Studies and Exercises in Formal Logic

by John Neville Keynes

CHAPTER X.

EXAMPLES OF ARGUMENTS AND FALLACIES.

382. In how many different moods may the argument implied in the following proposition be stated?
“No one can maintain that all persecution is justifiable who admits that persecution is sometimes ineffective.”
How would the formal correctness of the reasoning be affected by reading “deny” for “maintain”? [V.]

383. No one can maintain that all republics secure good government who bears in mind that good government is inconsistent with a licentious press.
What premisses must be supplied to express the above reasoning in Ferio, Festino and Ferison respectively? [V.]

384. Write the following arguments in syllogistic form, and reduce them to the first figure:—
(α) Falkland was a royalist and a patriot; therefore, some royalists were patriots.
(β) All who are punished should be responsible for their actions; therefore, if some lunatics are not responsible for their actions, they should not be punished.
(γ) All who have passed the Little-Go have a knowledge of Greek; hence A.B. cannot have passed the Little-Go, for he has no knowledge of Greek. [K.]

385. “It is impossible to maintain that the virtuous alone are happy, and at the same time that selfishness is compatible with happiness but incompatible with virtue.”
State the above argument syllogistically in as many different moods as possible. [J.]

432 386. Give the technical name of the following argument:—Payment by results sounds extremely promising; but payment by results necessarily means payment for a minimum of knowledge; payment for a minimum of knowledge means teaching in view of a minimum of knowledge; teaching in view of a minimum of knowledge means bad teaching. [K.]

387. From P follows Q ; and from R follows S ; but Q and S cannot both be true; shew that P and R cannot both be true. [De Morgan.]

388. If (1) it is false that whenever X is found Y is found with it, and (2) not less untrue that X is sometimes found without the accompaniment of Z, are you justified in denying that (3) whenever Z is found there also you may be sure of finding Y? And, however this may be, can you in the same circumstances judge anything about Y in terms of Z? [R.]

389. Can the following arguments be reduced to syllogistic form?
(1) The sun is a thing insensible;
The Persians worship the sun;
Therefore, the Persians worship a thing insensible.
(2) The Divine law commands us to honour kings;
Louis XIV. is a king;
Therefore, the Divine law commands us to honour Louis XIV. [Port Royal Logic.]

390. Examine the following arguments; where they are valid, reduce them if you can to syllogistic form; and where they are invalid, explain the nature of the fallacy:—
(1) We ought to believe the Scripture;
Tradition is not Scripture;
Therefore, we ought not to believe tradition.
(2) Every good pastor is ready to give his life for his sheep;
Now, there are few pastors in the present day who are ready to give their lives for their sheep;
Therefore, there are in the present day few good pastors.
(3) Those only who are friends of God are happy;
Now, there are rich men who are not friends of God;
Therefore, there are rich men who are not happy. 433
(4) The duty of a Christian is not to praise those who commit criminal actions;
Now, those who engage in a duel commit a criminal action;
Therefore, it is the duty of a Christian not to praise those who engage in duels.
(5) The gospel promises salvation to Christians;
Some wicked men are Christians;
Therefore, the gospel promises salvation to wicked men.
(6) He who says that you are an animal speaks truly;
He who says that you are a goose says that you are an animal;
Therefore, he who says that you are a goose speaks truly.
(7) You are not what I am;
I am a man;
Therefore, you are not a man.
(8) We can only be happy in this world by abandoning ourselves to our passions, or by combating them;
If we abandon ourselves to them, this is an unhappy state, since it is disgraceful, and we could never be content with it;
If we combat them, this is also an unhappy state, since there is nothing more painful than that inward war which we are continually obliged to carry on with ourselves;
Therefore, we cannot have in this life true happiness.
(9) Either our soul perishes with the body, and thus, having no feelings, we shall be incapable of any evil; or if the soul survives the body, it will be more happy than it was in the body;
Therefore, death is not to be feared. [Port Royal Logic.]

