Syllogistic Arguments into Standard Form
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Syllogistic Arguments into Standard Form
Topic 7 Reading Exercises from:
Copi, Irving M. Introduction to Logic, 14th Edition. Routledge.
Translate the following syllogistic arguments into standard form, and test their validity by using the syllogistic rules set forth in Chapter 6.
Some preachers are persons of unfailing vigor. No preachers are nonintellectuals. Therefore some intellectuals are persons of unfailing vigor.
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).
2. Some metals are rare and costly substances, but no welders materials are nonmetals; hence some welders 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.
Translate the following into standard-form categorical propositions:
Roses are fragrant.
Standard-form translation: All roses are fragrant things.
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 its a Junko, its the best that money can buy.
6. If it isnt a real beer, it isnt 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.
A. Translate the following propositions into standard form, using parameters where necessary.
He groans whenever he is reminded of his loss.
Standard-form translation: All times when he is reminded of his loss are times when he groans.
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.
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.
Since all knowledge comes from sensory impressions and since theres 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)
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: EAE1
c. Valid; Celarent
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 vicebecause 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 theres smoke theres fire, so theres no fire in the basement, because theres 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.
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