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3.E: Chapter Three (Exercises)

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    How can I tell one from the other?

    • Objections to inferences usually use phrases like “that doesn’t follow,” or “even if we accept x, we need not accept y.”
      • The objection is that the inference itself is incomplete or weak or invalid or simply doesn’t make any sense.
      • An objection to a hidden premise is actually an objection to an inference: you’re claiming that the inference rests on a weak hidden premise and so is an incomplete inference.
    • Objections to propositions/premises will always be arguing that some proposition is false rather than that a conclusion doesn’t follow.
      • The objection is that some particular claim is false or at least is likely or plausibly false.
    Exercise \(\PageIndex{1}\): Conjoint vs Independent Support

    For each, determine whether the support offered by the premises is conjoint or independent. Deploy the negative test when you’re unsure.

    A. Eating healthy food is important and Figs are super healthy, so we should eat more figs.

    B. I have to have a steady income to support my family, I already have a stable job, and grad school would require me to quit my job, so I shouldn’t go to grad school.

    C. All of the nurses have gone on the strike, the custodial staff is threatening the same, and the doctors are demanding better legal support. This hospital is in trouble right now.

    D. He is ten years younger than you and no one should date anyone ten years younger, so you can’t date him!

    E. An ergonomic desk can prevent permanent injury, is more comfortable to use, and is cost-effective, so can I please buy one for my office?

    F. A robust economic recovery will require higher taxes on the wealthy, and we need to have a strong recovery to prevent melt downs in the near future, so we must raise taxes on the wealthy.

    G. We’ve always been honest with each other and the honest thing to do right now is to tell you that that outfit is terrible, so I need to tell you the truth about that outfit.

    Exercise \(\PageIndex{2}\): Terminology

    Fill in the blank labels using one of each of the following key terms: (A) Sub-Conclusion, (B) Sub-Premise, (C) Main Premise, (D) A premise on level 4 of the argument map, (E) A premise on level 2 of the argument map, (F) Conjoint Premise, (G) Independent Premise.

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    Exercise \(\PageIndex{3}\): Simple Argument Maps

    For each, create an argument map. Be sure to distinguish between conjoint and independent support.

    A. (1) Eating healthy food is the most effective weight-loss strategy, since (2) the amount of calories one takes in while eating even small snacks takes a long time to burn off by exercising, and (3) almost no one can afford to spend hours and hours exercising throughout the day.

    B. (1) We’ve been out here in the sun all day, and (2) being in the sun for too long is unhealthy, so (3) let’s go inside.

    C. (1) He’s so popular. (2) Everyone wanted to be invited to his birthday party and (3) he had five people invite him to the dance.

    D. (1) We should ban all guns. (2) Guns are especially effective killing machines for mass killings. Also, (3) children often have fatal accidents with guns. Furthermore, (4) guns don’t have a non-violent use.

    E. (1) Having intercourse before 18 is wrong because, (2) you are not emotionally mature enough to deal with the awkwardness and intimacy of the situation, and (3) you are not mature enough to deal with the potential consequences of the situation (pregnancy or STIs).

    F. (1) Treating others with respect is important, so (2) we should all respect each other, and (3) we should try to teach our children to respect others.

    G. (1) Oreos aren’t healthy, since (2) Nabisco products generally aren’t healthy. Think about it: (3) Pringles aren’t healthy, (4) Pop Tarts aren’t healthy, and (5) neither are Chips Ahoy.

    H. (1) People are starting not to like you. (2) Tina said she wasn’t your friend anymore, (3) Beto said he doesn’t like you, and (4) I certainly don’t want to be around you.

    Exercise \(\PageIndex{4}\): More Complex Argument Maps

    For each, create an argument map. Be sure to distinguish between conjoint and independent support.

    A. (1) I know that Sally went to the park with Billy because (2) Sally said she’d go with him if he asked, and (3) Billy likes Sally (so he wouldn’t ask her as a prank) and (4) Billy asked Sally to go to the park.

    B. (1) Eating any meat is wrong because, (2) most meat is produced in factory farms, (3) animals in factory farms suffer greatly, and (4) even ‘free range’ and ‘organic’ meat causes animal suffering.

