Lesson Four Exercises
Thinking Critically about Deductive Reasoning
Part One: Exercises One through Three
Directions: Do all of the problems within each of the exercises. Check your even numbered answers against the sample answers that are posted within the Unit Two menu. Turn in the odd numbered problems for grading, by uploading your assignment into the course dropbox. This can be found on the course menu at the top of your computer screen. Once I have graded it, I will return your work to you at this same location. Be sure to keep a copy on file for yourself. Contact me if you have questions. This lesson, combined with your participation within the class discussion, is worth a possible 25 points.
Name: ____________________________
Exercise 4.1. Each of the following passages contains a categorical syllogism. Analyze each one by underlining the conclusion, and putting the two premises into parentheses. Circle any indicator words that you see.
- (Since most pineapples are fruits), it follows that most pineapples are sweet, (since most fruits are sweet).
- (Every day at the beach is a good day), (and every good day is my kind of day). Consequently, every day at the beach is my kind of day.
- (Many postal workers are stressed). (People who are stressed can become violent). Hence, many postal workers can become violent.
- (All cats are mammals) so no cats lay eggs, (because no mammals lay eggs).
- (Only apples are used for bobbing) and since most apples are sweet, (it follows that most things that are used for bobbing are sweet).
- Since oranges are not the only fruit used for juice, (oranges are not in this punch), (because not all of the fruit that can be used for juice is in this punch).
- (All dogs are messy). I know this because they have no table manners, and (anything without table manners is messy).
- (Some doctors are also lawyers). (All lawyers can sue patients). So some doctors can sue patients.
- (Since no dog bones are the Duke’s dog bones), and (no chew toys are dog bones), then not all the Duke’s dog bones are chew toys.
- (Many people hear him roar), thus many people hear him snore, (for those who hear his roaring also hear his snoring).
Exercise 4.2. Each of the following passages contains a categorical syllogism. Analyze each one by underlining the conclusion, and putting the two premises into parentheses. After you have done this, identify the three categories in the syllogism. If necessary, alter the language for the terms to make the grammar of each claim correct. Do not worry at this point, whether or not the syllogism follows a valid form of reasoning.
- Since most pineapples are fruits, it follows that most pineapples are sweet, since most fruits are sweet.
Category One: Since most pineapples are fruits
Category Two: Most fruits are sweet
Category Three: Most pineapples are sweet
- Every day at the beach is a good day, and every good day is my kind of day. Consequently, every day at the beach is my kind of day.
Category One: Every good day is my kind of day
Category Two: Every day at the beach is a good day
Category Three: Every day at the beach is my kind of day.
- Many postal workers are stressed. People who are stressed can become violent. Hence, many postal workers can become violent.
Category One: Many postal workers are stressed.
Category Two: People who are stressed can become violent
Category Three: Hence, many postal workers can become violent.
- All cats are mammals so no cats lay eggs, because no mammals lay eggs.
Category One: All cats are mammals
Category Two: No mammals lay eggs
Category Three: No cats lay eggs
- Only apples are used for bobbing and since most apples are sweet, it follows that most things that are used for bobbing are sweet.
Category One: Only apples are used for bobbing
Category Two: Most things that are used for bobbing are sweet
Category Three: Most apples are sweet
- Since oranges are not the only fruit used for juice, oranges are not in this punch, because not all of the fruit that can be used for juice is in this punch.
Category One: Not all of the fruit that can be used for juice is in this punch
Category Two: Oranges are not in this punch
Category Three: Oranges are not the only fruit used for juice
- All dogs are messy. I know this because they have no table manners, and anything without table manners is messy.
Category One: All dogs are messy
Category Two: Anything without table manners is messy
Category Three: All dogs have no table manners
- Some doctors are also lawyers. All lawyers can sue patients. So some doctors can sue patients.
Category One: Some doctors are also lawyers
Category Two: All lawyers can sue patients
Category Three: Some doctors can sue patients
- Since no dog bones are the Duke’s dog bones, and no chew toys are dog bones, then not all the Duke’s dog bones are chew toys.
Category One: No dog bones are the Duke’s dog bones
Category Two: No chew toys are dog bones
Category Three: Not all the Duke’s dog bones are chew toys.
- Many people hear him roar, thus many people hear him snore, for those who hear his roaring also hear his snoring.
Category One: Many people hear him roar
Category Two: Those who hear his roaring also hear his snoring
Category Three: Many people hear him snore
Exercise: 4.3. Here are some invalid arguments. Even if you think that some (or even all) of the claims used as premises within these arguments are true, and even if you are inclined to believe the conclusions within some (or even all) of these arguments, set these feelings aside and try to show that the reasoning within each of the arguments is invalid. Keep in mind that if the argument is invalid, this does not mean that the conclusion is “wrong.” It just means that it is not proven by the argument.
