(1) Matter, organic, inorganic.

(2) Undulations, polarized, non-polarized. (3) Figure, rectilinear, curvilinear.

2. Is it wrong to assert that animal cannot both be vertebrate and invertebrate, seeing that some animals are vertebrate and some are not? 3. Select from the following such terms as are negatives of the others, and such as are opposites :— Light, plenum, gain, heat, decrease, loss, darkness, cold, increase, vacuum.

4. How is Aristotle's dictum applicable to the following arguments?

(1) Silver is a good conductor of electricity; for such are all the metals.

(2) Comets cannot be without weight; for they are composed of matter, which is not without weight.

LESSON XV.-Syllogism: the Rules.

1. Distinguish mediate and immediate inference. 2. Define syllogism, and state with what it is synony

mous.

3. What are the six principal and two subordinate rules of the syllogism?

4. In the following syllogisms point out in succession

the conclusion, the middle term, the major term, the minor term, the major premise and the minor premise, observing this precise order.

(1) All men are fallible;

All kings are men ;

Therefore all kings are fallible.

(2) Platinum is a metal;

All metals combine with oxygen ;
Therefore Platinum combines with oxygen.

(3) Hottentots are capable of education; for Hottentots are men, and all men are capable of education.

5. Explain carefully what is meant by non-distribution of the middle term.

LESSON XVI.-The Moods and Figures of the
Syllogism.

1. Name the rules of the syllogism which are broken by any of the following moods, no regard being paid to figure :—

AIA, EEI, IEA, IOI, IIA, AEI.

2. Write out all the 64 moods of the syllogism and strike out the 53 invalid ones,

3. Show in what figures the following premises give a valid conclusion :-AA, AI, E A, OA.

4. In what figures are IEO and EIO valid?

5. To what moods do the following valid syllogisms belong? Arrange them in correct logical order.

(1) Some Y's are Z's.

No X's are Y's.

Some Z's are not X's.

(2) All Z's are Y's.

(3) No fish suckles its young; The whale suckles its young; Therefore the whale is no fish.

No Y's are X's.

No Z's are X's.

6. Deduce conclusions from the following premises : and state to what mood the syllogism belongs.

(1) Some amphibious animals are mammalian. All mammalian animals are vertebrate.

(2) All planets are heavenly bodies.

No planets are self-luminous.

(3) Mammalian animals are quadrupeds. No birds are quadrupeds.

(4) Ruminant animals are not predacious. The lion is predacious.

7. Invent examples to show that false premises may give true conclusions.

8. Supply premises to the following conclusions:(1) Some logicians are not good reasoners. (2) The rings of Saturn are material bodies. (3) Party government exists in every democracy. (4) All fixed stars obey the law of gravitation.

LESSON XVII.-The Syllogism; Reduction.

1. State and explain the mnemonic lines Barbara, Celarent, &c.

2. Construct syllogisms in each of the following moods, taking X, Y, Z, for the major, middle, and minor terms respectively, and show how to reduce them to the first figure:—

Cesare, Festino, Darapti, Datisi, Ferison, Camenes,
Fesapo.

3. What is the use of Reduction?

4. Prove that the following premises cannot give a universal conclusion-EI, IA, O A, IE.

5. Prove that the third figure must have an affirmative minor premise, and a particular conclusion.

6. Reduce the moods Cesare and Camenes by the Indirect method, or Reductio ad Impossibile.

LESSON XVIII.-Irregular and Compound Syllogisms. 1. Describe the meaning of each of the terms-Enthymeme, Prosyllogism, Episyllogism, Epicheirema, Sorites.

2. Make an example of a syllogism in which there are two prosyllogisms.

3. Construct a sorites of four premises and resolve it into distinct syllogisms.

4. What are the rules to which a sorites must conform?

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?