Translating Syllogistic Arguments into Standard-Form Categorical Propositions

Complete the exercises in the attached document, “Reading Exercises.”

Topic 7 Reading Exercises from:

Copi, Irving M. Introduction to Logic, 14th Edition. Routledge.

7.2 INSTRUCTIONS

Translate the following syllogistic arguments into standard form, and test their validity by using the syllogistic rules set forth in Chapter 6.

Example Problem

Some preachers are persons of unfailing vigor. No preachers are nonintellectuals. Therefore some intellectuals are persons of unfailing vigor. 

Example Solution

This argument may be translated into: Some preachers are persons of unfailing vigor. (Some P is V.) All preachers are intellectuals. (By obversion: All P is I.) Therefore some intellectuals are persons of unfailing vigor. (Some I is V.) Explain whether the syllogism is valid using the 6 rules (6.4) and mood (6.5).

PROBLEMS

2. Some metals are rare and costly substances, but no welder’s materials are nonmetals; hence some welder’s materials are rare and costly substances.

3. Some Asian nations were nonbelligerents, because all belligerents were allies either of Germany or Britain, and some Asian nations were not allies of either Germany or Britain.

4. Some nondrinkers are athletes, because no drinkers are persons in perfect physical condition, and some people in perfect physical condition are not nonathletes.

5. All things inflammable are unsafe things, so all things that are safe are nonexplosives, because all explosives are flammable things.

6. All worldly goods are changeable things, for no worldly goods are things immaterial, and no material things are unchangeable things.

7. All those who are neither members nor guests of members are those who are excluded; therefore no nonconformists are either members or guests of members, for all those who are included are conformists.

8. All mortals are imperfect beings, and no humans are immortals, whence it follows that all perfect beings are nonhumans. 

9. All things present are nonirritants; therefore no irritants are invisible objects, because all visible objects are absent things.

10. All useful things are objects no more than six feet long, because all difficult things to store are useless things, and no objects over six feet long are easy things to store.

7.3 INSTRUCTIONS

Translate the following into standard-form categorical propositions:

Example Problem

Roses are fragrant.

Example Solution

Standard-form translation: All roses are fragrant things.

PROBLEMS

2. Orchids are not fragrant.

3. Many a person has lived to regret a misspent youth.

4. Not everyone worth meeting is worth having as a friend.

5. If it’s a Junko, it’s the best that money can buy.

6. If it isn’t a real beer, it isn’t a Bud.

7. Nothing is both safe and exciting.

8. Only brave people have ever won the Congressional Medal of Honor.

9. Good counselors are not universally appreciated.

10. He sees not his shadow who faces the sun.

7.4 INSTRUCTIONS

A. Translate the following propositions into standard form, using parameters where necessary 

Example Problem

He groans whenever he is reminded of his loss.

Example Solution

Standard-form translation: All times when he is reminded of his loss are times when he groans.

PROBLEMS

2. She never drives her car to work.

3. He walks where he chooses.

4. He always orders the most expensive item on the menu.

5. She does not give her opinion unless she is asked to do so.

6. She tries to sell life insurance wherever she may happen to be.

7. His face gets red when he gets angry.

8. If he is asked to say a few words, he talks for hours.

9. Error of opinion may be tolerated where reason is left free to combat it.

10. People are never so likely to settle a question rightly as when they discuss it freely.

INSTRUCTIONS

For each of the following arguments,

a. Translate the argument into standard form.

b. Name the mood and figure of its standard-form translation.

c. Test its validity using the rules and mood. If it is valid, give its traditional name.

d. If it is invalid, name the fallacy it commits.

Example Problem

Since all knowledge comes from sensory impressions and since there’s no sensory impression of substance itself, it follows logically that there is no knowledge of substance.

—Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance

(New York: Bantam, 1975)

Example Solution

a. Standard-form translation:

No things derived from sensory impressions are items of knowledge of substance itself.

All items of knowledge are things derived from sensory impressions.

Therefore, no items of knowledge are items of knowledge of substance itself.

b. Mood and figure: EAE–1

c. Valid; Celarent

PROBLEMS

2. … no names come in contradictory pairs; but all predicables come in contradictory pairs; therefore no name is a predicable.

—Peter Thomas Geach, Reference and Generality

(Ithaca, NY: Cornell University Press, 1980)

3. Barcelona Traction was unable to pay interest on its debts; bankrupt companies are unable to pay interest on their debts; therefore, Barcelona Traction must be bankrupt.

—John Brooks, “Annals of Finance,” The New Yorker, 28 May 1979

4. Extremism in defense of liberty, or virtue, or whatever is always a vice—because extremism is but another name for fanaticism which is a vice by definition.

—Irving Kristol, “The Environmentalist Crusade,”

The Wall Street Journal, 16 December 1974

5. All syllogisms having two negative premises are invalid. Some valid syllogisms are sound. Therefore some unsound arguments are syllogisms having two negative premises.

6. Not all is gold that glitters, for some base metals glitter, and gold is not a base metal.

7. Where there’s smoke there’s fire, so there’s no fire in the basement, because there’s no smoke there.

8. It seems that mercy cannot be attributed to God. For mercy is a kind of sorrow, as Damascene says. But there is no sorrow in God; and therefore there is no mercy in Him.

—Thomas Aquinas, Summa Theologiae, I, question 21, art. 3

9. … because intense heat is nothing else but a particular kind of painful sensation; and pain cannot exist but in a perceiving being; it follows that no intense heat can really exist in an unperceiving corporeal substance.

—George Berkeley, Three Dialogues Between Hylas and Philonous,

in Opposition to Sceptics and Atheists, 1713

10. Only those who ignore the facts are likely to be mistaken. No one who is truly objective is likely to be mistaken. Hence no one who ignores the facts is truly objective.