The chief results, not including the semi-definite meaning, may be summed as follows, All S is P, Some S is not P. No S is P, Contradictories:-One must be true, and the other false. Contraries:-Both cannot be true, but both may be false. Subcontraries:-Both may be true, but both cannot be false. If the universal is true, the particular is true; Subalternates:- If the particular is false, the universal is false. The same matter may be tabulated also thus, Particulars The others undetermined. The others undetermined. If I is false, E is true, ....O true, ..A false. Hence by the truth of universals, and by the falsity of particulars, all others are determined; otherwise only the contradictory." 6 The old Latin logicians rather needlessly warn us that opposition cannot be correctly said to exist unless the predicate [and the subject] of both propositions is truly the same. We violate this precaution, say they, when we do not predicate in the same 1. Manner; as, Hector is and is not a man; i. e., he is a dead man, but not a living one. 2. Respect; as, Zoilus is and is not black; i. e., he is black-haired, but redfaced. 3. Degree; as, Socrates is and is not long-haired; i. e., he is, compared with Scipio, but not, compared with Xenophon. 4. Time; as, Nestor is and is not an old man; i. e., he is not when a boy, but is at the siege of Troy. § 9. Praxis. Draw an immediate inference from each of the following propositions by added determinants (§ 5): 1. The wages of sin is death. Use as determinants,-inevitable, and just. 2. Novelty is pleasure. Use as a determinant, the greater the. 3. War is an evil. Use,-unprovoked, welcomed with ardor, which reaches to our hearth-stones. Infer from the following by complex conceptions (§ 5):4. The ignorant are ceremonious. Use the concept,—an age. 5. Heaven from all creatures hides the book of fate.-Pope. Use, wisdom and love. Combine each of the following pairs into one proposition (§ 5) :— 6. Honesty deserves reward. Every man whom we meet is a neighbor. 7. The year is dying in the night.—Tennyson. Infinitate each of the following propositions (§ 6): 8. All knowledge is useful. 9. The Chinese are industrious. 10. No reptiles have feathers. 11. It is wrong to put an innocent man to death. 12. There are studies much vaunted, yet of little utility. 13. Some men's hearts are not in the right place. 14. In jewels and gold, men cannot grow old. 15. No brutes are responsible. Convert each of the following, affixing the symbols (§ 7): 16. Life every man holds dear. 17. Two straight lines cannot enclose a space. 18. None are free who do not govern themselves. 19. With man many things are impossible. 20. Few know themselves. 21. 'Tis cruelty to load a falling man. 22. Fame is no plant that grows on mortal soil. 23. Whoso loveth instruction, loveth knowledge. 24. Each mistake is no proof of ignorance. 25. Fair promises are often not to be trusted. 26. There falls no shadow on his tomb. 27. Full many a gem of purest ray serene, The dark unfathomed caves of ocean bear.-Gray. From each of the following premises obtain, by immediate inferences, the annexed conclusion (§§ 6 and 7):— 28. All the righteous are happy; .. Whoever is unhappy is wicked. 29. No human virtues are perfect; .. All perfect virtues are superhuman. 30. Some possible cases are improbable; .. Some improbable cases are not impossible. 31. Some true patriots are not popular; .. The unpopular are not always unpatriotic. 32. Certainty is a kind of light; .. Darkness is doubt. If the following propositions are true, what opposites are also true, and what false? (§ 8): 33. By night an atheist half believes a God.-Young. 34. No one is always happy. 35. Some democracies are unstable. 36. Some great orators are not statesmen. If the following are false, what opposite propositions are also false, and what true? (§ 8): 37. All self-confident persons have strong will. 38. No honest men become bankrupt. 39. Some private vices are public benefits. 