    C. (1) We already have almost all of the technology needed to clone dinosaurs and (2) human beings tend to do whatever they find they can do. (3) So, killer dinosaurs will roam the Earth one day. And since this is true, we can expect two things: (4) an armed response leading to the loss of innocent life, and (5) movie producers trying to buy the rights to the story.

    D. (1) Burning fossil fuels like petrol, coal, and natural gas contributes to global warming. (2) According to experts, the combustion reaction releases free molecules of CO2 into the atmosphere, and (3) Scientists wouldn’t lie about this. Think about it: (4) there’s no profit incentive for scientists to lie about this, but (5) there is a profit motive for other people to deny that it is true.

    E. The Republicans have argued repeatedly that (1) the Affordable Care Act is in a death spiral. Because, they say, (2) premiums are getting higher, and (3) as premiums get higher, the people will stop purchasing policies and (4) if the people stop purchasing policies, then the insurance companies will pull out of the exchanges, and (5) if that happens, then the whole system collapses.

    F. (1) We need to protect the environment, since (2) biodiversity is necessary to protect future food sources and (3) biodiversity is sustainable only in a relatively healthy global environment. Furthermore, (4) We take great pleasure in the natural wonders that the Earth has to offer (5) [suppressed premise]

    Exercise \(\PageIndex{5}\): Even More Complex Argument Maps

    For each, create an argument map. Be sure to distinguish between conjoint and independent support.

    A. (1) We need to buy a new trampoline, since (2) our son almost hurt himself really badly when this one broke last week, and (3) I don’t want to risk it again. (4) Even if you’re able to fix it, there’s no guarantee that it will be as safe as a new one. Think about it: (5) older trampolines like ours don’t have a net around them, and (6) the net makes it less likely that a kid will bounce off onto the ground and hurt themselves. Finally, (7) older trampolines like ours don’t have good spring covers, and (8) without spring covers, the risk of pinching oneself or falling through the springs and breaking a limb are very high.

    B. (1) Eating kale is sometimes unsatisfying, but the fact is that (2) Kale has countless health benefits. (3) It is rich in folate and (4) folate helps guard against bad epigenetic changes. (5) It has more minerals and vitamins than most meat sources and (6) vitamins and minerals got from whole food sources are better than those got from multivitamins and other supplements since (7) whole foods contain more bioavailable forms of vitamins and minerals.

    C. (1) We’ve already been in Afghanistan for over a decade and (2) no other American war has lasted this long, so (3) Afghanistan is the longest running American war. (4) We’ve shown little sign of progress in the past few years, and (5) we’ve sunk countless dollars into Afghan infrastructure and security projects with little to show for it. Given all of this, (6) we should pull out of Afghanistan and (7) we should divest interest in the Afghan society. (8) Since we’ve already tried so hard to fix it, (9) we should let them try to solve their own problems!

    D. (1) Epigenetics is the most important frontier in genetic research. (2) Countless traits and processes depend not on genetic changes, but on epigenetic changes, (3) epigenetic changes are easier to induce through therapies, chemicals, and other interventions in a clinical setting, and (4) we already know the basic rules of genetics, but are far behind in our understanding of epigenetics. Given all that, it follows that (5) we should shift the balance of funding in favor of epigenetic research and (6) we should fund more PhD’s in epigenetics as well.

    E. (1) We should put more direct emphasis in school and college on thinking clearly and critically. (2) The most important skill in life is thinking well. I think this because (3) other important skills like decision making and communication rely centrally on thinking well, and (4) a good citizen, employee, and overall person is one who can think clearly and rationally. (5) Citizens must weigh complex values in voting on candidates and referenda, (6) employees must make decisions in the workplace based on complex policies and competing needs, and (7) people in general need to have habits of self-critical and careful thinking in order to live good lives.

    Exercise \(\PageIndex{6}\): Hidden Assumptions

    For each inference, identify the most direct hidden assumption.