- All cats are mammals because no cats lay eggs, and no mammals lay eggs.
Original Argument
Premise 1: All cats are mammals
Premise 2: No mammals lay eggs
Conclusion: No cats lay eggs
Category One: All cats are mammals New Category One: No cats lay eggs
Category Two: No cats lay eggs New Category Two: No mammals lay eggs
Category Three: No mammals lay eggs New Category Three: All cats are mammals
New Argument
Premise 1: Mammals do not lay eggs
Premise 2: All cats are mammals
Conclusion: All cats do not lay eggs
- Because some doctors are also lawyers, and all lawyers can sue patients, we can conclude that all doctors can sue patients.
Original Argument
Premise 1: Some doctors are also lawyers
Premise 2: All lawyers can sue patients
Conclusion: Doctors can sue patients
Category One: Some doctors are also lawyers New Category One: Doctors can sue patients
Category Two: All lawyers can sue patients New Category Two: Doctors are also lawyers
Category Three: Doctors can sue patients New Category Three: Doctors are also lawyers and can sue patients
New Argument
Premise 1: All lawyers can sue patients
Premise 2: Some doctors can sue patients
Conclusion: Some doctors are also lawyers
- Every conservative believes in private property. Anyone who believes in capitalism also believes in private property. Thus, anyone who believes in capitalism must be a conservative.
Original Argument
Premise 1: Every conservative believes in private property
Premise 2: Anyone who believes in capitalism also believes in private property.
Conclusion: Thus, anyone who believes in capitalism must be a conservative
Category One: Every conservative believes in private property
Category Two: Anyone who believes in capitalism also believes in private property.
Category Three: Anyone who believes in capitalism must be a conservative
New Category One: Anyone who believes in capitalism must be a conservative
New Category Two: Anyone who believes in capitalism also believes in private property
New Category Three: Anyone who believes in capitalism is also conservative
New Argument
Premise 1: Anyone who believes in capitalism also believes in private property
Premise 2: Anyone who believes in capitalism must be conservative
Conclusion: Anyone who believes in private property must be conservative
- Many postal workers are stressed. People who are stressed can become violent. Every postal worker can become violent.
Original Argument
Premise 1: Many postal workers are stressed
Premise 2: People who are stressed can become violent
Conclusion: Every postal worker can become violent.
Category One: Many postal workers are stressed
Category Two: People who are stressed can become violent
Category Three: Every postal worker can become violent.
New Category One: People who are stressed can become violent
New Category Two: Every postal worker can become violent
New Category Three: Many postal workers are stressed
New Argument
Premise 1: People who are stressed can become violent
Premise 2: Many postal workers are stressed
Conclusion: Some postal workers can become violent
- Since most pineapples are fruits, it follows that most pineapples are sweet, since most fruits are sweet.
Original Argument
Premise 1: Since most pineapples are fruits
Premise 2: Most pineapples are sweet
Conclusion: Most fruits are sweet
Category One: Since most pineapples are fruits
Category Two: Most pineapples are sweet
Category Three: Most fruits are sweet
New Category One: Most fruits are sweet
New Category Two: Most pineapples are sweet
New Category Three: Most pineapples are fruits
New Argument
Premise 1: Most fruits are sweet
Premise 2: Most pineapples are fruits
Conclusion: Most pineapples are fruits
- All dogs are messy. I know this because they have no table manners, and some things without table manners are messy.
Original Argument
Premise 1: All dogs are messy
Premise 2: some things without table are manners messy
Conclusion: Dogs have no table manners
Category One: All dogs are messy
Category Two: some things without table are manners messy
Category Three: Dogs have no table manners
New Category One: Some things without table are manners messy
New Category Two: Dogs have no table manners
New Category Three: All dogs are messy
New Argument
Premise 1: All dogs are messy
Premise 2: Some things without table manners are messy
Conclusion: Some dogs do not have table manners
- No Greek poet was a genius, because some Greek poets were not eccentric, and all geniuses are eccentrics.
Original Argument
Premise 1: No Greek poet was a genius
Premise 2: Some Greek poets were not eccentric
Conclusion: All geniuses are eccentrics.
Category One: No Greek poet was a genius
Category Two: Some Greek poets were not eccentric
Category Three: All geniuses are eccentrics
New Category One: All geniuses are eccentrics
New Category Two: Some Greek poets were not eccentric
New Category Three: No Greek poet was a genius
New Argument
Premise 1: All geniuses are eccentrics
Premise 2: some Greek poets were not eccentric
Conclusion: Some Greek poets were not geniuses
- A good thing would never harm the person who owns it. But money sometimes harms its owner. Thus, we can see the money is not a good thing.
