This is not possible: by definition, if an argument is valid, it’s not possible for the premises to be true and the conclusion false. But if the premises of an argument are true, and the conclusion is false, then clearly this is something that can happen. 3. The Sun is bigger than the Moon. The Moon is bigger than the Earth. So the Sun is bigger than … Purchase answer to see full attachment

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Argument and their Elements 2 PHI 1101 Arguments in standard form • It can be useful to make the structure of an argument perfectly clear by writing its various claims in a numbered list, where: • the premises supporting a given conclusion (intermediate or final) precede it in the list; and • inferences are indicated by drawing a line and writing the numbers of the lines where the premises used in the inference may be found. Examples: (1) a simple argument • Argument: You should take the apartment: it isn’t too expensive, it’s clean and safe, and it’s close to your work. • In standard form: 1. The rent for the apartment is not too expensive (Pr). 2. The apartment is clean and safe (Pr). 3. The apartment is close to your work (Pr). 4. You should take the apartment. (FC, from 1, 2, 3) Examples (2): a complex argument • • Argument: It is clear that Smedley committed the murder. We know that only Smedley and Murgatroid could have committed the crime. But it couldn’t have been Murgatroid, because, as a reliable witness has told us, he was nowhere near the scene of the crime that day. In standard form: 1. A reliable witness informs us that M. was nowhere near the crime scene on the day of the murder (Pr). 2. M. was nowhere near the crime scene on the day of the murder. (IC, from 1) 3. M. did not commit the crime (IC, from 2) 4. Only S. or M. could have committed the murder (Pr). 5. Smedley committed the murder. (FC, from 3, 4) Principles or forms of inference • When reading or listening to arguments, we can often see that a conclusion has been drawn, but it is not always obvious how it has been drawn. • Usually, if not always, inferences exemplify repeatable patterns or forms. We can also say that they are governed by general principles. Examples • Argument: Either Smedley or Murgatroid committed the murder. It wasn’t Smedley. So it was Murgatroid. • Form: Either S or M. Not S. So M. • Principle: if there are only two possibilities and one of them is excluded, the other must be the case. Another example • Argument: Linda had a baby in January. So she must have been pregnant in December. • Form: X had a baby in January. So X was pregnant in December (of the previous year). • Principle: someone who has a baby in January had to have been pregnant in December of the previous year. Some cases are tricky • • Argument: Minou is a cat. So Minou is a mammal. Possible forms: (1) X is a P. So X is a Q. (2) X is a cat. So X is a mammal. • The principle of charity: when the goal is to promote reasonable belief, always adopt the interpretation that makes for the strongest possible argument that is compatible with the text. Unstated premises and conclusions • Some forms of inference are so well-known that authors and speakers sometimes leave parts of arguments in those forms unstated (tacit), with the expectation that their audience will supply them on their own. • Example: modus tollens is the form: If P then Q. Not Q. Not P. • Example: If the NDP had won the last federal election, Jagmeet Singh would be PM. Mr. Singh is not PM. So the NDP didn’t win the last federal election. Examples: • The NDP didn’t win the last federal election—if they had won, Singh would be PM (unstated premise: he isn’t). • If Hemingway is a great writer, then I’m William Shakespeare. (Unstated premise: I’m not Shakespeare; unstated conclusion: Hemingway is not a great writer.) • Figure it out for yourself: only Smedley or Murgatroid could have done it, and it sure wasn’t Smedley. (what’s the form in this case; and what’s missing?) Minou returns! • Recall