An Introduction to Logic

For each of the following enthymematic arguments:

a. Formulate the plausible premise or conclusion, if any, that is missing but understood.

b. Write the argument in standard form, including the missing premise or conclusion needed to make the completed argument valid—if possible—using parameters if necessary.

c. Name the order of the enthymeme.

d. If the argument is not valid even with the understood premise included, name the fallacy that it commits.

Example Problem

Transgenic animals are manmade and as such are patentable.

—Alan E. Smith, cited in Genetic Engineering
(San Diego, CA: Greenhaven Press, 1990)

Example Solution

a. The premise understood but not stated here is that whatever is manmade is patentable.

b. Standard-form translation:

All manmade things are patentable things.

All transgenic animals are manmade things.

Therefore, all transgenic animals are patentable things.

c. The enthymeme is first-order, because the premise taken as understood is the major premise of the completed argument.

d. This is a valid syllogism of the form AAA–1, Barbara.

PROBLEMS

*15. Man tends to increase at a greater rate than his means of subsistence; consequently he is occasionally subject to a severe struggle for existence. —Charles Darwin, The Descent of Man, 1871

16. No internal combustion engines are free from pollution; but no internal combustion engine is completely efficient. You may draw your own conclusion.

17. A nation without a conscience is a nation without a soul. A nation without a soul is a nation that cannot live. —Winston Churchill

18. Liberty means responsibility. That is why most men dread it. —George Bernard Shaw, Maxims for Revolutionists, 1903

19. Who controls the past controls the future. Who controls the present controls the past. —George Orwell, 1984

20. Productivity is desirable because it betters the condition of the vast majority of the people.

—Stephen Miller, “Adam Smith and the Commercial Republic,”
The Public Interest, Fall 1980

21. Advertisements perform a vital function in almost any society, for they help to bring buyers and sellers together.

—Burton M. Leiser, Liberty, Justice, and Morals, 1986

22. Logic is a matter of profound human importance precisely because it is empirically founded and experimentally applied.

—John Dewey, Reconstruction in Philosophy, 1920

23. Iphigeneia at Aulis is a tragedy because it demonstrates inexorably how human character, with its itch to be admired, combines with the malice of heaven to produce wars which no one in his right mind would want and which turn out to be utterly disastrous for everybody.

—George E. Dimock, Jr., Introduction to Iphigeneia at Aulis by Euripides, 1992

24. … the law does not expressly permit suicide, and what it does not expressly permit it forbids.

—Aristotle, Nicomachean Ethics

25. The man who says that all things come to pass by necessity cannot criticize one who denies that all things come to pass by necessity: for he admits that this too happens of necessity.

—Epicurus, Fragment XL, Vatican Collection

7.7 INSTRUCTIONS

Identify the form of each of the following arguments and state whether the argument is valid or invalid:

Example Problem

If a man could not have done otherwise than he in fact did, then he is not responsible for his action. But if determinism is true, it is true of every action that the agent could not have done otherwise. Therefore, if determinism is true, no one is ever responsible for what he does.

—Winston Nesbit and Stewart Candlish, “Determinism and the Ability to Do Otherwise,” Mind, July 1978

Example Solution

This is a pure hypothetical syllogism. Valid.

PROBLEMS

10. I have already said that he must have gone to King’s Pyland or to Capleton. He is not at King’s Pyland, therefore he is at Capleton.

—Arthur Conan Doyle, The Adventure of Silver Blaze

11. If then, it is agreed that things are either the result of coincidence or for an end, and that these cannot be the result of coincidence or spontaneity, it follows that they must be for an end.

—Aristotle, Physics

12. There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for in such a case it would be prior to itself, which is impossible.

—Thomas Aquinas, Summa Theologiae, I, question 2, article 3

13. Either wealth is an evil or wealth is a good; but wealth is not an evil; therefore wealth is a good.

—Sextus Empiricus, Against the Logicians, second century CE

14. I do know that this pencil exists; but I could not know this, if Hume’s principles were true; therefore, Hume’s principles, one or both of them, are false.

—G. E. Moore, Some Main Problems of Philosophy (New York: Allen & Unwin, 1953)

15. It is clear that we mean something, and something different in each case, by such words [as substance, cause, change, etc.]. If we did not we could not use them consistently, and it is obvious that on the whole we do consistently apply and withhold such names.

—C. D. Broad, Scientific Thought, 1923

7.8 INSTRUCTIONS

Bring together all tools for assessing arguments, discuss (in your own words) what might be offered to refute each of the following:

PROBLEMS

15. The decision of the Supreme Court in U.S. v. Nixon (1974), handed down the first day of the Judiciary Committee’s final debate, was critical. If the President defied the order, he would be impeached. If he obeyed the order, it was increasingly apparent, he would be impeached on the evidence.

—Victoria Schuck, “Watergate,” The Key Reporter, Winter 1975–1976

16. If we are to have peace, we must not encourage the competitive spirit, whereas if we are to make progress, we must encourage the competitive spirit. We must either encourage or not encourage the competitive spirit. Therefore we shall either have no peace or make no progress.

17. The argument under the present head may be put into a very concise form, which appears altogether conclusive. Either the mode in which the federal government is to be constructed will render it sufficiently dependent on the people, or it will not. On the first supposition, it will be restrained by that dependence from forming schemes obnoxious to their constituents. On the other supposition, it will not possess the confidence of the people, and its schemes of usurpation will be easily defeated by the State governments, who will be supported by the people.

—James Madison, The Federalist Papers, no. 46, 1788

18. … a man cannot enquire either about that which he knows, or about that which he does not know; for if he knows, he has no need to enquire; and if not, he cannot; for he does not know the very subject about which he is to enquire.

—Plato, Meno

19. We tell clients to try to go through the entire first interview without even mentioning money. If you ask for a salary that is too high, the employer concludes that he can’t afford you. If you ask for one that is too low, you’re essentially saying, “I’m not competent enough to handle the job that you’re offering.”

—James Challenger, “What to Do—and Not to Do—When Job Hunting,” U.S. News & World Report, 6 August 1984

20. “Pascal’s wager” is justifiably famous in the history of religion and also of betting. Pascal was arguing that agnostics—people unsure of God’s existence—are best off betting that He does exist. If He does but you end up living as an unbeliever, then you could be condemned to spend eternity in the flames of Hell. If, on the other hand, He doesn’t exist but you live as a believer, you suffer no corresponding penalty for being in error. Obviously, then, bettors on God start out with a big edge.

—Daniel Seligman, “Keeping Up,” Fortune, 7 January 1985