Original Argument
Premise 1: A good thing would never harm the person who owns it
Premise 2: Money sometimes harms its owner
Conclusion: Money is not a good thing
Category One: A good thing would never harm the person who owns it
Category Two: Money sometimes harms its owner
Category Three: Money is not a good thing
New Category One: Money sometimes harms its owner
New Category Two: Money is not a good thing
New Category Three: Money is not a good thing and can also harm its owner
New Argument
Premise 1: A good thing never harms its owner
Premise 2: Money sometimes harms its owner
Conclusion: Money is sometimes not a good thing
- Because all mammals are animals, and some mammals can’t swim underwater, we can conclude that some things that swim underwater are not animals.
Original Argument
Premise 1: Because all mammals are animals
Premise 2: some mammals can’t swim underwater
Conclusion: some things that swim underwater are not animals.
Category One: Because all mammals are animals
Category Two: some mammals can’t swim underwater
Category Three: some things that swim underwater are not animals
New Category One: some things that swim underwater are not animals
New Category Two: some mammals can’t swim underwater
New Category Three: Because all mammals are animals
New Argument
Premise 1: All mammals are animals
Premise 2: Some things that swim under water are not animals
Conclusion: Some that swim underwater are not mammals
- Some people who support terrorism also support an independent Palestinian state. My teacher also supports an independent Palestinian state, so I guess that she supports terrorism.
Original Argument
Premise 1: Some people who support terrorism also support an independent Palestinian state
Premise 2: My teacher also supports an independent Palestinian state
Conclusion: My teacher supports terrorism.
Category One: Some people who support terrorism also support an independent Palestinian state
Category Two: My teacher also supports an independent Palestinian state
Category Three: My teacher supports terrorism.
New Category One: My teacher also supports an independent Palestinian state
New Category Two: My teacher supports terrorism
New Category Three: My teacher also supports an independent Palestinian state
New Argument
Premise 1: My teacher also supports an independent Palestinian state
Premise 2: Some people who support terrorism also support an independent Palestinian state
Conclusion: Some people who support terrorism can be my teacher
- At the present time, there are no communists working for the state department. Since every person who works for the state department also works for the government, I guess it follows that at the present time, there are no communists working for the government.
Original Argument
Premise 1: At the present time, there are no communists working for the state department
Premise 2: Since every person who works for the state department also works for the government
Conclusion: At the present time, there are no communists working for the government.
Category One: At the present time, there are no communists working for the state department
Category Two: Every person who works for the state department also works for the government
Category Three: At the present time, there are no communists working for the government.
New Category One: Since every person who works for the state department also works for the government
New Category Two: the present time, there are no communists working for the government.
New Category Three: Every person who works at the state department is not a communist
New Argument
Premise 1: At the present time, there are no communists working for the state department
Premise 2: Every person who works for the state department also works for the government
Conclusion: There are no communists working for the government
- All cars are dangerous when improperly used. Since every car is a motor vehicle, it follows that all motor vehicles are dangerous when improperly used.
Original Argument
Premise 1: All cars are dangerous when improperly used
Premise 2: Every car is a motor vehicle
Conclusion: All motor vehicles are dangerous when improperly used.
Category One: All cars are dangerous when improperly used
Category Two: Every car is a motor vehicle
Category Three: All motor vehicles are dangerous when improperly used.
New Category One: All motor vehicles are dangerous when improperly used
New Category Two: All motor vehicles are dangerous when improperly used
New Category Three: Every car is a motor vehicle
New Argument
Premise 1: All cars are dangerous when improperly used
Premise 2: Since every car is a motor vehicle
Conclusion: All cars are dangerous when improperly used
- Those who opposed the Voting Rights Bill were opposed to unfair racial discrimination. Some conservatives did not support this bill. So they must not be opposed to unfair racial discrimination.
Original Argument
Premise 1: Those who opposed the Voting Rights Bill were opposed to unfair racial discrimination
Premise 2: Some conservatives did not support this bill
Conclusion: Conservatives must not be opposed to unfair racial discrimination
Category One: Those who opposed the Voting Rights Bill were opposed to unfair racial discrimination
Category Two: Some conservatives did not support this bill
Category Three: Conservatives must not be opposed to unfair racial discrimination
New Category One: Some conservatives must not be opposed to unfair racial discrimination
New Category Two: Some conservatives did not support this bill
New Category Three: Some conservatives must did not support this bill and also unfair racial discrimination
New Argument
Premise 1: Those who opposed the Voting Rights Bill were opposed to unfair racial discrimination
Premise 2: Some conservatives did not support this bill
Conclusion: Some conservatives opposed unfair racial discrimination