    A. Moby Dick is a whale. So Moby Dick is a mammal.

    B. Giving students a fail grade will damage their self-confidence. Therefore, we should not fail students.

    C. It should not be illegal for adults to smoke pot. After all, it does not harm anyone.

    D. There is nothing wrong with texting during lectures. Other students do it all the time.

    E. Traces of ammonia have been found in Mars' atmosphere. So there must be life on Mars.

    F. I don't like people who spit on the sidewalk, so littering should be illegal.

    G. No one even cares what you think, so what you think isn't important.

    H. Americans believe in freedom, so any law that restricts our freedom should be abolished.

    I. Trees are beautiful, so we should plant more of them.

    J. Carbon emissions contribute to global warming, so we should tax them.

    Exercise \(\PageIndex{7}\): Mapping Hidden Assumptions

    For each inference, identify the hidden assumption and then create a map of the inference including the hidden assumption.

    A. The truth is, (1) we can’t vote for the Republican candidate. (2) She doesn’t believe in global warming.

    B. (1) Nobody has ever been there and come back, and (2) I have children, so (3) I’m not going.

    C. (1) Freedom isn’t free. (2) So, someone has to pay the price for freedom. (3) The way people pay the price of freedom is by serving in the armed forces. (4) So we should institute a draft. [at least two hidden assumptions]

    D. (1) Nobody has ever seen a dinosaur, so (3) dinosaurs don’t exist.

    E. (1) We should reduce the penalty for drunken driving, as (2) a milder penalty would mean more convictions. (3) The only way to reduce the penalty is to elect more liberal judges and prosecutors, so (4) we should elect liberal judges and prosecutors.

    F. (1) Never again should we bow to tyrants, because (2) tyranny has been the mark of rule throughout human history, (3) as has cruelty and abject want. It follows that (4) we must rebel against the Imperial rule of England.

    G. (1) Only real marriages should be recognized by the state, so (2) polygamist marriages shouldn't be recognized by the state. (3) Any marriage not recognized by the state should be illegal. So (4) polygamist marriages should be illegal. (5) Another reason they should be illegal is that, polygamist marriages often result in abusive situations. [the hidden assumption is between 1 and 2]

    H. (1) No one believes in Odin anymore, so (2) why should anyone believe in God? [this is a rhetorical question, which is a claim that is disguised as a question. The claim appears to be "no one should believe in God”]. (3) If no one should rationally believe in something, then we should actively fight against belief in it. It follows that (4) we should actively fight against belied in the existence of God. (5) A world without believers would be a better world to live in. [the hidden assumption is between 1 and 2]

    I. (1) We can't let terrorists live here with us in Pakistan, so (2) we should expel all Christians from our country. (3) Christians also don't contribute to the economy and (4) could potentially be spies for the Americans. [Where's the most blatant hidden assumption? There are more than one, but one in particular is relatively clearly a missing assumption of the argument]

    Exercise \(\PageIndex{8}\): Identifying Types of Objections

    Identify which type of objection is illustrated: an objection to a premise or an objection to an inference (including pointing out that there’s a hidden premise and/or rejecting a hidden premise)?

    A. I agree with your conclusion, but it doesn’t follow from your assumptions.

    B. Interesting argument, but what I don’t understand is your claim that every case of tyranny is a case of injustice. That doesn’t seem quite right.

    C. You claim that there isn’t a threat to the Amazon. On the contrary, there are countless threats, one of which is people claiming that there isn’t a threat to the Amazon!

    D. So if I accept all of your assumptions, it doesn’t seem to me that I must accept your conclusion.

    E. If I have it right, it seems to me that your inference rests on a hidden assumption that we ought to do whatever is in our national interest. That’s not clearly true. Think about cases of humanitarian aid that only very indirectly if at all are in our national interest.

    F. I think I understand the general thrust of this argument, but one claim makes me uncomfortable. Your inference rests on the claim, as you stated it, that Great Britain is to blame for more historical atrocities than any other European nation. That’s not clearly right.

    G. I don’t think this is a good argument. We won’t clearly advance well beyond where we are today in terms of computing power because of the physical limits of the hardware we have available.

    Exercise \(\PageIndex{9}\): Mapping Ojections

    Identify which kind of objection is illustrated and then map the objection along with the original argument.

    A. Person A: (1) Edward Snowden released petabytes of classified data. (2) He should be convicted of treason.

    Person B: Wait a minute! (3) We shouldn’t just convict anyone who releases that much data of treason!