the argument: Minou is a cat. So Minou is a mammal. • We identified two possible forms of inference: (1) X is a P. So X is a Q. (2) X is a cat. So X is a mammal. • We might add as a third possibility: (3) X is a P. All P are Q. so X is Q. • In this case we would say that there is a tacit premise, i.e., All cats are mammals. • Both (2) and (3) are compatible with the principle of charity; notice, too, that the premise declared missing on interpretation (3) is the principle of inference used according to interpretation (2). Diagramming arguments • It can be a useful exercise to draw a diagram of an argument’s structure, one that shows which premises support which conclusion(s). • We’ll present a common way of constructing such diagrams. Simple arguments (1) • In the simplest case, we have one premise (P1) supporting one conclusion (C). • Here, we simply draw an arrow from P1 to C, placing the conclusion at the bottom: P1 C Simple arguments (2) • Premises provide independent support for the conclusion: (P1) We’ve got rice. (P2) We’ve got beans. So (C) We’ve got some food. P1 P2 C Simple arguments (3) • Premises provide linked support to the conclusion: • (P1) Smith or Jones won the race. (P2) Smith didn’t. (C) So Jones did. P1 P2 C Complex arguments 1. Fred was in Kingston on Monday. (Pr) 2. He wasn’t in Ottawa. (IC, 1) 3. The crime was committed in Ottawa on Monday. (Pr) 4. Fred is innocent. (FC, 2,3) P1 IC2 FC4 P3 Example • Re-write the following argument in standard form, then draw a diagram of its structure: Archy didn’t leave the house that day. If he had, the police would have found his footprints in the snow. But they didn’t find any. And if he never left home, there’s no way he could have been in town to rob the convenience store. So he didn’t do it. Archy didn’t leave the house that day. If Archy had left home had, the police would have found his footprints in the snow. The police didn’t find any footprints. If Archy never left home, there’s no way he could have been in town to rob the convenience store. (So) Archy didn’t rob the convenience store. (1) If Archy had left home, the police would have found his footprints in the snow. (Pr) (2) The police didn’t find any footprints. (Pr) (3) Archy didn’t leave the house that day. (IC, from 1, 2) (4) If Archy never left home, there’s no way he could have been in town to rob the convenience store. (Pr) (5) Archy didn’t rob the convenience store. (FC, 4, 5) P1 P2 IC3 P4 FC5 PHI 1101A (Reasoning and Critical Thinking) (spring/summer 2021) REVIEW FOR TEST 1 Overview of Units 1–6 Unit 1: Introduction – Truth – Belief – Knowledge – Reasonable Belief Unit 2: Arguments, Part 1 – The nature or arguments – Arguments and non-arguments – Indicator words – Explanations – The elements of arguments: – Premises – Conclusions – Inferences – Simple and Complex arguments; intermediate and final conclusions Unit 3: Arguments, Part 2 – Arguments in standard form – The principle of charity – Principles or forms of inference – Unstated premises and conclusions – Diagramming arguments Unit 4: Evaluating arguments, an Introduction – Two questions: – Are the premises good (true, reasonable)? – Is the reasoning (the inferences) good? – Strength of claims 1 – Scope of claims – Universal generalizations and counterexamples – Inconsistency – Evaluating reasoning: focussing on principles or forms Unit 5: Validity and Soundness 1 – Deductive and non-deductive arguments – Validity: a necessary connection between premises and conclusion – The sense of possibility – Implication and equivalence – Validity and soundness Unit 6: Validity and Soundness 2 – Truth preservation and formal validity: definitions – Showing invalidity with parallel instances – Proving validity using general arguments – Proofs and refutations: – General arguments: for proving universal claims and disproving particular claims – Examples/counterexamples: For proving particular claims or refuting universal ones 2 Test Format 1. [ARGUMENT IDENTIFICATION] Read the following passage, then choose the appropriate answer. (2 points each) 5 questions If Joe had gone shopping, there would be some food in the fridge, but there isn’t. So he must not have. A: The passage contains an argument; the final conclusion is: There is no food in the fridge. B: The passage contains an argument; the final conclusion is: Joe didn’t go shopping. C: The passage contains an argument; the final conclusion is: If Joe had gone shopping, there would be some food in the fridge. D: An explanation, not an argument. E: Neither an explanation nor an argument. 