13.2: What is Reasoning?
- Page ID
- 199351
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)What is Reasoning?
We reason all the time, but what are we doing exactly? This answer might not be immediately obvious, so let’s begin with some straightforward cases to see what they have in common:
- Solving a math problem
- Figuring out why your phone won’t work correctly
- Deciding who to vote for
- Working out why your friend is angry with you
- Determining whether you can afford to buy a new car
What do these have in common? We could pick out a number of features, but we will focus on two in particular. First, in each case our thinking is driving toward a specific outcome or conclusion (e.g. “my phone won’t work because…”, or “the answer is…”, etc.). Second, in each one of these cases this conclusion will be based on reasons. That is, we will arrive at a specific conclusion because we think we have good reasons for doing so. Let us take a closer look at each of these features.
Reasoning is a mental process that ends with a conclusion. Sometimes this conclusion is a newly formed belief. You might, for example, be asked to find the average of 88, 69, 94, and 77 and arrive at the new belief that the average of these numbers is 82. Alternatively, you might troubleshoot your phone and arrive at the new belief that the operating system wasn’t properly installed. While reasoning always leads to a conclusion, that conclusion need not be a new belief. In some cases, these processes lead us to be more (or less) confident in beliefs we already hold.& We can see both kinds of conclusion at work in the following example.
Ex. 1:
Talia wakes up one morning to discover that her car is missing. As she thinks about it she quickly concludes that her brother has probably borrowed it. Her reasons for drawing this conclusion are that he i) knows where her spare set of keys are, ii) has borrowed it without asking in the past, and iii) is supposed to pick up a cake at a bakery across town today. Just after she has come to this conclusion the phone rings. It is one of Talia’s friends who mentions that she saw Talia’s car parked at the bakery across town.
In the first part of Ex. 1 Talia is reasoning to a new belief, namely that her brother has borrowed her car. When her friend calls, she gets a new piece of information. However, this information does not lead her to any new belief; after all, this information is an additional reason for thinking that her brother has borrowed the car, and she already believes that.; Instead, as a result of this news, she is even more confident that her brother has borrowed the car. In light of this distinction, we will say that reasoning is a process that leads to a change in a person’s system of belief, and we will understand a person’s system of belief to include not only their beliefs, but also the relationships between those beliefs, and the confidence with which they are held.
The second defining feature of reasoning is that it is a process whereby we change our system of beliefs because we have reasons for doing so. In general, to have reasons for drawing some conclusion is to have some group of existing beliefs that indicate in one way or another that the conclusion in question is true. In the example above, Talia has a variety of existing beliefs about her brother and his circumstances, and she takes this information to point toward the fact that her brother has borrowed the car.
Importantly, our reasons can indicate the truth of the conclusion to different degrees. When we take ourselves to have solved a math problem correctly, for example, we take ourselves to have shown that the conclusion is correct. This is a bit different from Talia’s reasoning—she probably wouldn’t say that her reasons show or prove that her brother borrowed the car. Nonetheless, she thinks that her reasons are good enough to draw the conclusion. In general, reasons can support conclusions with different degrees of strength, and it should be no surprise that we have many different ways of talking about this support. We can say, for example, that when we reason we take our existing beliefs to indicate, give good reason for, offer evidence on behalf of, establish, warrant, or demonstrate a change to our system of beliefs. These differences will be important later, but for now we will simply say that when we reason, we take our existing beliefs to justify a particular change in our system of belief.
Now that we have taken a brief look at the reasoning process, we can return to the question we began with and define reasoning as follows:
Reasoning is the process whereby a person changes their system of belief on the basis of reasons which they take to justify this change.