4.E: Chapter Four (Exercises)
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Identify the vice of relevance being illustrated by each argument. Remember that “no vice present” is always an option. Try to decide whether this is virtuous reasoning or not.
A. You’ve attack me instead of my argument, so clearly you don’t know how to reason and I’m correct after all.
B. You’ve claimed that it’s wrong to use animals and so we should all become vegans, so you’re claiming that all living things are things we can’t eat? Does that mean that we can’t eat plants even? We have to eat something!!!
C. She’s from Kentucky, so clearly she doesn’t know a danged thing about sailing!
D. Look, you might as well just admit you’re wrong. Everyone will shun you if you don’t.
E. My opponent has argued that the death penalty is costly and so should be abolished, but she also supports cutting taxes! We can’t cut taxes in the middle of a budget crisis.
F. You’ve mentioned before that you reject the tenets of capitalism, but you went to a public school, so you’re not exactly an impartial judge of whether or not socialism is a good thing!
Identify the vice of presumption being illustrated by each argument. Remember that “no vice present” is always an option. Try to decide whether this is virtuous reasoning or not.
A. I believe that the government is poisoning us through breakfast cereals. If you want me to eat that, you’re going to have to prove to me that it’s safe.
B. There’s either no reason to go to space, or we should put billions into technologies which allow us to go into space. All or nothing.
C. You’re either a Raiders fan or you’re not a Raiders fan. Those are the only two options.
D. Look if it’s bad to steal things, then it’s wrong to take food that doesn’t belong to you. It is bad to steal things, so it follows that you shouldn’t take food from that vendor at the market.
E. The Republicans haven’t championed a single non-cynical or moral policy in decades. I invite you to come up with a single example.
F. We need to bolster our space travel infrastructure, because we need to have easy and cheap access to space in the next forty years. Look, there’s going to be an increased need for space travel in the near future, so we’ll need cheaper access to space. A space elevator would fit the bill, and we should build one since we need to have more robust space travel infrastructure.
G. Nobody likes you. I asked everyone on the playground and not a single person said they wanted to be friends with you.
H. There will always be income inequality since there will always be rich and poor no matter what we do.
I. We shouldn’t invade Iran since we shouldn’t pre-emptively attack a relatively non-violent sovereign nation.
Try to decide whether this is virtuous reasoning or not. If not, try to diagnose what specifically is going wrong in your own words. Then, identify the vice illustrated by each argument (can be vices of relevance or presumption). Remember that “no vice present” is always an option—it could be an example of basically virtuous reasoning!
A. You can’t be a half-hearted vegetarian. You have to choose sides: either you’re a vegan and an abolitionist or you’re a murderer and an enslaver.
B. Eating meat is wrong because it’s wrong to consume the flesh of another sentient (feeling, experiencing) being.
C. Written on a park table in Portland: “My bus costs $2.50. Does that mean I own it now?”
D. I saw some young folks at the park yesterday and they seemed to be on drugs. Isn’t it terrible what is happening to our youth these days?
E. I’m pretty sure we shouldn’t go to war, so that evidence that Assad is using nerve gas against his own citizens must be met with extreme suspicion.
F. We have the lowest prices since we always have lower prices than our competitors. You can be sure we always have lower prices than our competitors because we have the lowest prices available.
G. Andrew Lavin is the best textbook author because he wrote the best textbook and the author of the best textbook must be the best textbook author.
H. I won’t be manipulated into believing that Area 51 isn’t a storage facility for alien artifacts and specimens, you’ll have to prove it to me using evidence and reasons.
I. I wouldn’t want you to lose the next election, and I would know how to make that happen, so I expect you’ll be agreeing with our policy proposal.
J. I want to go to North Korea on vacation. You’ll have to prove to me it’s a bad idea if you don’t want me to go.
K. You want to watch the new Transformers movie? You know Michael Bay directed it, right? It’s going to be terrible.
L. That cheese comes from Turkey, where they don’t require pasteurization. I wouldn’t recommend eating it while pregnant since listeria and other bacterial infections can be deadly to a developing fetus.
M. I understand you’re frustrated with my habits, but you have some bad habits too, you know?
N. I understand that you don’t want me to go on this vacation, and I respect that, but remember when you went on that vacation to visit your nephew last summer? That was a good time, right? I’m so glad you got to go on that vacation. Good times.
O. That’s a slippery slope. I don’t think your position can possibly be correct with reasoning like that behind it!
P. I understand you have a history of mental illness, so tell me how are we to trust your reasoning when you argue based on evidence and reasons that the Democratic Party is hopelessly corrupt and must be dissolved?
Q. I don’t know. Lots of people seem pretty convinced that marriage is a love-based bond between two consenting adults, so it seems like that’s what marriage is.
R. Bieber can’t be the best musician. He’s from Canada! They don’t make good music in Canada.
S. Alanis Morrisette didn’t understand the concept of irony when she wrote “Ironic”. She’s clearly not the most astute student of the linguistic arts.
T. That car won’t run well. It was built in Russia. Cars from Russia don’t tend to run well.
U. Which color do you want your car to be? Black or Gray?
V. If everyone starts believing in the tooth fairy, we’ll have folks ripping out their teeth for money, so we can’t encourage people to start believing in the tooth fairy.
W. Miley Cyrus said that D’Addario strings are the best guitar strings. She’s a famous guitar player and musician, so I supposed D’Addario strings are really the best.
X. Rambo wasn’t the greatest movie of all time. Did you know that Sylvester Stallone had a role in creating the characters and story for Creed? It was Ryan Coogler’s break out film and he later went on to direct Black Panther.
Y. Veronica: I think I saw something out of the corner of my eye right now that may have been a ghost.
Hypatia: Are you saying there was definitely a ghost over there? Do you have any idea how implausible that is?
Z. Franz: There may be some reason to suspect that the threat from global warming has been overblown.
Valeria: Are you kidding me? You’re a climate denier? All of the evidence points to the fact that humans have played the decisive role in warming the global climate. I can’t believe you’d deny that!
AA. You’ve seen a ghost? That’s pretty spooky. But you take anti-depressants, right? So I guess you’re not that reliable [note: there is no known connection between anti-depressants and hallucinations].
BB. The CEO of Exxon Mobil has recently admitted that because of the overwhelming consensus among climate experts, we have to admit that global warming is real. But obviously they’re not an impartial person so we can reject their position. They’re probably doing this just for good press.
CC. My biology teacher says global warming was caused by humans burning fossil fuels and their deforestation practices. She’s a scientist, so she must be right about this.