Chapter 3 Answers to Exercises Exercises 3.a. In each of the following claims, identify as many categories of things as you can, by using the “things that are BLANK” format, as we have done above: [In these answers, we will only list a few of the many possible categories.] 1. Aristotle was an Ancient Greek philosopher who wrote many treatises. Things that are: Aristotle Ancient Greek Philosopher Greek Philosopher Ancient Greek Philosopher Treatises Philosopher who wrote many treatises 2. Rob has seen a few mailboxes painted like R2-D2, but most are blue. Things that are: Rob Seen Mailboxes Mailboxes painted like R2-D2 Mailboxes seen by Rob Painted R2-D2 Blue 3. Dinosaurs, like the Stegosaurus, roamed the Earth during the Jurassic Period. Things that: Are dinosaurs Are stegosauruses Are roamers Are the Earth Are The Jurassic Period Roamed the Earth during the Jurassic Period

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

4. People who are not handicapped but who take handicapped persons’ parking spots belong in jail. Things that are: People People who are not handicapped Parking Spots People who take handicapped persons’ parking spots People who are not handicapped but take handicapped persons’ parking spots In jail People who belong in jail

Exercises 3.b. Venn diagram the following A-claims using the capital letters given: 1. All cats (C) are mammals (M).

C

M

2. All Catholics (C) are Christians (X).

C

X

3. All voters in the United States (U) are at least 18 years old (E).

U

E

4. All things that are living (L) are things that require water (W).

L

W

5. All AC/DC songs (A) are songs that rock (R).

A

R

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

Rewrite each of the following claims as A-claims, then Venn diagram: 1. Every human is an air-breather. All things that are human (H) are things that are air-breathers (A).

H

A

2. Items in this bin are on sale. All things that are items in this bin (B) are things that are on sale (S).

B

S

3. Dinosaurs are extinct. All things that are dinosaurs (D) are things that are extinct (E).

D

E

4. Clocks tell time. All things that are clocks (C) are things that tell time (T).

C

T

5. Calculators perform calculations. All things that are calculators (C) are things that perform calculations (O).

C

O

Exercises 3.c. Venn diagram the following E-claims using the capital letters given: 1. No cats (C) are fish (F).

C

F

2. No Christians (C) are polytheists (P).

C

P

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

3. No voters in the US (U) are under 18 years old (E).

U

E

4. No things that are made by humans (H) are things that can be in two places at once (T).

H

T

5. Nothing in that can (C) is edible (E).

C

E

Rewrite each of the following claims as E-claims, then Venn diagram: 1. Every human male cannot give birth. No things that are human males (H) are things that can give birth (B).

H

B

2. Nothing in this drawer is sharp-edged. No things in this drawer (D) are things that are sharp-edged (S).

D

S

3. There are no U.S. Civil War veterans who are living. No things that are U.S. Civil War veterans (V) are things that are living (L).

V

L

4. No illegal immigrants deserve access to our health care system. No things that are illegal immigrants (I) are things that deserve access to our health care system (D).

I

D

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

5. All felons are prohibited from voting. No things that are felons (F) are things that are permitted to vote (V).

F

V

Exercises 3.d. Venn diagram the following I-claims using the capital letters given: 1. Some cats (A) are declawed (B).

A

x

B

2. Some Christians (A) are Presbyterian (B).

A

x

B

3. Some voters in the UK (A) are over 90 years old (B).

A

x

B

4. Some things that are made by humans (A) are things that will last 1,000 years (B).

A

x

B

5. Some Democrats (A) are conservative (B).

A

x

B

Rewrite each of the following claims as I-claims, then Venn diagram: 1. There are lots of human males that are brown-haired. Some things that are human males (H) are things that are brown-haired (B).

H

x

B

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

2. There are fire hydrants that are painted yellow. Some things that are fire hydrants (F) are things that are painted yellow (Y).

F

x

Y

3. Some like it hot! Some things that are things (we assume “people”) (P) are things that like it hot (H).

P

x

H

4. I know at least one 30-year-old man who likes Lady Gaga, and that’s me. Some things that are 30-year-old men (M) are things that like Lady Gaga (L).

M

x

L

5. C’mon, at least some Mormons are rational. Some things that are Mormon (M) are things that are rational (R).

M

x

R

Exercises 3.e. Venn diagram each of the following O-claims using the capital letters provided: 1. Some students at this college (A) are not sophomores (B).

