PHIL102: Introduction to Critical Thinking and Logic

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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.

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.

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

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.

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.

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).

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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.

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.

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

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.

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".

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.

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.

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.

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

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

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

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.