2. [UNSTATED PREMISES AND/OR CONCLUSIONS] Supply unstated premises and/or conclusions as necessary. Make sure to say whether the missing items are premises or conclusions. (2 points each) 2 questions Of course Sam deserved to fail the course. Everybody knows that’s the penalty for plagiarism. Missing premise: Sam plagiarized. 3 3. [ARGUMENTS IN STANDARD FORM] Rewrite the following arguments in standard form, supplying unstated premises and/or conclusions as necessary, clearly identifying intermediate and final conclusions, showing which premises support them, and whether these premises support these conclusions jointly or independently. (4 points each) 2 questions Dogs inevitably get fleas, and when they get fleas, they bring them into the house. So if you have a dog, you’re sure to have fleas in the house. But the fleas that bite dogs will also bite you given the chance. Thus if you’re not willing to put up with a few flea bites, you shouldn’t get a dog. (P1) Dogs inevitably get fleas, and when they get fleas, they bring them into the house. (IC2, from P1) So if you have a dog, you’re sure to have fleas in the house. (P3) Fleas that bite dogs will also bite you given the chance (FC) Thus if you’re not willing to put up with a few flea bites, you shouldn’t get a dog (from IC2, P3, jointly) 4. [REFUTATION BY COUNTEREXAMPLES] Can you refute the following claim by counterexample? If so, do so. If not, explain why not. (2 points each) 2 questions An alarming number of countries possess atomic weapons. Can’t be refuted by counterexample because it is not a universal generalization. Only birds can fly. Bats can fly and they are not birds. 4 5. [CONSISTENCY] Is the following set of claims consistent? (2 points each) 2 questions Peters will get into law school provided that she performs well on the LSAT and gets good letters of reference. She will get good letters of reference, and she will perform well on the LSAT. Still, she won’t get into law school. A: consistent B: inconsistent 6. [IMPLICATION AND EQUIVALENCE] Consider the following pair of statements. Are they equivalent? If not, does either one imply the other? (2 points each) 2 questions (a) The Conservatives will win a majority in the next election if Grabowski is replaced. (b) The Liberals will lose the next election if Grabowski is replaced. A: equivalent B: not equivalent. (a) implies (b) but (b) does not imply (a) C: not equivalent. (b) implies (a) but (a) does not imply (b) D: not equivalent. (a) does not imply (b) and (b) does not imply (a) 5 7. [TRUE OR FALSE] True or false? (2 points each) 4 questions Not all sound arguments have a true conclusion. A: true B: false Any set of claims that is consistent must contain at least one true claim. A: true B: false 8. [VALIDITY AND SOUNDNESS] Classify the following arguments as: (a) Sound; (b) Valid, but not sound; (c) Neither valid nor sound, (d) sound, but not valid. (2 points each) 4 questions Not all mammals are large and not all mammals are brown. So some small mammals are brown. A: sound B: valid, but not sound C: neither valid nor sound D: sound, but not valid 6 PHI 1101: Tutorial Exercises (2): Solutions PART I 1. MP: Either Fred or George made this mess. 2. MP: We were not born with wings. MC: We were not meant to fly. 3. MP: You stayed out too late. MC: You’re in trouble. 4. MP: The new OS is a complex program. 5. MP: Sam plagiarized. PART II 1. 