1: How to Reason Logically
- Page ID
- 21956
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The goal of this book is to improve your logical-reasoning skills. These skills are also called "critical thinking skills." They are a complex weave of abilities that help you get someone's point, generate reasons for your own point, evaluate the reasons given by others, decide what or what not to do, decide what information to accept or reject, explain a complicated idea, apply conscious quality control as you think, and resist propaganda. Your most important critical thinking skill is your skill at making judgments─not snap judgments that occur in the blink of an eye, but those that require careful reasoning.
You are not reasoning logically if, when you want a gorilla suit for a Halloween party, the first thing you do is search for the word "Gorilla" in the telephone book, and the problem here is not that you used a telephone book instead of the Internet.
High-quality reasoning is called logical reasoning or critical thinking. Logical reasoning skills can be learned and improved. It is not a case of "Either you're naturally good at it or you’re not." Rather, nearly everyone is capable of reasoning well, and everyone is capable of improvement. The opposite of logical reasoning is uncritical thinking, examples of which are fuzzy thinking, believing what somebody says simply because they raise their voice, and narrowly thinking about a problem without bringing in the most relevant information.
This first chapter explains what it means to be logical—to reason logically or critically. It demonstrates the usefulness of logical reasoning as a means of making more effective decisions about your own life—decisions about what to believe and decisions about what to do. The chapter begins a systematic program of study of all the major topics regarding logical reasoning. Along the way, the book focuses on developing the following five skills: (1) writing logically, (2) detecting inconsistency and lack of clarity in a group of sentences, (3) spotting issues and arguments, (4) detecting and avoiding fallacies (reasoning errors), and (5) generating and improving arguments and explanations. These skills will be taught here independent of subject matter. This book is not about what you ought to believe about some subject such as politics, religion, sports or business.
Although many scientific studies of decision-making have shown that people tend to sift sources of information looking to reinforce existing views rather than to accept the view that is backed up with the better argument, your book is designed to combat this tendency.
- 1.1: 1.1
- This page discusses the importance of enhancing logical reasoning and critical thinking skills for evaluating arguments and making informed decisions. It emphasizes that these skills can be learned, countering uncritical thinking. The first chapter outlines key skills such as logical writing, identifying inconsistencies, spotting arguments, avoiding fallacies, and improving arguments, aiming to develop these skills without reliance on specific subjects to reduce bias in information evaluation.
- 1.2: Facing a Decision as a Critical Thinker
- This page explores a dilemma faced by three friends on a backpacking trip regarding a compromised water supply. With no cell phones, they discuss whether to stay and boil the water or hike back, debating the risks of untreated stream water. Juanita urges leaving, while Emilio minimizes the danger. The narrator evaluates their arguments, seeks expert advice, and concludes to stay, emphasizing the importance of logical reasoning in decision-making.
- 1.3: Advice for Logical Reasoners
- This page covers essential principles of logical reasoning, emphasizing the significance of supporting claims with reasons for greater understanding and acceptance. It defines "arguments" and encourages tailoring to the audience. The discussion includes a decision-making framework that weighs pros and cons while recognizing the value of critical thinking in quick judgments.
- 1.4: Examples of Good Reasoning
- This page emphasizes the importance of logical reasoning in decision-making, illustrated through a jury deliberation on Jesse Mayfield's armed robbery case. It highlights Juror Washington Jones's use of logical principles to present reasonable doubt and the need to consider all evidence while avoiding irrelevant factors. Additionally, the page underscores that critical thinking extends beyond argumentation, aiming to develop various related skills.
- 1.5: Review of Major Points
- This page emphasizes the significance of logical reasoning in decision-making and discerning truth from falsehood. It presents case studies to illustrate common reasoning errors and outlines 23 principles of logical reasoning that serve as guidelines for evaluating arguments. The chapter aims to prepare readers for further exploration of logical intricacies, focusing on skills for recognizing, assessing, and constructing arguments.
- 1.6: Glossary
- This page introduces key concepts in argumentation and critical thinking, defining an argument as a conclusion backed by reasons. It critiques simplistic interpretations of critical thinking and clarifies the difference between issues (points of disagreement) and topics (broader subjects). Additionally, it outlines the importance of weighing pros and cons in decision-making, akin to cost-benefit analyses, emphasizing the necessity of these concepts for effective reasoning and discussion.
- 1.7: Exercises
- This page presents hypothetical reasoning and decision-making scenarios, such as responding to signals from extraterrestrial sources and evaluating the celebration of Columbus Day. It highlights the importance of weighing pros and cons, considering consequences, and recognizing biases in decision-making. Through various daily life and historical examples, the page encourages critical thinking and aims to enhance reasoning and judgment skills in both personal and societal contexts.