shows you three rhetorical devices to hint at further argument without actually going through the argument: assuring, guarding and discounting.

Complete Exercises 6 and 7, checking your answers against the keys on pages 210-211.

Book Hidden Assumptions, Inductive Reasoning, and Good Arguments
When arguments are stated verbally or in writing, their structure may not be completely explicit. "Hidden Assumptions" provides clues about how to identify hidden assumptions.  "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. "Good Arguments" puts together a number of the ideas laid out so far in order to describe the characteristics of a good argument.

Complete the exercises and check your answer.
2.3: Visualizing How Arguments Work File More Complex Argument Structures

Visualizing argument structure can be helpful for determining how directly or indirectly supporting evidence leads to a conclusion. Section 1.4, on pages 10-15,  gives examples of simple arguments and more complex arguments using arrows to represent the structure of an argument. 

Complete Exercise 4 on pages 14-15. A key for writing the arguments in standard form is on pages 208-209 but there is no key for 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 File Analogical Arguments

Read section 3.3 (p. 154-158) about a sort of 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 Exercise 24 and check against the answer key on pages 230-231.

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 as well as the most common ways in which they may be undermined.

2.5: Valid Argument Patterns Page Valid Argument Patterns

Read this tutorial on how to reduce valid arguments to their basic structure through the use of argument patterns. This reading provides a preview of the kind of analysis we will be doing a lot more of in unit 4. This kind of strategy is sometimes useful with 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).

2.6: Review of Argument Analysis URL Discussion: Argument Analysis

Try to formulate examples for three important patterns of argument: modus ponens, modus tollens, and reductio. Then, for the following argument sent to a newspaper by a reader responding to an article claiming that Shakespeare was Italian, identify the argument's main conclusion and spell out the argument's premises. 

"So Shakespeare was an Italian, because almost half of his plays are set in Italy. Almost all of Isaac Asimov's novels are set in outer space – does that mean he was a Martian?" – Graham Simpson

Share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Read arguments that other students may have constructed, as well as their attempts to analyze the Shakespeare argument. Respond to at least one or two other students' posts.

3.1.1: What Logic Is and Is Not Page What is Logic?

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

3.1.2: Logical Statements, Connectives, and Relations File Formal Methods of Evaluation

Read section 2.1 (p. 49-51) for your 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 a couple of 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.

3.1.3: Logic is Fun! Page Fun Logic Puzzles

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

3.1.4: Review of The Basics of Logic Page The World's Hardest Logic Puzzle Ever!

Complete this exercise, which will give you an opportunity 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 File Propositional Logic Functions

Read sections 2.2 through 2.4 (p. 51-75) 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.

Complete exercises 8, 9, 10, and 11, and check your answers against the answer keys on pages 211-215.

Note that the symbols used in some places can be slightly different from ones 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 File Truth Tables

Read these sections 2.6, 2.7, and 2.8 (p. 75-89) 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 the difference between a necessary condition and a sufficient condition.

Complete exercises 12 and 13, checking your answers against the answer keys on pages 215-217.

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 File Relationships in Truth Statements

Read sections 2.9 through 2.13 (pages 90–113) to learn more about relationships among truth statements and using and constructing logical proofs.

Section 2.9 reviews materially equivalent propositions. Section 2.10 reviews three other relationships among statements: tautological relationshipscontradictory relationships, and contingent relationships. Section 2.11 reviews the eight valid forms of inference: 1. modus ponens, 2. modus tollens, 3. hypothetical syllogism, 4. simplification, 5. conjunction, 6. disjunctive syllogism, 7. addition, and 8. constructive dilemma. Section 2.12 reviews constructing proofs, including strategies for working forward or backward, depending on which is easier according to your premises. Finally, section 2.13 summarizes everything you have learned about sentential and propositional logic.

Complete exercises 14, 15, 16, and 17 as you study. Check your answers against the answer keys on pages 217-224.