A

x

B

2. Some tables (A) are not four-legged (B).

A

x

B

3. Some members of the Labour Party (A) are not very liberal (B).

A

x

B

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

4. Some pottery that have been made by the ancient Greeks (A) are not things that will ever be discovered intact (B).

A

x

B

5. Some Muslims (A) are not violent (B).

A

x

B

Rewrite each of the following claims as O-claims, then Venn diagram: 1. A few of the students are not going to the show. Some things that are students (S) are things that are not going to the show (G).

S

x

G

2. There are U.S. mailboxes that aren’t painted the standard blue. Some U.S. mailboxes (M) are not painted the standard blue (B).

M

x

B

3. Yech! Some of those grapes did not taste sweet. (We removed “Yech!” because it is an emotive expression and not a claim.) Some things that are those grapes (T) are not things that tasted sweet (S).

T

x

S

[This one is tricky. If you identified the categories differently, you would have a different type of claim. For instance, instead of “things that tasted sweet,” we could have identified the category as “things that did not taste sweet.” If so, we would have an I-claim: Some things that are those grapes are things that did not taste sweet. Though the two claims mean the same thing, since we asked you to interpret it as an O-claim, this alternate interpretation would be incorrect.] 4. Hey, there are a few non-religious conservatives. Some things that are conservatives (C) are not things that are religious (R).

C

x

R

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

5. At least some of our students are not rational. Some things that are our students (S) are not things that are rational (R).

S

x

R

Exercises 3.f. Rewrite each of the following claims as an A-, E-, I-, or O-claim. Then draw diagrams for the following claims using circles, capital letters, and, where needed, a shaded area or an “X”. We’ve done the second for you: 1. Jane, Mona, and Sue are women. A-claim: All things that are Jane, Mona, and Sue (J) are things that are women (W).

J

W

2. Some women are firefighters. I-claim: Some things that are women (W) are things that are firefighters (F).

W

x

F

3. Jill and Sheri (both women) are firefighters. A-claim: All things that are Jill and Sheri (T) are things that are firefighters (F).

T

F

OR I-claim: Some things that are women (W) are things that are firefighters (F).

W

x

F

4. Jack, Frank, and Jim (all men) are firefighters. A-claim: All things that are Jack, Frank, and Jim (T) are things that are firefighters (F).

T

F

OR

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

I-claim: Some things that are men (M) are things that are firefighters (F).

M

x

F

5. Jerry is a Catholic. A-claim: All things that are Jerry (J) are things that are Catholic (C).

J

C

6. Shelly and Zoe (both women) are not Hindu. E-claim: No things that are Shelley and Zoe (S) are things that are Hindu (H).

S

H

OR O-claim: Some things that are women (W) are not things that are Hindu (H).

W

x

H

7. No Catholics are Hindu. E-claim: No things that are Catholic (C) are things that are Hindu (H).

I

D

8. Some CEOs are not greedy. O-claim: Some things that are CEOs (C) are not things that are greedy (G).

C

x

G

OR I-claim: Some things that are CEOs (C) are things that are not greedy (N).

C

x

N

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

9. Everyone in Virginia is in the Eastern Time Zone. A-claim: All things that are people in Virginia (V) are things that are in the Eastern Time Zone (E).

V

E

10. We’ve heard that no one in England works past 3PM. (“We’ve heard” indicates the source of the claim and may constitute some evidence for it—depending on who we heard it from—but it is extraneous to the claim.) E-claim: No things that are people in England (E) are things that work past 3PM (W).

E

W

Exercises 3.g. For the following seven claims, organize each into the four elements of a standard-form categorical claim, then Venn diagram. 1. Junk food is unhealthy for people. Quantifier Subject

Copula

Predicate

All

are

things that are unhealthy for people (U).

are

things that are healthy for people (H).

things that are junk food (J)

J

U

OR No

things that are junk food (J)

J

H

2. Abortions are immoral actions. Quantifier Subject

Copula

Predicate

All

are

things that are immoral actions (I).

are

things that are moral actions (M).

A

things that are abortions (A)

I

OR No

A

things that are abortions (A)

M

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

3. Metal music rocks! Quantifier Subject

Copula

Predicate

All

are

things that rock (R).

things that are metal music (M)

M

R

4. Country music does not rock! Quantifier Subject

Copula

Predicate

All

are

things that do not rock (D).

are

things that rock (R).

things that are country music (C)

C

D

OR No

things that are country music (C)

C

R

5. Believe it or not, peanuts are not nuts. Quantifier

Subject

Copula

Predicate

No

things that are peanuts (P)

are

things that are nuts (N).

