1 The Elements of Reasoning (Sixth Edition) Solutions to Exercises Chapter 1 A. (p. 10 ) 1. Not an argument. No claim here is intended to provide support for any other. 2. A simple argument. Although there are no indicator terms, the conclusion - “we were wise when we ceased the routine vaccination of children” – is evidently intended to follow from the other two claims. 3. A complex argument. In the first sentence, the word so indicates that what follows is a conclusion drawn from the previous claim. This conclusion in turn is a premise for “the job will go to Herbert”, as indicated by the conclusion indicator word thus . 4. Not an argument. This is a description of a series of procedures and observations. 5. A simple argument. Although there are no indicator words, the first three claims are each independent evidence for the last claim. 6. A complex argument. The second claim is intended to follow from the first, as indicated by the word thus ; and the last sentence contains the conclusion indicating phrase “that makes it obvious that” introducing the final conclusion “computers think”. 7. Not an argument. 8. A simple argument. No indicator words, but the conclusion is “the Taipei study doesn’t establish its conclusion at all”. 9. Not an argument. 2 10. A simple argument. The conclusion is “you should stop killing every spider you see”. 11. A simple argument. The first two sentences are claims intended to provide support for the last sentence. 12. A simple argument. The conclusion here is a claim disguised as a command. 13. A simple argument. The quoted passage constitutes the man’s support for the conclusion that his wife had the right to commit suicide. 14. Not an argument. 15. A simple argument. The conclusion is “we should not have a constitutional amendment banning flag burning.” The following claims are all in support of this conclusion. 16. Not an argument, but a description of a series of events. In the last sentence, thus means “in this way”. 17. A simple argument. We should regard “ritual or habitual cannibalism is either rare or non - existent” as the conclusion. What follows this claim is the support for it. 18. Not an argument. 19. There appear to be two distinct arguments here, one complex and one simple. The conclusion is the same in each case: there should be copyright laws. The complex argument goes like this: compensating people encourages more creative works and our society b enefits form these works; therefore people have a right to compensation for their creative work; therefore there should be copyright laws. The simple argument is a little harder to see, but try this: if there were no copyright laws then the only creative works would be those arising from the support of government and rich patrons; but there should be creative work arising other than from the support of government and rich patrons; therefore there should be copyright laws. 3 20. A simple argument. “It forms a strong presumption” operates as a kind of conclusion indicator. Here the conclusion is “there are no miracles.” B. (p. 12 ) 1. Unstated premise: anything that deliberately leads us to see an ordinary object in a new and interesting way is a genuine work of art. 2. Unstated premise: Tues day is the day of the test. 3. Unstated conclusion: Lopez ought to resign . 4. Unstated premise: Tiny is a pit bull. 5. Unstated conclusion: there is no justification for allowing Hovey to compete. 6. Unstated premise: taking a life is murder. 7. Unstated premise: any case of taking the life of a living human being is murder. 8. Unstated premise: any war (or perhaps anything at all) that causes the suffering of innocent people is unjust. 9. Unstated conclusion: I should not completely trust my senses. 10. Unstated premise: to count as a sport, an activity requires foot speed, stamina, or quick reflexes. 11. Unstated conclusion: there is no god . 12. Unstated premise: all forms of expression are constitutionally protected. 13. Unstated premise: anything that is offensive to a lot of us should be outlawed. 14. Unstated premise : anyone who takes a life should lose their life . 4 15. Unstated premise: if at one time there was nothing in existence, then now there would be nothing in existence (nothing comes from nothing) . 16. An atheist is someone who denies theistic claims. 17. Unstated premise: the table itself does not change as I change my perspective. 18. Unstated conclusion: animals do not reason. 19. Unstated conclusion: the killer was Colonel Sebastian Moran. 20. Anything desired by everyone is desirable. Chapter 2 A. (p. 24 ) 1. An explanation. 2. An argument. 3. An explanation. 4. Neither. 5. An explanation. 6. An argument. 7. Neither. 8. An argument. 9. Neither. 5 10. An explanation. 11. An argument. 12. An explanation. 13. Neither. 14. Neither. 15. An explanation. 16. An argument. 17. Neither. 18. An argument. 