Page Properties and Relations

Read this tutorial, which presents the same 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 are likely to 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 the introduction and section 3.1. The material 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 two tutorials, which provide information on how to determine if an argument – or sequent – is valid or not 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. There are some statements that 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 File Categorical Logic and The Venn Test of Validity for Immediate Categorical Inferences

Read sections 2.14 and 2.15 (p. 114-126) 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 exercises 18 and 19, checking your answers against the answer keys on pages 224-225, 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, as well as relations of all, every, and nothing.

4.1.2: More Complicated Venn Diagrams Page Venn Diagram Exercises

Working with Venn diagrams that involve three circles is almost exactly the same as working with ones that involve 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 File Universal Statements and Existential Commitment

Read section 2.16 (p. 126-128) to learn about a potentially counter-intuitive relationship between universal affirmatives and particular affirmatives – namely that the one does not imply the other. This is because universal affirmatives do not contain what is called an "existential commitment" that is, a statement that there is anything in the category the universal affirmative references.

Complete exercise 20, keeping in mind that universal affirmatives do not contain existential commitments. Check your validity answers against the key on page 225.

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 File Venn Validity for Categorical Syllogisms

Read section 2.17 on Venn diagrams (p. 128-138), 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 exercise 21, checking your validity answers against the key on pages 225-226.

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 as well as 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 in which you will determine whether these arguments are valid or not. Draw out the Venn diagrams with pencil and paper.  

URL Discussion: Venn Diagrams and Argument Validity

Consider how you might adapt Venn diagrams to evaluate the validity of the following arguments. 

  1. Most cooks are men. Most men are idiots. So most cooks are idiots. 
  2. Very few plants are purple. Very few purple things are edible. So very few plants are edible.

Share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Review and respond to at least one or two other students’ posts. 

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 which contain subtle errors of reasoning. It is important to know how to catch fallacies.

5.2: Types of Fallacies File Formal versus Informal Fallacies

Read section 4.1 (p. 185-186) 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 seen in the previous reading and is enough to get us started. We will look at a wider sample of fallacies later on in this course. For now, focus on being able to define each fallacy and identify the differences between the fallacies on the list.

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

Read sections 4.1.4 (p. 191-193), 4.2 (p. 197-199), and 4.3.6 (p. 206) to review three important types of fallacies you probably come across in life 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 four 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 drag and drop quiz, which will help you identify common fallacies.

5.3.1: Straw Man Fallacy File Straw Man Argument

You may have heard criticisms of a "straw man" argument before, and not known what that meant. Section 4.3.2 (p. 201-203) walks you through what a straw man argument is and shows you a couple of examples. After reading this section, try to come up with your own examples and be on the lookout 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.

File More on the Gambler's Fallacy

Read section 3.10 (p.184) for an introduction to the gambler's fallacy and an example of how it works. 

5.3.3: Begging the Question File Begging the Question

Read section 4.1.3 (p. 189-191) 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 own 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 a bit out of place when discussing logic, then you’re absolutely right! The red herring fallacy operates by bringing up irrelevant information. Oftentimes when we have arguments in our own lives, though, people do throw in "red herrings".

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

You have doubtless heard ad hominem attacks before – though you may not have known they were an informal fallacy. Read section 4.3.1 (p. 199-201) 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 the brief description of the "ad ignorantium", or "appeal to ignorance", fallacy on this page. This common fallacy insists on placing the burden of proof on whatever side is opposite it.

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

Read this article for a quick explanation and some 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.

5.3.11: Review of Fallacies URL Discussion: Fallacies

Consider the passages below. If the passage contains an argument, identify the premises and main conclusion. For each passage, assess whether it contains a fallacy. If it does, then identify the fallacy and explain why you made your assessment. Share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Review and respond to at least one or two other students’ posts. 

  1. God exists, because many people who believe in God go on to have healthy, happy, and meaningful lives.
  2. Bertrand Russell (1872–1970), the British philosopher, said that objective morality is possible without God. Russell was an atheist, and we all know that he slept around and seduced young girls and was nasty to lots of people. 
  3. Do you want four more years of this person in political office? Vote for me, Candidate X.