    Person A: (4) If we don’t, then we’ll be opening the door to more dangerous leaks.

    Person B: (5) Actually, come to think of it, I don’t think he did release petabytes. I think it was only Terabytes.

    B. The Republicans have argued repeatedly that (1) the Affordable Care Act is in a death spiral. Because, they say, (2) premiums are getting higher, and (3) as premiums get higher, the people will stop purchasing policies and (4) if the people stop purchasing policies, then the insurance companies will pull out of the exchanges, and (5) if that happens, then the whole system collapses. But their conclusion doesn't follow, since (6) people need health insurance and won't stop purchasing it if prices continue to rise incrementally.

    C. Person A: (1) College isn't designed around the goal of producing good plumbers and electricians and welders. (2) Furthermore, college is expensive and (3) college is time-consuming. So (4) we shouldn't expect everyone to go to college.

    Person B: I understand your inference, but (5) college does make one a better plumber, electrician, and welder because it gives you a host of intellectual resources to bring to bear on solving the many unforeseen problems that arise on jobs like that.

    Person C: I actually take issue with the inference here from your first claim to your conclusion, since (6) college isn't about job training, but is instead about creating a well-informed citizenry that can make rational and informed decisions at the voting booth.

    D. Obama argued that (1) we should pass the ACA, claiming that (2) there is an epidemic of chronically-ill citizens without health insurance due to their pre-existing conditions and that (3) many citizens simply can’t afford health insurance.

    But (4) the ACA won’t provide health insurance to a large group of relatively poor Americans.

    E. Her argument was as follows: “(1) No one wants to be put in the position where they are faced with a deadly intruder without the proper means to protect theirself and their family. (2) Gun laws make it probable that someone will end up in that situation. (3) Therefore, we can’t enact gun control legislation.”

    But that argument isn’t convincing. (4) Even if we accept the premises, we need not accept the conclusion. After all, there are reasons to pass gun control that must be addressed.

    Exercise \(\PageIndex{10}\): Hidden Assumptions and Objections

    Identify the hidden assumptions in the first argument and then map both the argument and the objections. Remember that objections to hidden assumptions are objections to inferences and so they should be mapped as such.

    A. Frank: (1) We'll never make it to the party on time, so (2) let's just turn around and head home. (3) Samir and Imani live miles away and (4) we can't go very fast in this traffic.

    Margaret: That's ridiculous, we'll absolutely make it on time. First, (5) we have 30 minutes to get there and also (6) we could be 15 minutes late and still be "on time" since it's a party.

    B. Tamil: (1) We need to protect the environment, since (2) biodiversity is necessary to protect future food sources and (3) biodiversity is sustainable only in a relatively healthy global environment. Furthermore, (4) we take great pleasure in the natural wonders that the Earth has to offer (5) [suppressed premise]

    Jamal: (6) I agree with your conclusion, but even if we accept that biodiversity is necessary and that protecting the environment is necessary for protecting biodiversity, we need not accept your conclusion.

    C. (1) Counting Crows wrote and performed Mrs. Robinson, so (2) They’re the best band ever.

    Ummm... (3) they wrote and performed “Mr. Jones”, not Mrs. Robinson. And either way (4) neither song would make them the best band ever.

    D. He said “(1) I need some space, so (2) we need to break up.” But (3) he doesn’t need space. And either way, (4) needing space isn’t a good enough reason to break up with someone.

    E. She said “(1) Potato chips are high in saturated fat and salt, and so (2) they should be consumed very sparingly.” But that’s a bad inference since (3) dietary research is overturning the idea that saturated fat is bad for humans and (4) humans need salt to maintain proper blood volume and electrolyte concentrations.

    F. Pablo: (1) We shouldn’t eat even fake animal meat since (2) we wouldn’t think it’s okay to eat fake human meat. Afterall, (3) eating fake human meat would be tacitly affirming that cannibalism is morally acceptable. Marisela: I disagree, (4) there’s a faulty hidden premise there: that eating fake animal meat is analogous to eating fake human meat. Furthermore, (5) the other inference for the claim that eating fake human Meat is wrong has a hidden assumption as well and I’m not so sure it’s correct.


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