19. An explanation. It is unlikely(though not impossible) that anyone would argue for the conclusion that Allen is very ill on the grounds that he was bitten by a rattlesnake. More likely, is illness is already a recognized fact and the snake bite is the explanation of that fact. 20. An explanation. Again, it is likely that the deaths of thousands would be a fact known prior to the claim about farming methods; that claim constitutes an explanation of the deaths. B. (p. 25 ) 1. No matter what the fast drivers think, [higher speed limits will result in more needless deaths on the highway] 1 . (So) [the speed limits should not be raised] 2 . Diagram 1 ↓ 2 6 Standard Form 1. Higher speed limits will result in more needless deaths on the highway ∴ 2. The speed limits should not be raised. 2. [The Cat90 is the best lawn mower you can buy] 1 . (Since) [you want the best] 2 , [you should buy the Cat90] 3 . Diagram 1 + 2 ↓ 3 Standard Form 1. The Cat90 is the best lawn mower you can buy. 2. You want the best (lawn mower you can buy). ∴ 3. You should buy the Cat90. 3. [Without a tax increase there will soon be runaway inflation] 1 . But [Congress refuses to raise taxes] 2 . (Thus), [before long there will be runaway inflation] 3 . (That means that) [you should borrow all the money you can right now] 4 . Diagram 1 + 2 ↓ 3 ↓ 4 Standard Form 7 1. Without a tax increase there will soon be runaway inflation 2. Congress refuses to raise taxes. ∴ 3. Before long there will be runaway inflation. (1,2) ∴ 4. You should borrow all the money you can right now.(3) 4. Because [Henry has started on a weight - lifting program] 1 and [weight lifters are very strong] 2 , (it follows that) [Henry will soon be very strong] 3 . And [anyone who is unusually strong can make the football team] 4 . (So) [Henry will make the team this year] 5 . Diagram 1 + 2 ↓ 3 + 4 ↓ 5 Standard Form 1. Henry has started on a weight - lifting program. 2. Weight lifters are very strong ∴ 3.. Henry will soon be very strong 4. Anyone who is unusually strong can make the football team. ∴ 5. Henry will make the team this year. 5. [People who study history are wiser than those who do not] 1 . [Studying history makes a person less likely to repeat the mistakes of the past] 2 , and [not repeating past mistakes is a sign of wisdom] 3 . And (because) [the primary aim of education is producing wisdom] 4 , [all universities should require the study of history] 5 . 8 Diagram 2 + 3 ↓ 1 + 4 ↓ 5 Standard Form 1. Studying history makes a person less likely to repeat the mistakes of the past. 2. Not repeating past mistakes is a sign of wisdom. ∴ 3. People who study history are wiser than those who do not. (1,2) 4. The prime aim of education is producing wisdom. ∴ 5. All universities should require the study of history. (3,4) 6. [Never, never pass up a four - leaf clover] 1 ! [They are very rare] 2 (because) [a clover normally has three leaves] 3 , and [the four - leaved ones bring good luck] 4 . Diagram 3 ↓ 2 + 4 ↓ 1 Standard Form 1. A clover normally has three leaves. ∴ 2. (Four - leaf clovers) are very rare. (1) 3. The four - leaved ones bring good luck. ∴ 4. Never, never pass up a four - leaf clover. (2, 3) 9 7. [Anything worth recording has been entered in the ship’s log] 1 , (so) [I can be sure I’ve never met a mermaid] 2 . [A mermaid would be worth recording] 3 , and [there’s nothing about meeting a mermaid in my ship’s log] 4 . Diagram 1 2+3 ↓ 4 Standard Form 1. Anything worth recording is in the ship’s log. 2. A mermaid would be worth recording 3. There is nothing about meeting a mermaid in the ship’s log. ∴ 4. I can be sure I’ve never seen a mermaid. 8. [AIDS may be the most horrible disease in the world’s history] 1 . [It is always lethal] 2 . [There is no cure] 3 . And [it is most often transmitted through pleasure] 4 . Diagram 2 3 4 ↓ 1 Standard Form 1. [AIDS] is always lethal. 2. There is no cure [for AIDS]. 3. [AIDS] is most often transmitted through pleasure. ∴ 4. AIDS may be the most horrible disease in the world’s history. 10 9. [Higher education should increase our ability to think critically and to appreciate a greater variety of experiences] 1 . (Thus), [it is good to take courses in the humanities, science, and social science] 2 . (So), [students who take the advanced - level course in twentieth - century American poetry have made a wise choice] 3 . Diagram 1 ↓ 2 ↓ 3 Standard Form 1. Higher education should increase our ability to think critically and to appreciate a greater variety of experiences. ∴ 2. It is good to take courses in the humanities, science, and social science. (1) ∴ 3. Students who take the advanced - level course in twentieth - century American poetry have made a wise choice.(2) 10. [We should go for a hike in the canyon this weekend] 1 . [The air is crisp] 2 , and [the leaves are turning to lovely reds and yellows] 3 . And [the exercise will be good for us] 4 , (since) [we haven’t been out all week] 5 . (So), [let’s take the hike] 6 . Diagram 1+2 ↓ 3 4+5 ↓ 6 11 Standard Form 1. The air is crisp. 2. The leaves are turning to lovely reds and yellows. ∴ 3. We should go for a hike in the canyon this weekend. (1,2) 4. We haven’t been out all week. 5. The exercise will be good for us. ∴ 6. Let’s take a hike.