391. Examine the following arguments:—
(1) “He that is of God heareth my words: ye therefore hear them not, because ye are not of God.”
(2) All the fish that the net inclosed were an indiscriminate mixture of various kinds: those that were set aside and saved as valuable, were fish that the net inclosed: therefore, those that were set aside and saved as valuable, were an indiscriminate mixture of various kinds.
(3) Testimony is a kind of evidence which is very likely to be false: the evidence on which most men believe that there are pyramids in Egypt is testimony: therefore, the evidence on which most men believe that there are pyramids in Egypt is very likely to be false. 434
(4) If Paley’s system is to be received, one who has no knowledge of a future state has no means of distinguishing virtue and vice: now one who has no means of distinguishing virtue and vice can commit no sin: therefore, if Paley’s system is to be received, one who has no knowledge of a future state can commit no sin.
(5) If Abraham were justified, it must have been either by faith or by works: now he was not justified by faith (according to James), nor by works (according to Paul): therefore, Abraham was not justified.
(6) For those who are bent on cultivating their minds by diligent study, the incitement of academical honours is unnecessary; and it is ineffectual, for the idle, and such as are indifferent to mental improvement: therefore, the incitement of academical honours is either unnecessary or ineffectual.
(7) He who is most hungry eats most; he who eats least is most hungry: therefore, he who eats least eats most.
(8) A monopoly of the sugar-refining business is beneficial to sugar-refiners: and of the corn-trade to corn-growers: and of the silk-manufacture to silk-weavers, &c., &c.; and thus each class of men are benefited by some restrictions. Now all these classes of men make up the whole community: therefore, a system of restrictions is beneficial to the community. [Whately, Logic.]

392. The following are a few examples in which the reader can try his skill in detecting fallacies, determining the peculiar form of syllogisms, and supplying the suppressed premisses of enthymemes:
(1) None but those who are contented with their lot in life can justly be considered happy. But the truly wise man will always make himself contented with his lot in life, and, therefore, he may justly be considered happy.
(2) All intelligible propositions must be either true or false. The two propositions “Caesar is living still,” and “Caesar is dead,” are both intelligible propositions; therefore, they are both true, or both false.
(3) Many things are more difficult than to do nothing. Nothing is more difficult to do than to walk on one’s head. Therefore, many things are more difficult than to walk on one’s head.
(4) None but Whigs vote for Mr B. All who vote for Mr B. are ten-pound householders. Therefore, none but Whigs are ten-pound householders. 435
(5) If the Mosaic account of the cosmogony is strictly correct, the sun was not created till the fourth day. And if the sun was not created till the fourth day, it could not have been the cause of the alternation of day and night for the first three days. But either the word “day” is used in Scripture in a different sense to that in which it is commonly accepted now, or else the sun must have been the cause of the alternation of day and night for the first three days. Hence it follows that either the Mosaic account of the cosmogony is not strictly correct, or else the word “day” is used in Scripture in a different sense to that in which it is commonly accepted now.
(6) Suffering is a title to an excellent inheritance; for God chastens every son whom he receives.
(7) It will certainly rain, for the sky looks very black. [Solly, Syllabus of Logic.]

393. Examine the following arguments; so far as they are valid, reduce them to syllogistic form; and where they are invalid, explain the nature of the fallacy involved:—
(1) If you argue on a subject which you do not understand, you will prove yourself a fool; for this is a mistake that fools always make.
(2) It is not the case that any metals are compounds, and it is incorrect to say that every metal is heavy; it may, therefore, be inferred that some elements are not heavy, and also that some heavy substances are not elements.
(3) No young man is wise; for only experience can give wisdom, and experience comes only with age. [K.]

394. Examine technically the following argument:—
Everyone is either well informed of the facts or already convinced on the subject; no one can be at the same time both already convinced on the subject and amenable to argument: hence it follows that only those who are well informed of the facts are amenable to argument. [J.]

