PHI-105 Homework #2

Label the following deductive argument form. If S, then J. Not S. Not J. A. Affirming the consequent B. Denying the antecedent C. Modus ponens D. Modus tollens

B. Denying the antecedent (The antecedent of the first premise is S. The second premise denies S. This is a formal fallacy.)

Determine whether the following inductive argument is strong or weak: Some cows are brown. That farmer has a cow, so it probably is brown. A. Strong B. Weak

B. Weak

Label the following deductive argument form. If P, then D. If D, then S. If P, then S. A. Disjunctive syllogism B. Hypothetical syllogism C. Modus ponens D. Modus tollens

B. Hypothetical syllogism (This is the correct form of a hypothetical syllogism, a valid argument form. The consequent of the first premise is the antecedent of the second premise, which allows an inference to "If P, then S.")

Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid: Tom was born before 1970. Jerry was born before 1971. Therefore, Tom was born before Jerry. A. Tom was born in 1967. Jerry was born in 1968. Thus, Tom was born before Jerry. B. Tom was born in 1968. Jerry was born in 1970. Thus, Tom was born before Jerry. C. Tom was born in 1961. Jerry was born in 1960. Thus, Tom was born before Jerry. D. Tom was born in 1975. Jerry was born in 1980. Thus, Tom was born before Jerry.

C. Tom was born in 1961. Jerry was born in 1960. Thus, Tom was born before Jerry.

Label the following deductive argument form. If P, then D. D. P A. Affirming the consequent B. Denying the antecedent C. Modus ponens D. Modus tollens

A. Affirming the consequent (The consequent of the first premise is D, and the second premise affirms D. This is an invalid argument form, a formal fallacy.)

Determine whether the following argument is best classified as deductive or inductive: It normally takes a week to get home delivery of appliances, and you bought the appliance today, so it will probably be delivered next week. A. Deductive B. Inductive

B. Inductive

Consider this argument: "Your car will not start, so you are probably out of gas." Would adding the following claim strengthen or weaken that argument? "You just filled up the tank last night." A. Strengthen B. Weaken

B. Weaken (If you just filled the tank, then this lowers the probability that you are out of gas.)

Determine whether the following inductive argument is strong or weak: Approximately 75% of men above the age of 50 live to be 85. Arthur is 51, so Arthur will live to be at least 85. A. Strong B. Weak

A. Strong (Given this information, it is likely to conclude that Arthur will live to be at least 85, so the conclusion is probable.)

Determine whether the following inductive argument is strong or weak: Most sea creatures are animals with gills. The aquarium near my house has just acquired a new sea creature, so it is probably an animal with gills. A. Strong B. Weak

A. Strong (If the premise are assumed to be true, then the conclusion is probably true.)

Determine whether the following inductive argument is strong or weak: Only 10% of people have ever served on a jury. Therefore, my grandfather probably has not served on a jury. A. Strong B. Weak

A. Strong (It is extremely unlikely for the conclusion to be false given the premise, so it is a strong argument.)

Determine whether the following inductive argument is strong or weak: The majority of birds sing. My aunt has a parakeet, so it probably sings. A. Strong B. Weak

A. Strong (The premises make the conclusion highly likely to be true.)

Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid: All movie stars are millionaires. All movie stars are famous people. So, all millionaires are famous people. A) All S are F. All S are P. So, all F are P. Let S = puppies, F = mammals, and P = dogs. B) All S are F. All S are P. So, all F are P. Let S = puppies, F = dogs, and P = mammals. C) All F are S. All S are P. So, all F are P. Let S = puppies, F = mammals, and P = dogs. D) All S are F. All P are F. So, all S are P. Let S = puppies, F = mammals, and P = dogs.

A) All S are F. All S are P. So, all F are P. Let S = puppies, F = mammals, and P = dogs. (Only in this choice are both premises true and the conclusion false. Therefore, the counterexample shows that the argument is invalid. The other choices either do not model the argument form correctly or the counterexample does not have a false conclusion.)

