Logic Problems and Questions (with solutions) December 23, 2005

Explain why the following argument is either deductive or nondeductive Explain why the following argument is either deductive or nondeductive. Suppose you had to do this in a paragraph containing at least three complete sentences. What would you say?   Less than four percent of all Ruritanian-American college students are planning to vote for the liberal candidate Mary is a Ruritanian-American college student. Therefore: Mary is not planning to vote for the liberal candidate.  Answer: This is a nondeductive argument. A nondeductive argument is one in which the arguer claims (either explicitly or implicitly) that, on the assumption that the premises of the argument are true, the conclusion is probably true. The argument above does not contain any "probability language," but it is, none the less, probabilistic. It is an attempt to prove that Mary is not planning to vote for the liberal candidate on the grounds that she is a Ruritanian-American college student and that very few Ruritanian-American college students are planning to vote for the liberal candidate. The first premise is a statistical statement; it does not cover all Ruritanian-American college students. It leaves open the possibility that Mary is one of the few Ruritanian-American college students who might vote for the liberal candidate; but it seems clear that the intention of the arguer in the argument under consideration is to show that, on the basis of the premises, it is probable that Mary is not planning to vote for the liberal candidate. Therefore, the argument is nondeductive. 2/4/2019 Number 1

Explain why the following argument is either deductive or nondeductive Explain why the following argument is either deductive or nondeductive. Suppose you had to do this in a paragraph containing at least three complete sentences. What would you say? All conduct that undermines the social order is morally wrong. Homosexual conduct does not undermine the social order. Therefore: Homosexual conduct is definitely not morally wrong. Answer: This is a deductive argument. An argument is deductive when the arguer claims that the truth of the conclusion follows with the force of absolute logical necessity from the assumed truth of the premises. The conclusion of this argument states that "Homosexual conduct is definitely not morally wrong" (emphasis added). "Definitely" is the key word. It indicates that the arguer is claiming that, on the basis of the premises, the conclusion of the argument "definitely" follows. "Definitely," in this context, is a synonym for "necessarily." Therefore, the argument contains a deductive inferential claim. 2/4/2019 Number 2

For the following deductive argument, explain why the argument is either valid or invalid. Suppose you had to present an answer in a paragraph containing at least three complete sentences. What would you write?   All dogs are cats. All tigers are dogs. Therefore: All tigers are cats. Answer: A deductive argument is valid when the truth of the conclusion follows with the force of absolute logical necessity from the assumed truth of the premises; and it is invalid when the conclusion does not follow necessarily from the premises. This argument is valid. If all dogs were cats (1st premise), and if all tigers were dogs (2nd premise), then all tigers would be cats (conclusion). If all dogs are members of the cat class, and if all tigers are members of the dog class, then, obviously, all tigers would have to be members of the cat class. 2/4/2019 Number 3

For the following deductive argument, explain why the argument is either valid or invalid. Suppose you had to present an answer in a paragraph containing at least three complete sentences. What would you write? If Rover is a cat, then Rover is an animal. Rover is an animal. Therefore: Rover is a cat. Answer: This deductive argument is invalid. The conclusion does not follow necessarily from the assumed truth of the premises. The first premise states that if Rover is a cat, then Rover is an animal. It does not indicate whether Rover is, in fact, a cat or not. The second premise states merely that Rover is an animal. It gives no indication as to what kind of an animal Rover might be. There are many animals that are not cats, and Rover might be one of them. On the basis of the premises, it does not follow necessarily that Rover is a cat (conclusion). Thus, the argument is invalid. 2/4/2019 Number 4

For the following deductive argument, explain why the argument is either valid or invalid. Suppose you had to present an answer in a paragraph containing at least three complete sentences. What would you write? Either Mary is a doctor or she is a lawyer. Mary is a lawyer. Therefore: Mary is not a doctor. Answer: This argument is invalid. The first premise states that Mary is either a doctor or a lawyer. But that statement does not rule out the possibility that Mary is both a doctor and a lawyer. So we cannot conclude necessarily that Mary is not a doctor (conclusion) just because she is a lawyer (2nd premise). She might be both. 2/4/2019 Number 5

