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(3) Hottentots are capable of education ; for Hotten

tots are men, and all men are capable of edu

cation. 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, EA, O A. 4. In what figures are I EO 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. (2) All Z's are Y's. No X's are Y's.

No Y's are X's.
Some Z's are not X's.

No Z's are X's. (3) No fish suckles its young ;

The whale suckles its young ;

Therefore the whale is no fish. 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 tigure :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-En

thymeme, Prosyllogism, Episyllogism, Epichei

rema, 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 gun

powder; 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 his

tory; 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 other

wise they would not obey the law of gravitation. 13. Lithium is an element; for it is an alkali-pro

ducing 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 pur

suits 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?

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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 argu-

ments, and reduce them to the categorical forın;

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; igno-

ratio elenchi; argumentum ad hominem; argu-
mentum ad populum ; petitio principii; circulus
in probando; non sequitur; post hoc ergo
propter hoc.

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