395. Dr Johnson remarked that “a man who sold a penknife was not necessarily an ironmonger.” Against what logical fallacy was this remark directed? [C.]

396. Examine the following arguments, pointing out any fallacies that they contain: 436
(a) The more correct the logic, the more certainly will the conclusion be wrong if the premisses are false. Therefore, where the premisses are wholly uncertain the best logician is the least safe guide.
(b) The spread of education among the lower orders will make them unfit for their work: for it has always had that effect on those among them who happen to have acquired it in previous times.
(c) This pamphlet contains seditious doctrines. The spread of seditious doctrines may be dangerous to the State. Therefore, this pamphlet must be suppressed. [C.]

397. Examine the following arguments:—
(1) A telescope with the eye-piece at one side of the tube is probably a reflector; Lord Rosse’s telescope is a reflector; therefore, Lord Rosse’s telescope probably has the eye-piece at one side of the tube.
(2) Good workmen do not complain of their tools; my pupils do not complain of their tools; therefore, my pupils are probably good workmen.
(3) If, on the one hand, the heathen, through want of better knowledge, cannot help breaking the Ten Commandments, then they do not stand condemned; if, on the other hand, they are condemned, it is for doing that which they well knew was wicked, and which they were well able to refrain from doing; therefore, whatever happens to them, justice is satisfied. [K.]

398. Discuss the nature of the reasoning contained, or apparently intended, in the following sentences:—
It is impossible to prove that persecution is justifiable if you cannot prove that some non-effective measures are justifiable; for no persecution has ever been effective.
This deed may be genuine though it is not stamped, for some unstamped deeds are genuine. [C.]

399. State the following arguments in logical form, and examine their validity:—
(1) Poetry must be either true or false: if the latter, it is misleading; if the former, it is disguised history, and savours of imposture as trying to pass itself off for more than it is. Some philosophers have therefore wisely excluded poetry from the ideal commonwealth. 437
(2) If we never find skins except as the teguments of animals, we may safely conclude that animals cannot exist without skins. If colour cannot exist by itself, it follows that neither can anything that is coloured exist without colour. So if language without thought is unreal, thought without language must also be so.
(3) Had an armistice been beneficial to France and Germany, it would have been agreed upon by those powers; but such has not been the case; it is plain therefore that an armistice would not have been advantageous to either of the belligerents.
(4) If we are marked to die, we are enow
To do our country loss: and, if to live.
The fewer men, the greater share of honour. [O.]

400. Examine logically the following arguments:—
(a) If truthfulness is never found save with scrupulousness, and if truthfulness is incompatible with stupidity, it follows that stupidity and scrupulousness can never be associated.
(b) You say that there is no rule without an exception. I answer that, in that case, what you have just said must have an exception, and so prove that you have contradicted yourself.
(c) Knowledge gives power; consequently, since power is desirable, knowledge is desirable. [L.]

401. Examine the following arguments, stating them in syllogistic form, and pointing out fallacies, if any:—
(a) Some who are truly wise are not learned; but the virtuous alone are truly wise; the learned, therefore, are not always virtuous.
(b) If all the accused were innocent, some at least would have been acquitted; we may infer, then, that none were innocent, since none have been acquitted.
(c) Every statement of fact deserves belief; many statements, not unworthy of belief, are asserted in a manner which is anything but strong; we may infer, therefore, that some statements not strongly asserted are statements of fact.
(d) That many persons who commit errors are blameworthy is proved by numerous instances in which the commission of errors arises from gross carelessness. [M.]

