Translating into Categorical Statements

A-Statement – All S are P

1. Synonyms for ‘All’ – ‘Every’, ‘Any’, ‘Something’, ‘Whatever’, ‘Whenever’

E.g., “Every dog is a mammal” is equivalent to “All dogs are mammals.”

2. Lack of a Quantifier – If a subject of a statement is a category without a quantifier, then it means ‘All ..’.

E.g., “Dogs are mammals” is equivalent to “All dogs are mammals.”

3. Affirmative Singular Statements – The subject is translated into “All things identical with …”, even though it sounds awkward.

E.g., “Kofi Annan is a world leader” is equivalent to “All people identical with Kofi Annan are world leaders.

E-Statement – No S are P

1. Synonyms for ‘No’ – ‘Nothing’, ‘None’

E.g., “Nothing is that room is a valuable item” is equivalent to “No things in that room are valuable items.

2. Universal statements with Negated Predicates – If a universal statement has a negated predicate, restate it as an E-Statement.

E.g., “All dogs are not reptiles,” “Dogs are not reptiles” are equivalent to “No dogs are reptiles. Also, “Mark is not an athlete” is equivalent to “No people identical with Mark are athletes.”

I-Statement – Some S are P

1. Synonyms for “Some” – ‘A few’, ‘Many’, ‘Several’ ‘Most’, ‘23%’, ‘At least one’, ‘There are’

E.g., ‘A few students are senior citizens, and ‘There are students who are senior citizens” are equivalent to “Some students are senior citizens.”

O-Statement – Some S are not P

1. Particular Statements with Negated Predicates – If a particular statement has a negated subject predicate, restate it as an O-Statement.

E.g., “Some professionals are nonadults” is equivalent to “Some professionals are not adults.”

2. Negation of ‘All’ – If the word ‘All’ or its equivalent is negated, translate the statement into an O-Statement.

E.g., “Not all textbooks are expensive items” is equivalent to “Some textbooks are not expensive items.

Practice Exercises

1. Any bank that makes too many risky loans will fail.

2. Women military officers are not eligible for combat duty.

3. Terrorist attacks succeed whenever security measures are lax.

4. Bromine is extractable from seawater.

5. Not all guilt feelings are psychological aberrations.

6. Every jazz fan admires Duke Ellington.

7. None of the computers in this closet are functioning.

8. A television show that depicts violence incites violence.

9. Manipulators do not make good marriage partners.

10. At least one painting in the museum is over 500 years old.

11. She gains weight whenever she’s depressed.

12. She’s depressed whenever she gains weight.

13. A few members are nonparticipants.

14. Warmth always relieves pain.

15. Joseph J. Thompson discovered the electron.

16. A few organic silicones are used as lubricants.

17. Feathers are not heavy.

18. Movies are entertaining.

19. Not every college student is at least 18 years old.

20. Nothing in this room should be thrown out.

Answers

1. All banks that makes too many risky loans are banks that will fail.

2. No women military officers are soldiers eligible for combat duty.

3. All situations in which security measures are lax are situations in which terrorist attacks succeed.

4. All Bromine is a substance extractable from seawater.

5. Some guilt feelings are not psychological aberrations.

6. All jazz fans are people who admire Duke Ellington.

7. No computer in this closet is a functioning computer.

8. All television shows that depict violence are things that incite violence.

9. No manipulators are good marriage partners.

10. Some paintings in the museum are over 500 years old.

11. All times when she’s depressed are times when she gains weight.

12. All times when she gains weight are times when she’s depressed.

13. Some members are not participants.

14. All applications of warmth are treatments that relieve pain.

15. All people identical with Joseph J. Thompson are people that discovered the electron.

16. Some organic silicones are substances used as lubricants.

17. No feathers are heavy things.

18. All movies are things that are entertaining.

19. Some college students are not at least 18 years old.

20. No thing in this room is something that should be thrown out.