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5. The reader is requested to analyse the following arguments, to detect those which are false, and to ascertain the rules of the syllogism which they break; if the argument appears valid he is to ascertain the figure and mood to which it belongs, to state it in correct logical form, and then if it be in an imperfect figure to prove it by reduction to the first figure. The first six of the examples should be arranged both in the extensive and intensive orders.

1. None but mortals are men.

Monarchs are men.

Therefore monarchs are mortals.

2. Personal deformity is an affliction of nature. Disgrace is not an affliction of nature.

Therefore personal deformity is not disgrace. 3. Some statesmen are also authors; for such are Mr Gladstone, Lord Derby, Lord Russell, and Sir G. C. Lewis.

4. This explosion must have been occasioned by gunpowder; for nothing else would have possessed sufficient force.

5. Every man should be moderate; for excess will cause disease.

6. Blessed are the merciful; for they shall obtain mercy.

7. As almost all the organs of the body have a known use, the spleen must have some use. 8. Cogito, ergo sum. (I think, therefore I exist.) 9. Some speculative men are unworthy of trust; for they are unwise, and no unwise man can be trusted.

10. No idle person can be a successful writer of history; therefore Hume, Macaulay, Hallam and Grote must have been industrious.

11. Who spareth the rod, hateth his child; the parent who loveth his child therefore spareth not the

rod.

12. Comets must consist of heavy matter; for otherwise they would not obey the law of gravitation. 13. Lithium is an element; for it is an alkali-producing substance, which is a metal, which is an element.

14. Rational beings are accountable for their actions; brutes not being rational, are therefore exempt from responsibility.

15. A singular proposition is a universal one; for it applies to the whole of its subject.

16. Whatever tends to withdraw the mind from pursuits of a low nature deserves to be promoted; classical learning does this, since it gives us a taste for intellectual enjoyments; therefore it deserves to be promoted.

17. Bacon was a great lawyer and statesman; and as he was also a philosopher, we may infer that any philosopher may be a great lawyer and statesman. 18. Immoral companions should be avoided; but some immoral companions are intelligent persons, so that some intelligent persons should be avoided. 19. Mathematical study undoubtedly improves the reasoning powers; but, as the study of logic is not mathematical study, we may infer that it does not improve the reasoning powers.

20. Every candid man acknowledges merit in a rival; every learned man does not do so; therefore every learned man is not candid.

LESSON XIX.-Conditional Arguments.

1. What are the kinds of conditional propositions, and by what signs can you recognise them?

2. What are the rules of the hypothetical syllogism? 3. To what categorical fallacies do breaches of these rules correspond?

4. Select from the following such as are valid arguments, and reduce them to the categorical form; explain the fallacious reasoning in the others (1) Rain has fallen if the ground is wet; but the ground is not wet; therefore rain has not fallen. (2) If rain has fallen, the ground is wet; but rain has not fallen; therefore the ground is not wet. (3) The ground is wet, if rain has fallen; the ground is wet; therefore rain has fallen.

(4) If the ground is wet, rain has fallen; but rain has fallen; therefore the ground is wet.

N. B. In these as in other logical examples the student must argue only from the premises, and not from any other knowledge of the subject-matter.

5. Show that the canons of syllogism (p. 121) may be stated indifferently in the hypothetical or categorical form.

6. State the following in the form of a Disjunctive or Dilemmatic argument, and name the kind to which it belongs.

If pain is severe it will be brief; and if it last long it will be slight; therefore it is to be patiently borne.

LESSONS XX. and XXI-Fallacies.

1. Classify fallacies.

2. Explain the following expressions:

A dicto secundum quid ad dictum simpliciter; ignoratio elenchi; argumentum ad hominem; argumentum ad populum; petitio principii; circulus in probando; non sequitur; post hoc ergo propter hoc.

3. What is arguing in a circle; and what is a question-begging epithet?

4. What differences of meaning may be produced in the following sentence by varying the accent? "Newton's discovery of gravitation is not generally believed to have been at all anticipated by several philosophers in England and Holland." 5. Point out the misinterpretations to which the following sentences might be liable.

(1) He went to London and then to Brighton by
the express train.

(2) Did you make a long speech at the meeting?
(3) How much is five times seven and nine?

MISCELLANEOUS EXAMPLES.

LESSONS IX. to XXI.

(Continued from p. 313.)

The following examples consist partly of true and partly of false arguments. The reader is requested to treat them as follows:

1. If the example is not in a simple and complete logical form, to complete it in the form which appears most appropriate.

2. To ascertain whether it is a valid or fallacious argument.

3. To assign the exact name of the argument or fallacy as the case may be.

4. If a categorical syllogism, to reduce it to the first figure.

5. If a hypothetical syllogism, to state it in the categorical form.

21. Elementary substances alone are metals. Iron is

a metal; therefore it is an elementary substance.

22. No Athenians could have been Helots; for all the Helots were slaves, and all Athenians were free

men.

23. Aristotle must have been a man of extraordinary industry; for only such a man could have produced his works.

24. Nothing is better than wisdom; dry bread is better than nothing; therefore dry bread is better than wisdom.

25. Pitt was not a great and useful minister; for though he would have been so had he carried

out Adam Smith's doctrines of Free Trade, he did not carry out those doctrines.

26. Only the virtuous are truly noble; some who are called noble are not virtuous; therefore some who are called noble are not truly noble.

27. Ireland is idle and therefore starves; she starves, and therefore rebels.

28. No designing person ought to be trusted; engravers are by profession designers; therefore they ought not to be trusted.

29. Logic as it was cultivated by the schoolmen

proved a fruitless study; therefore Logic as it is cultivated at the present day must be a fruitless study likewise.

30. Is a stone a body? Yes. Then is not an animal a body? Yes. Are you an animal? I think so. Ergo, you are a stone, being a body.—Lucian. 31. If ye were Abraham's children, ye would do the works of Abraham.-John viii. 39.

32. He that is of God heareth God's words: ye therefore hear them not, because ye are not of God. -John viii. 47.

33. Mahomet was a wise lawgiver; for he studied the character of his people.

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