1: Basic Concepts
- Page ID
- 223680
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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 most important thing we do as human beings is learn how to think. This is important in two senses of the word: it’s important to human beings because it is the most distinctively unique fact about our species—we think rationally and abstractly—but it’s also important because it the most wide reaching capacity we have—it touches virtually all aspects of our lives. Having a heart that pumps blood or a body capable of certain physical activities might be more fundamental meaning more crucial to simply surviving, but thinking underlies a broad range of activities without which we would be living less than full human lives.
The common title of this course is “Logic and Critical Thinking.” So, we can think about the course as having two main components: the study of formal logic and the study of the tools and strategies of critical thinking. This text is structured in a bit of a “sandwich”. Units on critical thinking and then formal logic, and then units on more critical thinking topics.
First, Logic. We’ll define logic more fully later, but for now: logic is a sort of reasoning that is mathematical in its precision and proofs. It’s like math with words and concepts, in a sense.
Don’t worry, dear student. Logic is more straightforward than a lot of the complex concepts that get discussed in math classes. Even better, all of logic can be broken down into simple, step-by-step processes that a computer can do. You just need to follow the steps carefully and you’ll be guaranteed the right answer every time. There’s no magic to it, no special skills or abilities needed. You just need to follow directions carefully and put a bit of work into it.
Next, let’s get a bit of a definition of critical thinking going. Critical thinking is primarily the ability to think carefully about thinking and reasoning—to have the ability to criticize your own reasoning. ‘Criticize’ here isn’t meant in the sense of being mean or talking down or making fun of. Instead, I mean the word in the sense of, for example, how a coach might take a critical stance toward her players’ skills—he throws high every time, she doesn’t lead with her foot, they ride too forward in the saddle, etc. ‘Critical’ here means something more like ‘reflective’ or ‘careful’ or ‘attention to potential errors’.
So to engage in critical thinking is to engage in self-critical, self-reflective, self-aware thinking and reasoning—thinking and reasoning aimed at self-improvement, at truth, and at careful, deliberate, proper patterns of reasoning.
There are many definitions of what critical thinking is, but here’re my thoughts:
As you can see, being a critical thinker involves training yourself to have a lot of good habits and dispositions. It involves developing rational virtues so that when the time comes to think about something complex, you are naturally disposed to think well. It doesn’t happen overnight and it certainly doesn’t come for free—no one is born with it. We all need to train ourselves and educate ourselves to stay guarded against errors in reasoning.