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.]