Determine whether the following argument is best classified as deductive or inductive: All ducks quack. Spike is a duck, so Spike quacks. A. Deductive B. Inductive

A. Deductive

Determine whether the following argument is best classified as deductive or inductive: Every diamond is made from carbon. I have a diamond ring, so it is made from carbon. A. Deductive B. Inductive

A. Deductive

Determine whether the following argument is best classified as deductive or inductive: Jack is 25 years old. Anyone older than 18 is eligible to vote, so Jack is eligible to vote. A. Deductive B. Inductive

A. Deductive

Determine whether the following argument is best classified as deductive or inductive: Robbie has a limited range of motion because every robot has a limited range of motion, and Robbie is a robot. A. Deductive B. Inductive

A. Deductive

Determine whether the following argument is best classified as deductive or inductive: Winners never quit and quitters never win. Mike and Tom both quit, so they won't win. A. Deductive B. Inductive

A. Deductive

Determine whether the following argument is best classified as deductive or inductive: The syllabus states that if a student receives at least a ninety on every exam and homework, then he or she will get an "A" for the course. I have at least a ninety on every exam and homework, thus I will get an "A" for the course. A. Deductive B. Inductive

A. Deductive (The first premise specifies the conditions whereby one will get an "A." The second premise tells us that the person in question meets those conditions. If both premises are assumed to be true, then the conclusion is necessarily true.)

Label the following deductive argument form. L or D. Not L. D. A. Disjunctive syllogism B. Hypothetical syllogism C. Modus ponens D. Modus tollens

A. Disjunctive syllogism (This is the correct form of a disjunctive syllogism. The first premise asserts a disjunction. The second premise negates one of the disjuncts, and the conclusion affirms the remaining disjunct.)

Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid: No aardvarks are vegetarians. Some predators are not vegetarians. Therefore, some predators are aardvarks. A. No A are V. Some P are not V. So some P are A. Let A = cars, V = cats, P = mammals. B. No A are V. Some P are V. So some P are A. Let A = dogs, V = cats, P = mammals. C. No A are V. Some P are not V. So some P are A. Let A = dogs, V = cats, P = mammals. D. No A are V. Some P are V. So some P are A. Let A = cars, V = cats, P = mammals.

A. No A are V. Some P are not V. So some P are A. Let A = cars, V = cats, P = mammals.

Consider this argument: "Craig is weak. So, he is probably hungry." Would the following claim strengthen or weaken the argument? "Craig has not eaten for four days." A. Strengthen B. Weaken

A. Strengthen (If Craig has not eaten for 4 days, this raises the probability that Craig is hungry.)

Consider this argument: The gas pump automatically stopped pumping gas, so the car's gas tank is full. Would the following claim strengthen or weaken that argument? The gas gauge in the car reads "Full." A. Strengthen B. Weaken

A. Strengthen (If the gas gauge is functioning properly, then it supports the claim that the gas tank is full.)

Consider this argument: "Your car will not start, so you are probably out of gas." Would adding the following claim strengthen or weaken that argument? "The gas tank gauge indicates that the tank is empty." A. Strengthen B. Weaken

A. Strengthen (The gas gauge reading increases the probability that you are out of gas.)

Consider this argument: "Your car will not start, so you are probably out of gas." Would the following claim strengthen or weaken that argument? "You have not put in any gas for two weeks." A. Strengthen B. Weaken

A. Strengthen (If you haven't added any gas recently, then this raises the probability that you used it all up.)

Determine whether the following inductive argument is strong or weak: Sixty percent of all Kenyans are capable of running one mile in ten minutes. John Keter is a Kenyan. Quite likely, therefore, John Keter is capable of running one mile in ten minutes. A. Strong B. Weak

A. Strong (Assuming the premises of the argument are true, the conclusion is quite likely true. Since the percentage of the runners is above fifty, the conclusion becomes more likely.)

Determine whether the following inductive argument is strong or weak: Almost no 3D TVs last more than 10 years. I just bought a new 3D TV, so probably it won't last more than 10 years. A. Strong B. Weak

A. Strong (Given the premises, it is unlikely that the conclusion is false, so this argument is strong.)

Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid: All judges are people with advanced degrees. All lawyers are people with advanced degrees. Thus, all judges are lawyers. A) All C are E. All E are A. So, all C are A. Let C= cats, E = mammals, and A = dogs. B) All C are E. All A are E. So, all C are A. Let C= cats, E = mammals, and A = dogs. C) All E are C. All A are E. So, all C are A. Let C= cats, E = mammals, and A = felines. D) All C are E. All A are E. So, all C are A. Let C= cats, E = mammals, and A = felines.