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 own reasoning and helps us to assess other people’s reasoning.

Page Cognitive Biases Explained

Watch this video to learn about the availability, representativeness, and confirmation biases. Note that there are many other types of 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 two tutorials on scientific reasoning. Science itself is almost infinitely varied, but its basic method is surprisingly simple. These tutorials will introduce you to 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 two videos. Pay particular attention to the discussion of the difference between the terms theory and evidence, as well as the discussion of the reasoning method called Ockham's Razor (which is 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.

URL Discussion: Scientific Theories
Consider the following prompts. Share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Review and respond to at least one or two other students’ posts.  

  1. Given what you know about criteria for theory choice in science, such as predictive power, mechanism, fruitfulness, simplicity, and coherence, is there anything other than evidence that scientists use in determining whether to accept a theory? Should there be? 
  2. Are simpler theories more likely to be true? Is Ockham’s Razor always a good rule of scientific reasoning?

6.2.1: The Basics of Causality File Causal Reasoning

Read section 3,4 (p. 158-169) to investigate the complications of causality, particularly as it relates to correlation. Sometimes, two correlated events share a common cause, and sometimes correlation is merely accidental. 

Complete exercises 25 and 26 to practice determining sufficient evidence for causation and determining accidental correlation. Check your answers against the answer keys on pages 232-233.

Page Causation

Read this tutorial, which outlines some important terminological distinctions for dealing with 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 event requires precision and subtlety.

6.2.2: Five Ways to Identify a Cause 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 in which a cause might be identified through observation. While these methods may appear to be close to common sense, it is important to see that they represent distinct modes of inference.

6.2.3: 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.

6.2.4: The Difference Between Causation and Correlation 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.

6.2.5: Ways of Representing Cause and Effect 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 as well as 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.

6.2.6: Fallacies About Causation URL Discussion: Causation

The following passage is an extract from a report by Arizona Daily Wildcat (June 16, 1999) concerning a study to show that certain people can communicate with the dead. Using what you have learned about causation, correlation, and causal fallacies, consider the potential flaws with the experiment. Assume that the report is mostly correct. Summarize your evaluation of the flaws in the experiment, and share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Review and respond to at least one or two other students’ posts.


Gary Schwartz, psychology professor and co-founder of the University of Arizona Human Energy Systems Lab, speaks about his work at the University of Arizona. A team of scientists and students conducted a unique experiment this weekend, probing the possibility of an afterlife by studying how mediums commune with the dead.

Researchers invited a panel of mediums to meet with 10 people whose loved ones had recently died. While under observation, the mediums tried to receive information from the deceased without prior knowledge about the deceased. Schwartz invited four mediums to participate in the study, including famous "superstars" of the psychic world, such as author John Edwards, and unknowns, such as California housewife Laurie Campbell. The medium sat facing a wall while a researcher looked on. A "sitter," who had recently lost a relative or friend, would then enter the room and sit six feet behind the medium. Schwartz acknowledged that a few of the sitters were acquaintances of the mediums.

For up to 10 minutes, the medium and the sitter would sit in silence. The medium, who could not see the sitter, would concentrate on receiving psychic impressions. A question and answer session followed, in which the sitter was allowed only to answer "yes" or "no." Schwartz said the study was set up to minimize communication between the medium and the sitter, avoiding conscious or subconscious prompting between the two. While the final results have not been written up, Schwartz said he was impressed with the mediums’ performance. He said that on several occasions the mediums were able to pick out the names and personal information of the deceased.

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 procedure for problem solving.

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

Page Creative Heuristics and Group Creativity

Read these tutorials, which offer procedures for initiating creative thinking on the basis of factual knowledge we already possess. 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.

URL Discussion: Creative Thinking

Consider your experiences with thinking creatively. In particular, using a personal experience as an example, discuss whether, and to what extent, one of the strategies in this section for thinking creatively has been/would have been helpful. 

Share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Review and respond to at least one or two other students’ posts. 

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