1. Gladys and Fred have both had affairs (Pr.) 2. Gladys and Fred are always fighting about how to rise their kids (Pr.) 3. Gladys and Fred have money problems (Pr.) 4. Gladys and Fred’s marriage probably won’t last much longer (FC, 1, 2, 3, independently) P1 P2 P3 F C4 2. 1. 2. 3. 4. Joe either took the bus or he took a cab. (Pr.) Joe didn’t have enough money to pay for a cab. (Pr.) Joe didn’t take a cab. (IC, 2) Joe came on the bus. (FC, 1, 3, jointly) P2 IC3 P1 F C4 3. 1. 2. 3. 4. 5. 6. Featherstone handled the crisis in Myanmar well under pressure. (Pr.) Featherstone works well under pressure. (IC, 1) Featherstone acted decisively in dealing with the Jones case. (Pr.) Featherstone is decisive. (IC, 3) No other candidate is available. (Pr.) Featherstone is the best candidate for the job. (FC, 2, 4, 5, independently) P1 IC2 P3 P5 IC4 F C6 4. 1. Tests performed by the consumers’ association indicate that Brand X is the most reliable one. (Pr.) 2. Brand X is the most reliable. (IC, 1) 3. Brand X is not too expensive. (Pr.) 4. Brand X is the best one to buy. (FC, 2, 3, independently) P1 IC2 P3 F C4 2 5. 1. 2. 3. 4. Sam is a great baseball player. (Pr.) Sam can play in the major leagues. (IC, 1) Major league baseball players make lots of money. (Pr.) Sam can be rich if he wants to. (FC, 2, 3, jointly) P1 P3 IC2 F C4 6. 1. Dogs inevitably get fleas (Pr.) 2. When dogs get fleas, they bring them into the house. (Pr.) 3. If you have a dog, you’re sure to have fleas in your house. (IC, 1, 2, jointly) 4. The fleas that bite dogs will also bite you given the chance. (Pr.) 5. If you’re not willing to put up with a few flea bites, you shouldn’t get a dog. (FC, 3, 4, jointly) P1 P2 IC3 P4 F C5 3 7. 1. Once you kill someone, there’s no way to bring him back to life. (Pr.) 2. If the state mistakenly executes someone, there’s no way to fix the mistake. (IC, 1) 3. In the cases of G. P. Morin and Donald Marshall, the justice system made serious mistakes. (Pr.) 4. The justice system is known to make serious mistakes. (IC, 3) 5. If we reinstate the death penalty, it is entirely possible that we will commit irreversible injustice by killing innocent people. (IC, 2,4, jointly) 6. We should not reinstate the death penalty. (FC, 5) P1 P3 IC2 IC4 IC5 F C6 8. 1. Only an idiot would have played with matches next to a gas pump. (Pr.) 2. Sekeras is no idiot. (Pr.) 3. Sekeras didn’t play with matches next to a gas pump. (IC, 1, 2, unstated, jointly) 4. The Police say that Sekeras did play with matches next to a gas pump. (Pr.) 5. The Police must be lying. (FC, 3, 4, jointly) P1 P2 P4 IC3 F C5 9. 1. If Archy had left the house that day, the police would have found his footprints in the snow. (Pr.) 2. The police didn’t find his footprints. (Pr., unstated) 3. Archy didn’t leave the house that day. (IC, 1, 2, jointly) 4. If Archy didn’t leave home that day, he couldn’t have been in town to rob the convenience store. (Pr.) 5. Archy wasn’t in town to rob the convenience store. (IC, 3,4, unstated, jointly) 6. Archy didn’t rob the convenience store. (FC, 5) P1 P2 IC3 P4 IC5 F C6 10. 1. Manned space travel is incredibly expensive. (Pr.) 2. American voters will demand that money be spent on things other than manned space travel. (Pr.) 3. The US isn’t likely to send a manned mission to Mars within the next 15 years. (FC, 1, 2, jointly) P1 P2 F C3 5 PART III 1. Refutable: ducks, geese, etc. 2. Refutable: birds are warm-blooded, but they aren’t mammals. 3. Refutable: bats 4. Not refutable by counterexample, because it is not a universal statement. 5. Refutable: Chernobyl, Three Mile Island, etc. 6. Not refutable by counterexample, because it is not a universal statement. Besides, it’s true. 7. Not refutable by counterexample, because it is not a universal statement. Besides, it’s true. 8. Not refutable by counterexample, because it is not a universal statement. 9. Refutable: Johnson, Clinton, Trump. 