B) All C are E. All A are E. So, all C are A. Let C= cats, E = mammals, and A = dogs.

Determine whether the following argument is best classified as deductive or inductive: Most campers take along rain gear. My cousin went camping this weekend, so he probably took along rain gear. A. Deductive B. Inductive

B. Inductive

Determine whether the following argument is best classified as deductive or inductive: Most cars produce some carbon emissions. I drive a car, so my car produces some carbon emissions. A. Deductive B. Inductive

B. Inductive

Determine whether the following argument is best classified as deductive or inductive: Most cats are independent. . My sister just got a cat. Therefore, my sister's cat is independent. A. Deductive B. Inductive

B. Inductive

Determine whether the following argument is best classified as deductive or inductive: Ninety-five percent of students at the University of Kentucky support the Kentucky Wildcats basketball team. You are a student at the University of Kentucky. Quite likely, therefore, you are a supporter of the Kentucky Wildcats basketball team. A. Deductive B. Inductive

B. Inductive

Determine whether the following argument is best classified as deductive or inductive: The treasure is probably under one of the stones in the yard. Once we check under every stone, we should find the treasure. A. Deductive B. Inductive

B. Inductive

Determine whether the following argument is best classified as deductive or inductive: Creative people almost always have disciplined work habits. Susan is a creative person. Thus, she has disciplined work habits. A. Deductive B. Inductive

B. Inductive ("Almost always" indicated that the speaker claims the conclusion will follow with a high degree of probability, so this is inductive.)

Determine whether the following argument is best classified as deductive or inductive: Many forest fires are caused by careless people. A new fire has started in the forest near our home. It follows that the fire was caused by a careless person. A. Deductive B. Inductive

B. Inductive (The first premise asserts something about many forest fires. If both premises are assumed to be true, then the conclusion is probably true.)

Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid: Some rice products are pastry items. All pastry items are tasty treats. So, some tasty treats are not rice products. A. Some A are B. All C are B. So, some C are not A. Let A = animals, B = cats, and C = dogs. B. Some A are B. All B are C. So, some C are not A. Let A = animals, B = cats, and C = mammals. C. Some B are A. All C are B. So, some C are not A. Let A = cats, B = mammals, and C = felines. D. Some A are B. All B are C. So, some C are not A. Let A = cats, B = tigers, and C = felines.

B. Some A are B. All B are C. So, some C are not A. Let A = animals, B = cats, and C = mammals. (Only in this choice are both premises true and the conclusion false. Therefore, the counterexample shows that the argument is invalid.)

Determine whether the following inductive argument is strong or weak: Thirty percent of all Kenyans are capable of running one mile in ten minutes. John Keter is a Kenyan. Quite likely, therefore, John Keter is capable of running one mile in ten minutes. A. Strong B. Weak

B. Weak

Determine whether the following inductive argument is strong or weak: After the odometer reached 200,000 miles, some 2004 Toyota Corolla engines stalled. You own a 2004 Toyota Corolla and your odometer reading is now at 199,995. Quite likely, your engine is about to stall. A. Strong B. Weak

B. Weak (The key word in the first premise is "some." Assuming the premises are true, the conclusion is not probably true).

Determine whether the following inductive argument is strong or weak: Hanna tossed a coin five times, and in each case it came up tails. Thus, the next toss will be heads. A. Strong B. Weak

B. Weak (That it came up tails 5 times in a row has no bearing on the next toss; each coin toss is an independent event, each having a 50-50 chance of coming up heads or tails.)

