REFERENCES Creighton, An Introductory Logic, Chs. XIV and XVII. Hibben, Logic, Deductive and Inductive, Pt. II, Chs. III, XIII, and XIV. Aikins, The Principles of Logic, Chs. XXX-XXXII. Minto, Logic, Inductive and Deductive, Bk. II, Chs. IX and X. Mill, System of Logic, Bk. III, Chs. III, XVII, XVIII, and XX. Bosanquet, Logic, Vol. II, Ch. III. Sigwart, Logic, Vol. II, Pt. III, Ch. V, §§ 101 and 102. REVIEW QUESTIONS 1. What kind of knowledge does perfect induction yield? 2. When may perfect induction be used in scientific inquiry? 3. How does logical enumeration differ from arithmetical enumeration? 4. What is the nature of imperfect enumerative induction? 5. In what ways is imperfect enumerative induction useful? 6. What kind of knowledge does imperfect induction give? 7. Wherein lies the skill in imperfect induction? 8. What is the inductive "leap"? 9. What do you understand by the postulate of the uniformity of nature, and how is it to be interpreted? 10. How is induction related to mathematical processes? 11. What do you understand by the Theory of Probability? 12. How do we express the probability of countable cases? 13. What is statistics? 14. When are statistics most useful? With what kind of phenomena? 15. Why are they helpful to science? 16. What is analogical reasoning? 17. Why is analogy still useful? 18. Why do we so frequently err in using analogy? 19. In what three ways may analogical reasoning be safeguarded? EXERCISES ON CHAPTER XVI 1. Name two instances of generalizations due to perfect enumerative induction. 2. Cite five cases (drawn from your own recent experience if possible) which should be generalized by imperfect induction. 3. Put each of the cases cited in answer to Exercise 2 in the form of an imperfect inductive syllogism. 4. Estimate and express by a fraction the probability of drawing an ace of diamonds from a deck of playing cards. 5. Estimate and express by a fraction the probability of making a sum of four spots by the throw of two dice from a box. 6. Estimate and express by a fraction the probability of holding five trumps in a hand of whist. 7. Assuming that you hold five trumps in whist, estimate the probability of your partner's having four trumps, and express fractionally. 8. Assuming that a friend takes a five-o'clock train four evenings out of the week, and that you have forgotten what those evenings are, what is the probability that you will meet him if you chance to take that train any particular evening? 9. Make statistics showing the blondes and brunettes in your class. 10. Make statistics showing those in your class that you would estimate to be over and under and just five feet five inches tall. 11. Make statistics showing the ages of any five members (named as Miss A, Miss B, Mr. C, etc.) of your class and find the average age. 12. Name five cases where you think that statistics could be used to advantage. 13. Cite two cases where you would employ analogical reasoning, and work out or explain the analogy. 14. In the two cases above cited (Exercise 13) indicate the degree of likelihood, try to find other similarities which support the one upon which the reasoning was based, and show whether the likeness is profound or superficial and why. CHAPTER XVII.-METHODS OF DISCOVER ING CAUSAL RELATION 103. EVENTS AND EXPERIENCE.-What we ordinarily call by the general name of events or happenings are really interdependent factors in a net-work of experience. The untutored mind tends to see facts or events in isolation. The moon rises. The dew falls. The winds blow. The water flows in streams, moves in ocean currents, and falls in rains. Yet, wanting some sort of explanation of these natural events, the savage attributes them to the caprice of a will indefinitely like that known in himself. In other words, he relies upon a simple analogical interpretation of these changes in nature. The cultured and scientific mind is past the stage where these simple attempts at accounting for natural occurrences can satisfy. One may believe that such occurrences are indirectly attributable to a mind something like his own, only vastly more capable, just as the events themselves are infinitely more stupendous than his own puny undertakings. But he knows, as the result of numerous recorded experiences, that this presumed intelligence to which all nature is due works only indirectly, and that he must look to the connections between the events themselves for scientific explanation. He knows that the cause of a happening in the natural world is always some other happening in the same natural world, and that therefore scientific explanation must limit itself to fathoming these causal connections, leaving the question of an Ultimate Cause to be solved by religious faith or philosophy. The scientist also knows, from past experience in dealing with natural phenomena, that each event has as its immediate forerunner an almost infinite number of other events; hence, that it is his business to disentangle from this intricate complex of events that one which is the sole and indispensable condition of the happening of the event under investigation. The group of circumstances that precede an occurrence and contain among them the factor without which it would not happen is called the antecedent of the phenomenon. That sole factor in the antecedent which is indispensable to the occurrence of the event under investigation is called the cause of the phenomenon. The group of circumstances that follows an event and contains the factor which invariably follows upon the occurrence of the event under investigation is called the consequent of the phenomenon. That sole factor in the consequent which invariably follows the occurrence of the event under investigation is called the effect of the phenomenon. The term event means any occurrence or happening. It is almost synonymous with phenomenon (defined on page 202). The antecedent always contains the cause; the consequent the effect. Every cause is in its turn the effect of some other cause, and every effect is likewise the cause of some other effect; in other words, the causal series is infinite until our thinking brings us to the First Cause, or the Self-caused (causa sui). But while this is log ically and metaphysically true, practical science deals always with what we may call causal couples, i. e., a causal pair limited to a cause and its effect. Hence, when science attempts to disclose the nature of a thing or to explain, it really does nothing more than to assign the indispensable condition of a thing or its inevitable result (its material cause or effect). 104. GENERAL NATURE OF THE MILL METHODS.Now the methods of determining causal connection from the stand-point of scientific explanation, more popularly known as Mill's Methods or Canons, are really methodical procedures for analyzing the antecedent to find the causal factor or the consequent to find the effect. Their place in inductive inquiry belongs to them because from a certain number of instances examined we conclude by imperfect induction to all like cases. They prove causal connection not on a rational but on an empirical basis. In other words, they do not assign a reason why a given cause produces a given effect based upon the essential nature of the cause and effect, but merely show that a given cause has uniformly produced a given effect, and assume by imperfect induction, utilizing the postulate of the uniformity of nature, that it will continue to produce just that effect and no other. Hence Mill's Methods are methods rather of scientific analysis than of philosophical explanation. But since they involve method, rely upon induction, and make a claim to give us practical truth they appropriately find a place in logic. The mind having once discovered generalizations respecting cases examined referring to common qualities or functions of the |