P

N

6. Several checks bounced. Quantifier

Subject

Copula

Predicate

Some

things that are checks (C)

are

things that bounced (B).

C

x

B

7. Lots of people are not afraid to speak in public. Quantifier Subject

Copula

Predicate

Some

are not

things that are afraid to speak in public (A).

P

things that are people (P)

x

A

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

Exercises 3.h. In the following claims, identify as many categories of things as you can, by using the “the category of things that are [BLANK]” format: 1. The honey bee lives in a community. Things that are: honey bees communities things that live in communities bees 2. 80% of the people polled think that Frank is doing a lousy job. Things that are: people people polled Frank people who think Frank is doing a lousy job 3. She sells seashells at the seashore. Things that are: she seashells seashores things that are sold things that are sold at seashores seashells sold at seashores 4. Logic is the science of sound reasoning. Things that are: logic science sound reasoning the science of sound reasoning 5. Jen told me that Al Gore claimed that he invented the Internet. Things that are: Jen Al Gore me Al Gore’s claims the Internet things that invented the Internet

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

Exercises 3.i. Translate each of the following claims into one of the four standard-form categorical claims: A-claim, E-claim, I-claim, or O-claim, then Venn diagram. 1. Some primates have hair. I-claim: Some things that are primates (P) are things that have hair (H). 2. She placed the keys in the drawer. A-claim: All things that are she (S) are things that placed the keys in the drawer (P). 3. Some fruits are not edible. O-claim: Some things that are fruit (H) are not things that are edible (E). 4. If you build it, they will come. A-claim: All things that are ‘things that are the i you build’ are things that they will come to. 5. The only thing we have to fear is fear itself. A-claim: All the things we have to fear are things that are fear itself. 6. The timing is off here. A-claim: All things that are the time are things that are off here. 7. Nothing Frank and John have produced has been of top quality. E-claim: No things produced by Frank and John are things that have been of top quality. 8. If it barks, then it’s not a duck. E-claim: No things that bark are things that are ducks. 9. They concluded the show with a bang. A-claim: All the things they concluded the show with are things that are a bang. 10. Some polls indicated that John would not win in tomorrow’s election. O-claim: Some things that are polls are not things that indicated that John would win in tomorrow’s election. OR I-claim: Some things that are polls are things that indicated that John would not win in tomorrow’s election. 11. His stats have been unmatched. A-claim: All things that are his stats are things that have been unmatched. OR E-claim: No things that are his stats are things that have been matched. 12. Some men discovered that pearl. I-claim: Some things that are men are things that discovered that pearl.

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

13. Water splashed him again. A-claim: All things that are water are things that splashed him again. 14. Only the strong survive. E-claim: No things that are not strong are things that survive. OR A-claim: All things that are strong are things that survive. 15. He does not want help. E-claim: No things that he wants are things that are help.

Exercises 3.j. For each of the following arguments: (i) Translate the claims into standard-form categorical claims: A-claim, E-claim, I-claim, or O-claim; (ii) organize the claims into a categorical syllogism (one conclusion and two premises); (iii) use the Venn diagram method to test for validity, indicating whether the argument is valid or invalid. 1. Idiots make bad choices. There are a few idiots who are living next door. So, I guess some people living next door make bad choices. 1. All things that are idiots are things that make bad choices. 2. Some things that are idiots are things living next door. 3. Thus, some things living next door make bad choices.

I

M x L

The conclusion is expressed in the diagram; therefore, this argument is valid. 2. Dinosaurs are extinct. Some extinct things are not fossilized. Hence, some fossilized things are not dinosaurs. 1. All things that are dinosaurs are things that are extinct. 2. Some things that are extinct are not things that are fossilized. 3. Hence, some things that are fossilized are things that are not dinosaurs.

D

E

? F The conclusion is not expressed in the Venn diagram; therefore, this argument is invalid. 3. Metallica rocks. If it rocks, it rolls, too. Metallica does not roll. 1. All things that are Metallica are things that rock. 2. All things that rock are things that roll.

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

3. Hence, no things that are Metallica are things that roll.

M

R

(roll) L The conclusion is not expressed in the Venn diagram; therefore, this argument in invalid. 4. There are a few cats that are tabby cats. All cats are sweet. So, there are a few sweet things that are tabby cats. 1. Some things that are cats are things that are tabby cats. 2. All things that are cats are things that are sweet. 3. So, some things that are sweet are things that are tabby cats.