40. Some plants do not produce seed. III. INNOVATIONS. § 1. Since the revival in England of the study of Logic, which was brought about by the publication of Whately's treatise, there has been manifested much dissatisfaction with the Aristotelic doctrines as inherited from the scholastic or Latin logicians of the Middle Ages. This body of doctrine we have spoken of as the old, or Latin Logic, not meaning to intimate thereby that it is obsolete, or even likely to vanish away, but simply to distinguish it from recent doctrines. The dissatisfaction has arisen not so much from a supposed inaccuracy of the old doctrines as from their supposed inadequacy. Many important modifications and additions have been proposed by high authorities, such as Hamilton, De Morgan, Mansel, Boole, Thomson, Mill, Bain, Jevons, and others, but as yet few have been generally accepted, and the old Logic holds its ground. Hamilton has been the chief innovator, his views have been most widely discussed, and made the deepest impression; and, therefore, we will give our attention especially to them. § 2. Hamilton's doctrine of the semi-definite "Some" has already been stated. But it is very questionable whether it should be received into Logic at all, even as a mere exception. "Some," if not wholly and simply indefinite, probably always designates either a wholly definite judgment imperfectly expressed, or else a compound judgment whose two elements are cach wholly indefinite. If we say "Some members of this University are now studying Logic," this judgment in our minds would be wholly definite, a certain "Some," i. e., "All the members of the Philosophy Class are now studying Logic," without any thought whatever of other members of the University. Ini, § 8. It may be remarked that, if fully adopted, its consequence to the old doctrine of Opposition (ii, § 8), enlarged by the addition of four judgments, is something fearful. The student is referred to the tabulated statement in the Appendix to Hamilton's Logic, p. 535, where the whole scheme is elaborately worked out. Instead of thus replacing entirely the old doctrine of Opposition with the new one of "Incompossibility," it would seem simpler and sufficient, and hence better, to treat the cases of the semi-definite meaning as exceptions to the old rules. The judgment then is A, and the proposition should be reduced to that form, in conformity with the thought. Again, if we say "Some flowers are fragrant," meaning "some at most, not all," then this implies the counter-thought that "Some flowers are not fragrant." If this double thought be expressed in a grammatically simple sentence, for the logician postulates that it be expressed, then we have "Only some flowers are fragrant." This is an exponible compound proposition which analyzes into "Some flowers (I know not how many) are fragrant" (I), and "Some flowers (I know not how many) are not fragrant" (O). Each of these elements considered in itself, entirely apart from the other, is wholly indefinite; for the meaning of "I know not how many" must in that case be "perhaps all." The semi-definite character does not at all appear unless one judgment is recognized as limiting the other; and when this is the case the judgment is not simple, but compound. Now Logic, professing to be a thorough analysis of thought, must not stop short of its simple elements, must not recognize the compound as co-ordinate with the simple, and does not, cannot, undertake to formulate the compound modes of thought, which are legion, but evolving their elements formulates only these. Therefore the semi-definite judgment, being compound, must be denied a position among the elementary forms of thought, and if recognized at all must take its place among the abbreviated, imperfect modes of statement, subject at any moment to analysis and full discrete expression. § 3. The most important addition to the old Logic proposed by Hamilton is his doctrine of "The Thorough-going Quantification of the Predicate."" The old Logic teaches that negatives distribute the predicate, affirmatives do not (i, § 9). Hamilton teaches that in both affirmative and negative judgments the predicate may be either distributed or undistributed. Hence, to the four Aristotelic judgments of the old Logic he has superadded four others, commonly 2 See Hamilton's Logic, Appendix, p. 509 sq. As Bacon called his great work the Novum Organum, in allusion to the Aristotelic Organon, so Hamilton calls his treatment of these forms the "New Analytic," in allusion to Aristotle's "Analytics," and proposes thereby "to place the keystone in the Aristotelic arch." For an excellent statement of Hamilton's views, warmly approved by himself, see An Essay on the New Analytic of Logical Forms, by Thomas Spencer Baynes, an admiring pupil of Hamilton's. The Essay is the more interesting from having been a prize examination paper. |