term, there would be no distribution of the middle term. Of course it cannot be distributed as the predicate of an affirmative proposition (in the first premise), so it must be distributed as the subject of the second premise. Hence this premise must be universal (the I and O do not distribute their subjects). What is said of B holds good of C and any other middle terms that are used in the course of the argument. Likewise no premise but the last may be negative. For if any other were negative, it would make the con D C B A clusion negative; hence its major term would be distributed. But such distribution could be provided for only if the last premise (where the major term occurs in the sorites) were negative. In this arrangement of the sorites the subject of the first premise is the subject of the conclusion, and the predicate of the last premise is the predicate of the conclusion. It is commonly called the Aristotelian sorites. It can be graphically represented by a number of concentric circles, the smallest representing the denotation of A, the next that of B, the next that of C, etc. The following is a concrete example of the sorites: ARISTOTELIAN SORITES All whales are mammals; All mammals are warm-blooded; All warm-blooded animals are vertebrates; Therefore all whales have a spinal-cord. There is another form of the sorites called the Goclenian,' in which the subject of the last premise and the predicate of the first are united in the conclusion. Schematically represented, it is as follows: It will be remarked that the suppressed conclusions form the minor premises of the following syllogism in the Aristotelian sorites, whereas in the Goclenian they form the major premise. The rule respecting the character of the premises is the reverse of that given for the Aristotelian form. In the Goclenian sorites only the first premise may be 1 After Rudolf Goclenius (1547–1628), who invented it. negative and only the last particular. If the second or any other than the first were negative we should have a negative conclusion; hence a distributed major term. But if the second (for instance) were negative the first would have to be affirmative (Rule of the Syllogism 1, II); hence the major term would not be distributed in it (because in the predicate position); hence there would be illicit major. Were any but the last premise of the Goclenian sorites particular we should have undistributed middle. For the middle term would be the subject in one premise of a particular proposition, and hence undistributed there; and the predicate in the other premise of an A proposition (Rule of the Syllogism 2, II prevents two particulars, and the first premise is the only one that may be negative; hence we are limited to A), and hence undistributed there. The following is a concrete example of the Goclenian sorites: GOCLENIAN SORITES All vertebrates have a spinal cord; All whales are mammals; Therefore all whales have a spinal cord. REFERENCES Creighton, An Introductory Logic, Ch. X. Jevons-Hill, Elements of Logic, Ch. III, § V. Welton, Manual of Logic, Vol. I, Bk. IV, Ch. VI. Bradley, The Principles of Logic, pp. 348-360. Hibben, Logic, Deductive and Inductive, Pt. I, Ch. XVIII. REVIEW QUESTIONS 1. Define enthymeme and give its derivation. 2. Which premise is most frequently suppressed, why, and what is such an enthymeme called? 3. What is an enthymeme of the second order? of the third order? 4. What is a prosyllogism? an episyllogism? 5. Define epicheirema. 6. Define sorites; Aristotelian sorites; Goclenian sorites. 7. What rule governs the Aristotelian sorites? Be prepared to demonstrate both parts of this rule. 8. What rule governs the Goclenian sorites? Be prepared to demonstrate both parts of this rule. 9. What terms form the subject and predicate of the conclusion in each kind of sorites. 10. Which premise does the suppressed conclusion make in each form of sorites? EXERCISES ON CHAPTER XIII 1. Construct an enthymeme of each of the three orders. 2. Make a prosyllogism and an episyllogism. 3. Make an epicheirema. 4. Make an Aristotelian sorites and then rearrange it in the Goclenian form. CHAPTER XIV.-DEDUCTIVE FALLACIES 85. CLASSIFICATION OF THE DEDUCTIVE FALLACIES. -Fallacy is the generic term applied to errors in the process of reasoning, whether inductive or deductive, and especially in syllogistic reasoning. While engaged upon the deductive syllogism we noticed certain tendencies toward formal errors in the construction of arguments. We shall now name all the more common errors incidental to deduction, and shall describe more particularly those errors that lie not in the form but in the subject-matter of deductive reasoning. No classification of such errors can be perfectly satisfactory or scientific, because many of the types are extremely subtle and are easily confounded. Again, many fallacious arguments are intricate and complex almost beyond the power of analysis, and really involve several fallacies. Yet some sort of classification, even though it be only tentative, will aid us in comprehending this difficult and important chapter in logic. The subject of fallacies is important because they are so insidious and common. Particularly where wordy debates take the place of modest and careful statements of the reasons for and against a position, we find fallacies lurking. And since proneness to talk much and say little is a universal human failing, we may readily see how many are the opportunities for fallacy. It is to make the student feel the danger and keep his attention |