4.1: Arguments
- Page ID
- 306933
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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 way to determine whether a claim is true or false, when this is possible, is to evaluate the evidence and argument for and against it. Sometimes good reasons take the form of simple observations. I have a good reason for thinking my bicycle has a flat tire when I see the tire sagging on the rim. But often the business of identifying and evaluating reasons is a bit more involved.
An argument is a reason for taking something to be true. Arguments consist of two or more claims, one of which is a conclusion. The conclusion is the claim the argument aims to establish as true. The other claims, there can be one or many, are the premises. The premises of an argument taken together are offered as a reason for believing its conclusion to be true.
Some arguments provide better reasons for believing their conclusions than others. In case you have any doubt about that, consider the following examples:
- Sam is a line cook.
- Line cooks generally have good of kitchen skills.
- So, Sam can probably cook well.
and
- Sam is a line cook.
- Line cooks usually aren’t paid very well.
- So, Sam is probably a millionaire.
The premises in the first argument provide pretty good support for thinking Sam can cook well. That is, assuming the premises in the first argument are true, we have a good reason to think that its conclusion is true. The premises in the second argument constitute a pretty poor reason to think Sam is a millionaire. So, whether or not the premises of an argument support its conclusion is one important factor in evaluating an argument.
Now consider these examples:
- Boston is in Massachusetts.
- Massachusetts is east of the Rockies.
- So, Boston is east of the Rockies.
and
- Boston is in California.
- California is west of the Rockies.
- So, Boston is west of the Rockies.
Again, the first of these two arguments looks good, the second not so much. But the problem with the second of these arguments is different. The premises of both arguments provide good support for the conclusion. That is, in both arguments, if the premises were true, we’d have good reason for accepting the conclusion. In fact, for both arguments, if the premises were true, the conclusion would have to be true. So, in both of these arguments we have a good relation of logical support between the premises and the conclusion. But the first premise of the second argument just isn’t true. Boston is not in California. So, the latter pair of arguments suggests another key issue for evaluating arguments. Good arguments have true premises.
That is pretty much it. A good argument is an argument that has true premises that support its conclusion. So, evaluating an argument involves these two steps:
- Determine whether or not the premises are true.
- Determine whether or not the premises support the conclusion (that is, whether we have grounds to think the conclusion is true if all of the premises are true).
Determining whether an argument’s premises are true may involve evaluating further arguments in support of those premises. An argument might be the last link in a long chain of reasoning. In this case, the quality of the argument depends on the whole chain. And since arguments can have multiple premises, each of which might be supported by further arguments, evaluating an argument might be more involved yet, since its conclusion is really supported by a rich network of reasoning, not just one link and then another. While the potential for complication should be clear, the basic idea should be pretty familiar. Think of the regress of “why” questions many of us tormented our parents with as children. Even at a young age we understood that the reasons for believing one thing can depend on the reasons for believing a great many other things.