34. What is a Syllogism? Find, without reference to the mnemonic verses, in what different ways it is possible to prove syllogistically the conclusion _No S is P_; and show the equivalence between these different ways. [S]
35. From what points of view can the syllogism be regarded
(1) as being, (2) as not being, a _pet.i.tio principii_? [S]
36. What are the figures of syllogism? For what kind of arguments are they severally adapted? [S]
37. What is meant by Mood and Figure? How can the validity of a Mood be tested? Should there be four Figures or three? [S]
38. Construct syllogisms in Camenes, Datisi and Baroco, and reduce them to the corresponding moods of the first figure.
39. Explain the meaning of "ostensive" and "indirect" Reduction. Show that any Mood of the second Figure may be reduced in either way.
40. Show that A cannot be proved except in the First Figure. Express the following reasoning in as many syllogistic figures as you can: Some theorists cannot be trusted, for they are unwise. [S]
41. Discuss the possibility of reducing the argument _a fortiori_ to the syllogistic form. [S]
42. Can a false conclusion be reached through true premises, or a true conclusion through false premises? Give reasons for your answer. [S]
43. Can we under any circ.u.mstances infer a relation between X and Z from the premises--
Some Y"s are X"s Some Y"s are Z"s? [S]
44. Take an apparent syllogism subject to the fallacy of negative premises, and inquire whether you can correct the reasoning by converting one or both of the premises into the affirmative form. [S]
45. Enumerate the faults to which a syllogism is liable, giving instances of each. [S]
46. State any Enthymeme, and expand it into (1) a Syllogism, (2) an Epicheirema, (3) a Sorites; and give in each case the technical name of the Mood or Order that results.
47. State any Disjunctive Syllogism, and change it (1) into a Hypothetical, (2) into a Categorical; and discuss the loss or gain, in cogency or significance involved in this process.
48. Can the Syllogism be treated as merely a consequence of the "Laws of Thought"? If not, why not; and what else does it imply?
49. Prove that with three given propositions (of the forms A., E., I., O.) it is never possible to construct more than one valid syllogism. [C]
50. Distinguish between a Constructive and a Destructive Hypothetical Syllogism; and show how one may be reduced to the other. [C]
IV. INDUCTION, ETC.
51. What const.i.tutes a Valid Induction? Distinguish it from a legitimate hypothesis. [S]
52. Is it possible to form true universal propositions about facts if we have not actually observed all the individuals designated by the subject of the proposition? If so, how? [S]
53. "Perfect induction is demonstrative and syllogistic; imperfect induction is neither." Explain the difference between perfect and imperfect induction, and examine the truth of this a.s.sertion. [S]
54. Why is it that one should not regard night as the cause, nor even as a universal condition of day? Explain "cause" and "condition." [S]
55. What do you understand by an experiment? Can you say how many experiments are required to establish (1) a fact, (2) a law of nature?
56. How would you define _antecedent_, _cause_, _effect_, _consequent_?
[S]
57. England is the richest country in the world, and has a gold currency. Russia and India, in proportion to population, are poor countries and have little or no gold currency. How far are such kind of facts logically sufficient to prove that a gold currency is the cause of a nation"s wealth? [S]
58. A man having been shot through the heart immediately falls dead.
Investigate the logical value of such a fact as proving that all men shot through the heart will fall dead. [S]
59. Explain the process of induction called the Method of Difference, and give some new instances of its application. How is it related to the Method of Concomitant Variations? What is the Major Premise implied in all these methods? [S]
59A. Examine the position, that the Canons of Experiment are useless, because the work of preparing the experiments must have been done before the canons can be applied.
60. Explain the logical cogency of experiments in the search for physical causes. [S]
61. If the effects of A B C D are fully expressed by a b c d, and those of B C D by b c d, what inductive inference can be drawn and on what principle? State the canon according to which it is drawn. [S]
62. Compare the advantage of observation and experiment as means of gaining data for Reasoning. [S]
63. Compare the cogency of different Inductive Methods, showing the kind of evidence each requires, and the principle on which it is based. [S]
64. Compare the Canons of Agreement and Difference (1) as to the difficulty of finding or preparing actual Instances for them, and (2) as to their conclusiveness.
65. Describe what is meant by residual phenomena, and estimate their value in inductive science. [S]
66. What is the argument from a.n.a.logy? How does it differ from (a) Induction, (b) metaphorical argument? [S]
67. What are the various senses in which the word a.n.a.logy has been used?
Distinguish, giving instances, between good and bad a.n.a.logies. [S]
68. How do you distinguish between what Mill calls the Geometrical, Physical, and Historical Methods?
68A. The Comparative Method is appealed to where direct evidence is wanting. Explain this.
69. What is meant by a doctrine being unverifiable? If a conclusion reached by deduction does not agree with the facts, where must we look for error?
70. There are certain cases in which failure of verification is fatal to a theory, and other cases in which it is of comparatively little cogency. How would you distinguish between these cla.s.ses of cases? [S]
71. Taking the "evolution," or any other proposed hypothesis, how should one proceed (a) to show whether it satisfies the conditions of a legitimate hypothesis sufficiently to ent.i.tle it to investigation, and (b) to test it with a view to its acceptance or rejection as a truth of science? [S]
72. What do you mean by saying that "a phenomenon has been satisfactorily explained"?
73. Explain and ill.u.s.trate the Historical Method of Sociological inquiry. [S]
74. What is the relation of the theory of Probability to Logic? [S]
75. Explain and discuss the doctrine that Induction is based upon the Theory of Probability. [S]
75A. What are the logical grounds of the Law of Error?