Consider this argument: "Your car will not start, so you are probably out of gas." Would adding the following claim strengthen or weaken that argument? "The gas tank gauge indicates the tank is at least half full." A. Strengthen B. Weaken

B. Weaken

Consider this argument: The gas pump automatically stopped pumping gas, so the car's gas tank is full. Would the following claim strengthen or weaken that argument? You pre-paid $5.00 for gas. A. Strengthen B. Weaken

B. Weaken ($5.00 is probably not enough to fill the tank.)

Consider this argument: The lamp in your room does not work, so the lightbulb is defective. Would adding the following claim strengthen or weaken that argument? There is a major power outage in your neighborhood. A. Strengthen B. Weaken

B. Weaken (The major power outage is probably affecting your house).

Consider this argument: The gas pump automatically stopped pumping gas, so the car's gas tank is full. Would the following claim strengthen or weaken that argument? The gas pump is defective. A. Strengthen B. Weaken

B. Weaken (The pump might have stopped because of the defect.)

Consider this argument: The gas pump automatically stopped pumping gas, so the car's gas tank is full. Would the following claim strengthen or weaken that argument? Electricity to run the gas pump was interrupted. A. Strengthen B. Weaken

B. Weaken (If the pump requires electricity, then the interruption might have caused the pump to stop.)

Choose which argument form correctly models the following argument, and which substitutions create a counterexample that shows the argument is invalid: All smokers are people who put their health at risk. All smokers are people who lack self-control. Therefore, all people who put their health at risk are people who lack self-control. A) All A are B. All B are C. So, all B are C. Let A=Collies, B=Animals, C=Dogs. B) All A are B. All C are B. So, all A are C. Let A=Collies, B=Animals, C=Dogs. C) All A are B. All A are C. So, all B are C. Let A=Collies, B=Animals, C=Dogs. D) All A are C. All B are A. So, all B are C. Let A=Collies, B=Animals, C=Dogs.

C) All A are B. All A are C. So, all B are C. Let A=Collies, B=Animals, C=Dogs.

Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid: All hockey players are good ice skaters. Some hockey players are not Canadian citizens. So, some Canadian citizens are not good ice skaters. A. All A are B. Some A are C. So, no C are not B. Let A = dogs, B = animals, and C = beagles. B. All B are A. Some A are C. So, some C are not B. Let A = animals, B = living things, and C = famous things. C. All A are B. Some A are not C. So, some C are not B. Let A = dogs, B = animals, and C = beagles. D. All A are B. Some A are not C. So, some C are not B. Let A = animals, B = living things, and C = famous things.

C. All A are B. Some A are not C. So, some C are not B. Let A = dogs, B = animals, and C = beagles.

Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid: No underdeveloped countries are members of the United Nations Security Council. No South American countries are members of the United Nations Security Council. So, no underdeveloped countries are South American countries. A) No I are U. No C are I. So, no U are C. Let U = cats, I = snakes, and C = mammals. B) No U are I. No C are I. So, no U are C. Let U = umbrellas, I = icebergs, and C = cats. C) No U are I. No I are C. So, no U are C. Let U = cats, I = snakes, and C = mammals. D) No U are I. No C are I. So, no U are C. Let U = cats, I = snakes, and C = mammals.

D) No U are I. No C are I. So, no U are C. Let U = cats, I = snakes, and C = mammals.

Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid: All traffic citations are misdemeanors. All parking tickets are misdemeanors. Therefore, all traffic citations are parking tickets. A. All A are B. All B are C. So, all A are C. Let A = cats, B = animals, and C = dogs. B. All A are B. All C are B. So, all A are C. Let A = animals, B = cats, and C = dogs. C. All A are B. All C are B. So, all C are A. Let A = cats, B = animals, and C = dogs. D. All A are B. All C are B. So, all A are C. Let A = cats, B = animals, and C = dogs.

D. All A are B. All C are B. So, all A are C. Let A = cats, B = animals, and C = dogs.

Label the following deductive argument form. If P, then D. Not D. Not P. A. Affirming the consequent B. Denying the antecedent C. Modus ponens D. Modus tollens

D. Modus tollens

Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid: No basketballs are cardboard spheres. Some disks are cardboard spheres. So, no disks are basketballs. A. No B are C. Some D are C. So, no D are B. Let B = people, C = cats, and D = pets. B. No B are C. No D are C. So, no D are B. Let B = beagles, C = collies, and D = dogs. C. No B are C. Some D are not C. So, no D are B. Let B = people, C = cats, and D = pets. D. No B are C. Some D are C. So, no D are B. Let B = beagles, C = collies, and D = dogs.

D. No B are C. Some D are C. So, no D are B. Let B = beagles, C = collies, and D = dogs.