10. Not refutable by counterexample, because it is not a universal statement. Besides, it’s true. PART IV 1. Inconsistent 6. Inconsistent 2. Inconsistent 7. Inconsistent 3. Consistent 8. Consistent 4. Inconsistent 9. Consistent 5. Consistent 10. Inconsistent PART VI 1. (a) In the vast majority of cases, A happened before B did. So A leads to B. (b) The vast majority of bank robbers drank milk before turning to bank robbery. So milk drinking leads to bank robbery. 2. (a) If A happens, B might happen. A won’t happen. So B won’t happen. (b) If Joe drinks poison, he could die. Joe won’t drink poison. So Joe won’t die. 3. (a) No one has conclusively proven that A is true. So A is false. (b) No one has conclusively proven that there are no pink elephants dancing on the dark side of the moon. So there are pink elephants etc. 4. If P then Q. Not P . So not Q. If Julius Caesar committed suicide, he’d be dead. Caesar did not commit suicide. So he’s not dead. 5. (a) All P are Q. So all Q are P . (b) All dogs are mammals. So all mammals are dogs. 6 PHI 1101: Tutorial Exercises (3): Solutions PART I 1. Invalid: suppose it is the 3rd of March. 2. Invalid. Again, suppose it is the 3rd of March. 3. Invalid: suppose we solve global warming but the Earth is hit by a giant asteroid. 4. Invalid: suppose they get eaten by a rabbit. 5. Invalid: suppose Bill Gates was terrible at business, but won the lottery. 6. Invalid: suppose that there were women golfers and women hockey players, but none of the hockey players played golf and vice versa. 7. Invalid: suppose they won a minority. 8. Invalid: suppose all the non-European members left the alliance. PART II 1. (a) implies (b), but not vice versa. 2. (a) implies (b), but not vice versa. 3. Equivalent 4. Equivalent 5. Neither implies the other. 6. Neither implies the other. 7. Neither implies the other. 8. Neither implies the other. 9. Equivalent 10. Neither implies the other. PART III 1. Sound (a) if answered on Wednesday; otherwise, (b) valid but not sound. 2. Neither valid nor sound (c). 3. Valid but not sound (b). 1 4. Valid but not sound (b). 5. Neither valid nor sound (c). 6. Sound (a). 7. Neither valid nor sound (c). 8. Sound (a). 9. Neither valid nor sound (c). 10. Neither valid nor sound (c). 11. Valid but not sound (b). 12. Neither valid nor sound (c). PART IV 1. (a) Not P . So neither P nor Q. (b) I never played in the NHL. So neither I nor Wayne Gretzky ever played in the NHL. 2. (a) Not both P and Q. So not P . (b) Wayne Gretzky and I didn’t both play in the NHL. So Wayne Gretzky didn’t play in the NHL. 3. (a) All P are Q. So all Q are P . (b) All cars are vehicles. So all vehicles are cars. 4. (a) Not all P are Q. So not all Q are P . (b) Not all mammals are bats. So not all bats are mammals. 5. (a) Some P are not Q. So some Q are not P . (b) Some amphibians are not frogs. So some frogs are not amphibians. 6. (a) If not P then Q. P . So not Q. (b) If Napoleon did not live past 1800, he’d be dead now. He did live past 1800. So he’s not dead now. 7. (a) All P are Q. All P are R. So all Q are R. (b) All birds are warmblooded animals. All birds have feathers. So all warm-blooded animals have feathers. 8. (a) P if Q. P so Q. (b) Julius Caesar would be dead if he’d been killed in battle. Caesar is dead. So he was killed in battle. 9. (a) Not all P are Q. Not all Q are R. So not all P are R. (b) Not all cats are pets. Not all pets are mammals. So not all cats are mammals. 10. (a) Some P are not Q. Some Q are not R. So some P are not R. (b) Some dogs are not pets. Some pets are not mammals. So some dogs are not mammals. 2 PART V 1. The Sun is bigger than the Earth, and the Earth is bigger than the Moon. So the Sun is bigger than the Moon. 2. This is not possible: by definition, if an argument is valid, it’s not possible for the premises to be true and the conclusion false. But if the premises of an argument are true, and the conclusion is false, then clearly this is something that can happen. 3. The Sun is bigger than the Moon. The Moon is bigger than the Earth. So the Sun is bigger than …
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