402. Examine technically the following arguments:—
(1) Those who hold that the insane should not be punished ought in consistency to admit also that they should not be threatened; 438 for it is clearly unjust to punish any one without previously threatening him.
(2) If he pleads that he did not steal the goods, why, I ask, did he hide them, as no thief ever fails to do?
(3) Knavery and folly always go together; so, knowing him to be a fool, I distrusted him.
(4) How can you deny that the infliction of pain is justifiable if punishment is sometimes justifiable and yet always involves pain?
(5) If I deny that poverty and virtue are inconsistent, and you deny that they are inseparable, we can at least agree that some poor are virtuous. [V.]

403. Detect the fallacy in the following argument:—
“A vacuum is impossible, for if there is nothing between two bodies they must touch.” [N.]

404. Consider the following argument:—
Granted that A is B, to prove that B is A. B (like everything else) is either A or not A. If B is not A then by our first premiss we have the syllogism—A is B, B is not A, therefore, A is not A, which is absurd. Hence it follows that B is A. [Professor Jastrow, in the Journal of Education February, 1897.]

405. Examine the following argument:—
It is impossible to prove that society can continue to exist without competition unless you can also prove that the absence of competition would not lead to the deterioration of individuals; for a society whose members deteriorate cannot long continue to exist. [M.]

406. Express the following propositions in their simplest logical form; examine their mutual consistency or inconsistency, and the validity of the final conclusion:—
Some of Mr N’s published views are new, and some true; in fact, they are all one or the other; and, though it cannot be maintained in general that a view that is not new is on that account necessarily not true, yet it can be confidently asserted that every possible false view on this subject was propounded by some one or other before Mr N. wrote: from which it would appear that while it may or may not be that Mr N.’s views are all new, it is certain that they are all true. [J.]

439 407. Examine technically the following arguments:—

(a)

“’Tis only the present that pains,
And the present will pass.”

(b) All legislative restraint is either unjust or unnecessary; since, for the sake of a single man’s interests, to restrain all the rest of the community is unjust, and to restrain the man himself is unnecessary.
(c) Only Conservatives—and not all of them—are Protectionists; only Liberals—and not all of them—are Home Rulers; but both parties contain supporters of women’s franchise. Hence only Unionists—and not all of them—are Protectionists, while the supporters of women’s franchise contain both Unionists and Free-traders.
(d) No school-boy can be expected to understand Constitutional History, and none but school-boys can be expected to remember dates; so that no one can be expected both to remember dates and to understand Constitutional History.
(e) To be wealthy is not to be healthy; not to be healthy is to be miserable; therefore, to be wealthy is to be miserable.
(f) Whatever any man desires is desirable; every man desires his own happiness; therefore, the happiness of every man is desirable. [J.]

408. Examine the validity of the following arguments:—
(1) I knew he was a Bohemian, for he was a good musician, and Bohemians are always good musicians.
(2) Bullies are always cowards, but not always liars; liars, therefore, are not always cowards.
(3) If all the soldiers had been English, they would not all have run away; but some did run away; and we may, therefore, infer that some of them at least were not English.
(4) None but the good are really to be envied; all truly wise men are good; therefore, all truly wise men are to be envied.
(5) You cannot affirm that all his acts were virtuous, for you deny that they were all praiseworthy, and you allow that nothing that is not praiseworthy is virtuous.
(6) Since the end of poetry is pleasure, that cannot be unpoetical with which all are pleased.
(7) Most M is P, Most S is M, therefore, Some S is P. 440
(8) Old Parr, healthy as the wild animals, attained to the age of 152 years; all men might be as healthy as the wild animals; therefore, all men might attain to the age of 152 years.
(9) It is quite absurd to say “I would rather not exist than be unhappy,” for he who says “I will this, rather than that,” chooses something. Non-existence, however, is no something, but nothing, and it is impossible to choose rationally when the object to be chosen is nothing.
(10) Because the quality of having warm red blood belongs to all known birds, it must be part of their specific nature; but unknown birds have the same specific nature as known birds; therefore, the quality of having warm red blood must belong to the unknown as well as the known birds, i.e., be a universal and essential property of the species. [K.]