C

T x S

The conclusion is expressed in the Venn diagram; therefore, the argument is valid. 5. Atheists are unbelievers, and some unbelievers are baptized persons; so, some baptized persons are atheists. 1. All things that are atheists are things that are unbelievers. 2. Some things that are unbelievers are things that are baptized persons. 3. So, some things that are baptized persons are things that are atheists.

A

U

? B The conclusion is not expressed in the Venn diagram; therefore, the argument is invalid. Notice: the claim says that all atheists are unbelievers. It is not clear that the converse (that all unbelievers are atheists) is true. Perhaps there are agnostics or children who are unbelievers (for instance, people who have never formed a belief either way). These may be baptized persons. And it may be true that no atheists are baptized persons; but from the diagram we cannot tell. 6. Teens are not professional drivers. Some teens, however, are people who are good at simulated driving. Therefore, some people who are good at simulated driving are not professional drivers. 1. No things that are teens are things that are professional drivers. 2. Some things that are teens are things that are good at simulated driving. 3. Therefore, some things that are good at simulated driving are not professional drivers.

T

P x S

The conclusion is expressed in the Venn diagram; therefore, this argument is valid.

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

7. There are bears that aren’t brown. Bears are hibernating animals. Thus, there are hibernating animals that aren’t brown. 1. Some things that are bears are not things that are brown. 2. All things that are bears are things that are hibernating animals. 3. Thus, some things that are hibernating animals are things that are not brown.

B

R (brown) x H

The conclusion is expressed in the Venn diagram; therefore, this argument is valid. 8. Minds calculate. Computers calculate. Therefore, minds are computers. 1. All things that are minds are things that calculate. 2. All things that are computers are things that calculate. 3. Therefore, all things that are minds are things that are computers.

O (calculate)

M

C The conclusion is not expressed in the Venn diagram; therefore, this argument is invalid. 9. Exercising is good for you. Some activities are not exercising. So, some exercising is not good for you. 1. All things that are exercising are things that are good for you. 2. Some things that are activities are not things that are exercising. 3. So, some things that are exercising are not things that are good for you.

E

G

? A The conclusion is not expressed in the Venn diagram; therefore, this argument is invalid. 10. Catholics are not Muslims. Some Muslims are Shiite. Some Shiites are not Catholic. 1. No things that are Catholic are things that are Muslims. 2. Some things that are Muslims are things that are Shiite. 3. Therefore, some things that are Shiite are not things that are Catholic.

C

M x S

The conclusion is expressed in the Venn diagram; therefore, this argument is valid.

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

11. Starbucks serves coffee. Some coffee is decaf. So, Starbucks serves decaf coffee. 1. All things that are Starbucks are things that serve coffee. 2. Some things that are coffee are things that are decaf. 3. So, all things that are Starbucks are things that serve decaf coffee. There is no traditional Venn diagram for this argument. Since there are four categories of objects, this argument cannot be diagrammed according to our method, and must be considered invalid. 12. Most airplanes have a transponder. All airplanes winged vehicles. Therefore, some winged vehicles have a transponder. 1. Some things that are airplanes are things that have a transponder. 2. All things that are airplanes are things that are winged vehicles. 3. Therefore, some things that are winged vehicles are things that have a transponder.

A

T x W

The conclusion is expressed in the Venn diagram; therefore, this argument is valid. 13. No news is good news. Good news travels fast. Thus, no news travels fast! 1. All things that are “no news” are things that are “good news.” 2. All things that are “good news” are things that travel fast. 3. Thus, all things that are “no news” are things that travel fast.

N

G

T The conclusion is expressed in the Venn diagram; therefore, this argument is valid. This one is tricky. “No news” should not be interpreted as “No things that are new are things that are good news,” because the meaning in this context is that the lack of news is something good. Therefore the “lack of news” or “things that are ‘no news’” must be interpreted as a category of things. 14. No voters are persons under eighteen. All infants are persons under eighteen. Thus, no infants are voters. 1. No things that are voters are things that are persons under eighteen. 2. All things that are infants are things that are under eighteen. 3. Thus, no things that are infants are voters.

V

U

I The conclusion is expressed in the Venn diagram; therefore, this argument is valid.

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.

15. All cats are mammals. Some mammals are not indigenous to Africa. So, some cats are not indigenous to Africa. 1. All things that are cats are things that are mammals. 2. Some things that are mammals are not things that are indigenous to Africa. 3. So, some things that are cats are not things that are indigenous to Africa.

C

M

? I The conclusion is not expressed in the Venn diagram; therefore, this argument is invalid.

© Jamie Carlin Watson and Robert Arp (2011) Critical Thinking: An Introduction to Reasoning Well. London: Continuum.