For the following deductive argument, explain why the argument is either valid or invalid. Suppose you had to present an answer in a paragraph containing at least three complete sentences. What would you write? If God existed, then there would be no pointless evil. There is pointless evil. Therefore: God does not exist. Answer: This argument is valid. The first premise asserts that the existence of God would rule out the existence of pointless evil, and the second premise states that pointless evil does exist. From those premises, it necessarily follows that God does not exist (conclusion). If God and pointless evil cannot co-exist (1st premise), and if pointless evil exists (2nd premise), then the existence of God is impossible. This argument may be unsound (because there might be some reasonable basis for disputing the truth of one or both of its premises), but it nonetheless contains a valid inference. 2/4/2019 Number 6

For the following deductive argument, explain why the argument is either valid or invalid. Suppose you had to present an answer in a paragraph containing at least three complete sentences. What would you write? Islam is a theistic religion. Professor Hasan is a devout Muslim. Therefore: Professor Hasan believes in the existence of God. Answer: This argument is valid. A theistic religion is one that affirms the existence of God, and the first premise states that Islam is a theistic religion. The second premise goes on to say that Professor Hasan is a devout Muslim. A Muslim is a follower of Islam, and a devout Muslim is one who accepts all of the basic teachings of his religion, such as the Islamic doctrine that God exists. Thus, the conclusion that Professor Hasan believes in the existence of God follows necessarily from the assumed truth of the premises, and the argument is valid. 2/4/2019 Number 7

For the following nondeductive argument, explain why the argument is either strong or weak. Suppose you had to present an answer in a paragraph containing at least three complete sentences. What would you write? All previous American Presidents were women. Therefore: It is probable that the next American President will be a woman. Answer: A nondeductive argument is strong when, on the assumption that its premises are true, its conclusion is probably true; and a nondeductive argument is weak when, on the assumption that its premises are true, the argument does not establish the probable truth of its conclusion. This argument is strong. IF it were true that all previous American Presidents were women (which is, of course, actually false) (Premise), then it would follow with a significant degree of probability that the next American President will be a woman (Conclusion). On the assumption that the premise of the argument is true, the conclusion seems probably true. Thus, the argument is strong (i.e., it contains a strong inference). 2/4/2019 Number 8

For the following nondeductive argument, explain why the argument is either strong or weak. Suppose you had to present an answer in a paragraph containing at least three complete sentences. What would you write? Only two American Presidents were members of the Federalist Party. Therefore: It is probable that the next American President will be a man. Answer: This argument is weak. There is no clear logical relationship between the premise and the conclusion. The premise is actually true. The first two American Presidents (George Washington and John Adams) were the only American Presidents who were members of the Federalist Party, which has been long defunct. So the premise is true. The conclusion also seems true. It does seem probable, not on the basis of the premise in this argument but on the basis of past experience, that the next President will be a man (although there is currently a potential woman candidate, Hilary Clinton, and other women might also emerge eventually as viable presidential candidates). The problem with the argument, as stated above, is that the premise is about party membership and the conclusion is about gender, and the premises do not give us any reason to believe that the two are logically or factually connected. Thus, this nondeductive argument is weak. 2/4/2019 Number 9

  For the following nondeductive argument, explain why the argument is either strong or weak. Suppose you had to present an answer in a paragraph containing at least three complete sentences. What would you write? The college's basketball team wore its new red and white uniforms last Wednesday and won for the first time in five games. On Monday, the team switched back to the old yellow and green uniforms and lost. Therefore: The team will probably win the next game if the players wear the new uniforms. Answer: Is there any connection between winning basketball games and the colors of the players' uniforms? Not likely. This argument is based on the assumption that there is such a connection, which is very doubtful. So even if the premises are true, it does not seem probable that the conclusion is true. Thus, the argument is weak. 2/4/2019 Number 10