14.1: Introduction
- Page ID
- 199358
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)"Argumentation gives priority to logical appeals while recognizing the importance of ethical and emotional appeals;
persuasion gives priority to ethical and emotional appeals while recognizing the importance of logical appeals."
-Professor James Sawyer
The Focus of this Chapter
As we learned in previous readings, reasoning is the process of creating or generating conclusions from evidence or premises. Reasoning is what links your evidence to your conclusions. This is the “logical” part of your argument. In this chapter, we look will look at logic and find that:
- There are two general categories of reasoning: deductive and inductive.
- Deductive reasoning argues from the general rule to a specific conclusion and follows the rules of syllogisms.
- Inductive reasoning moves from specifics to create a general rule.
- We will examine five types of inductive reasoning. Each type has tests that we can make to insure the reasoning is sound.
- Unsound reasoning is known as fallacies. Recognizing fallacies in an argument allows us to reject an appeal that is illogical.
Overview of Reasoning
Again, reasoning is the process of creating or generating conclusions from evidence or premises. This is the logic of an argument: the consistency between data and conclusion. Reasoning constructs a logical or rational connection between the evidence and the contention. The more reasonable the argument, the more valid is the conclusion.
Checking the validity of your own arguments will allow you to improve the quality of the arguments you use. When you create logically unsound arguments, you are much less likely to convince people to agree with you. If you are trying to convince an employer that you are indeed the person for a promotion, you want to make sure your arguments are as valid as possible. Not only do you give him or her a reason to accept your argument, but also you can better defend your position if it is challenged.
When you understand how arguments are supposed to be constructed and also how they shouldn't be constructed, you will find all sorts of bad arguments vying for your attention. I am guessing that you are not surprised at how many people are swayed by bad argument
"Bad Arguments" by Ali Almossawi is Fair Use
Ali Almossawi has written an entertaining book that introduces logic, Bad Arguments. Here, in the final words in the preface of the book, he explains the limits to logic:
“In closing, the rules of logic are not laws of the natural world, nor do they constitute all of human reasoning. As Marvin Minsky asserts, ordinary commonsense reasoning is difficult to explain in terms of logical principles, as are analogies. He adds, 'Logic no more explains how we think than grammar explains how we speak.' Logic does not generate new truths, but rather allows one to evaluate existing chains of thought for consistency and coherence. It is precisely for that reason that it proves an effective tool for the analysis and communication of ideas and arguments." -- A.A., San Francisco, October 2013
As Spock from Star Trek would realize, “Logic is the beginning of wisdom, not the end."
Testing Arguments
Testing an argument to see if it is reasonable or logical is a great first step in deciding if you should accept or reject the claim of the argument. If the argument is not reasonable, then you can feel comfortable rejecting the claim. If the argument appears reasonable, then you can go to the next step and check for the accuracy of the statements contained within the argument. Don’t be fooled by an argument just because it is repeated over and over. Instead, examine the validity and accuracy of that argument. The critical thinker must remember that there is a difference between the reasoning needed to establish the validity of the argument and the level of evidence needed to substantiate the accuracy of an argument. Evaluating arguments involves analyzing both the validity of the type of reasoning used and the accuracy of the evidence presented.
Example: Black cats run the world because they are adorable.
Is the above argument reasonable? No. It isn't. Black cats do not run the world and cannot run the world. This is an invalid assertion.
Is the above argument accurate? Nope. Black cats being adorable is a matter of opinion, and again, there is no evidence - commonsense or otherwise - that black cats run the world (although one does a pretty good job of running my life).
When an argument includes both quality evidence and a valid reasoning foundation, the argument is considered to be sound.
This chapter will focus on three elements of reasoning: inductive reasoning, how we create generalizations; deductive reasoning, and how we apply those generalizations.