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LESSON XII.-The Predicables, etc.
1. Define each of the five predicables.
2. In what sense may we say that the genus is part of the species, and in what sense that the species is part of the genus?
3. Select from the terms in the 6th Question of Lesson V., p. 299, such as are genera, species, highest genera, or lowest species of other terms. 4. Explain the expressions sui generis, homogeneous, heterogeneous, summum genus, infima species, tree of Porphyry.
5. Name a property and accident of each of the follow-
6. What are the rules of correct logical division.
(2) Triangle. Equiangular
(3) Reasoning. Induction (Imperfect)
8. Divide any of the following classes :-Governments, Sciences, Logical terms, Propositions.
9. Of what does a logical definition consist?
IO. What are the rules of correct definition?
(3) Illative conversion is that in which the truth of the converse can be inferred from that of the convertend.
(4) Mineral substances are those which have not been produced by the powers of vegetable or animal life.
(5) An equilateral triangle is a triangle whose sides and angles are respectively equal.
(6) An acute-angled triangle is one which has an acute angle.
LESSON XIII.-Pascal and Descartes on Method. (1) What is the use of nominal definitions?
(2) How must we employ definitions in order to avoid confusion?
(3) How far can we be said to be free to use any name for any object?
(4) What according to Pascal is the true method of avoiding error?
(5) How do we learn the meanings of words which cannot be defined?
(6) Give instances of words which can be clearly defined and of others which cannot.
(7) State the five rules of method given in the Port Royal Logic.
(8) Explain Descartes' rules for the attainment of truth.
LESSON XIV.-Laws of Thought.
1. State the three Fundamental Laws of Thought, and apply them to the following notions:
(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
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 ;
(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
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, 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. (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.
(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.
(3) Mammalian animals 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:-
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,
3. What is the use of Reduction?
4. Prove that the following premises cannot give a universal conclusion-EI, IA, OA, 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?