(3, 4, 5) 11. The hike has been nice, but [we must be pretty far from civilization] 1 , (because) [the only people we have seen in the last three hours have been toting big backpacks] 2 . (So) [we better turn around before we get lost in the middle of nowhere] 3 . Diagram 2 1 3 Standard Form 1. The only people we have seen in the last three hours have been toting big backpacks. ∴ 2. We must be pretty far from civilization. 1 ∴ 3. We had better turn around before we get lost in the middle of nowhere. 2 12. [The fate of the hikers will forever be a mystery] 1 . [The Weekly World News said they were devoured by army ants] 2 , but [not much in WWN is true] 3 , (so) [probably they weren’t] 4 . [If they weren’t, we just don’t know what happened to them] 5 . (So), [we will always be wondering] 1 . Diagram 2 + 3 12 ↓ 4 + 5 ↓ 1 Standard Form 1. The Weekly World News said [the hikers] were devoured by army ants. 2. Not much in WWN is true. ∴ 3. Probably [the hikers] weren’t [devoured by army ants]. (1,2) 4. If they weren’t, we just don’t know what happened to them. ∴ 5. The fate of the hikers will forever be a mystery.(3,4) 13. (It is obvious that) [the judge committed the murder] 1 , (given that) [either the butler or the judge did it] 2 . (Since) [the butler was passionately in love with the victim] 3 , [it was not she who committed the murder] 4 . Diagram 3 . ↓ 4 + 2 ↓ 1 Standard Form 1. The butler was passionately in love with the victim. ∴ 2. [The butler] did not commit the murder. 1 3. Either the butler or the judge [committed the murder]. ∴ 4. The judge committed the murder. 2, 3 14. [The detective is unlikely to be a convincing witness] 1 (because) [he has the reputation of being a racist] 2 . (Probably, then), [the defendant will be acquitted] 3 . 13 Diagram 2 ↓ 1 ↓ 3 Standard Form 1. [The detective] has the reputation of being a racist. ∴ 2. The detective is unlikely to be a convincing witness. ∴ 3. The defendant will be acquitted. 15. [If the detective really is a racist] 1 — (which) [he is] 2 — [then he never should have been allowed to testify at all] 1 , (since) [white racists are especially unreliable witnesses when the accused is a person of color] 3 . (So), [the detective should not have been allowed to testify at all] 4 . Diagram 3 ↓ 1 + 2 ↓ 4 Standard Form 1. White racists are especially unreliable witnesses when the accused is a person of color. ∴ 2. If the detective is really a racist he should not have been allowed to testify. 1 3. The detective is a racist. ∴ 4. The detective should not have been allowed to testify. 2, 3 14 16. [The eighteenth - century philosopher David Hume (was undoubtedly) a finer thinker than his even more celebrated successor Immanuel Kant] 1 . [Hume was by far the more lucid writer] 2 . [His contributions were more diverse than Kant’s] 3 , (for) [he was a first - rate historian as well as a philosopher] 4 . (Further), [Hume’s ethical thought did not suffer from the rigidity of Kant’s] 5 . [Hume, unlike Kant, would never have said the duty not to lie is so absolute that we should answer truthfully even when a would - be mur derer asks where his intended victim is hiding] 6 . (Thus), [there can be little doubt that, of the two, Hume was the superior thinker] 7 . Diagram 4 6 ↓ ↓ 3 + 5 + 2 ↓ 1 Standard Form 1. [Hume] was a first - rate historian as well as a philosopher. ∴ 2. [Hume’s] contributions were more diverse than Kant’s. (1) 1’. Hume would never have said the duty not to lie is so absolute that we should answer truthfully even when a would - be murderer asks where his intended victim is hiding. ∴ 2’. Hume’s ethical thought did not suffer from the rigidity of Kant’s. (1’) 1*. [Hume’s] contributions were more diverse than Kant’s. (1) 2*. Hume’s ethical thought did not suffer from the rigidity of Kant’s. (1’) 3*. Hume was by far the more lucid writer. ∴ 4*. David Hume was undoubtedly a finer thinker than his even more celebrated successor Immanuel Kant. 15 17. [Either the market has bottomed out or we’re in for several more months of rocky times for investors] 1 . [If this is the market’s lowest point, then the Fed will not be thinking of lowering interest rates further] 2 , but [the latest report from the chairman of the Fed tells us that interest rates will go down further] 3 . (So clearly) [this isn’t the bottom of the market] 4 , (and consequently) [it’s a bleak time ahead for investors] 5 . Diagram 1 2+3 ↓ 4 1 ↓ 5 Standard Form 1. Either this is the bottom of the market or it is a bad time for investors. 2. If this is the bottom of the market, then the Fed will not lower rates. 3. The Fed will lower rates. ∴ 4. This is not the bottom of the market. 2, 3 ∴ 5. This is a bad time for investors. 1, 4 18. [Dozens of people have claimed to have seen Elvis Presley since he was supposed to have died in 1978] 1 , (so) [he must still be alive] 2 , (since) [that many people wouldn’t be wrong] 3 . (On account of the fact that) Elvis is alive, [“Hound Dog” will soon again be a best - selling single.] 4 Diagram 1 + 3 ↓ 2 ↓ 4 Standard Form