rupeds, and bipeds." Bipeds and bimana overlap in man. Leibnitz calls this last fault "communicant species." So, "Imaginative writers are poets, dramatists, and writers of tales." Again, "Sciences are deductive and inductive." These species are communicant, since the latter makes large use of deduction. There is no science non-deductive. 3d. Divisio ne faciat saltum. Each species must emerge directly from its own proximate genus. Thought must not overlook and overleap its immediate parts and spring from the divisum to remote species. This the theory requires; but practically, for the sake of brevity, such a saltus is allowed, thought passing through intermediate steps to guard against error. Thus we may say that "Mathematics treats of infinitesimals, as well as of magnitudes of assignable quantity." This last member equals "noninfinitesimals." The genus" mathematical subjects" is far from being proximate to these species." § 7. Praxis. Are the following sixteen examples Partitions or Divisions, or neither? If Divisions, are they correct? If not, point out the defects. If correct, reduce to dichotomous statement. 1. Propositions are affirmative, hypothetical, and negative. 2. Thought is by conception, or by judgment, or by reasoning. 3. The mental faculties are sensation, perception, imagination, memory, and judgment. 4. Is the year or are the seasons divided into spring, summer, autumn, and winter? 5. A flower consists of calyx, corolla, stamens, and pistil; and the pistil consists of ovary, style, and stigma. 6. Literature consists of writings historical, religious, poetical, classical, and current. 7. Matter is solid, liquid, and aeriform. What is the principle? 8. Languages are Aryan, Semitic, and Turanian. 9. Rectilineal figures are triangles, rectangles, parallelograms, and figures of more than four sides. 2 See Hamilton's Logic, Lect. xxv. His doctrine is drawn mostly from Esser's Logic, SS 134-137. See also Thomson's Outline, § 55; and Drobisch's Logic, § 119. Division was a favorite method with Plato for the demonstration of Definitions, which Aristotle censures (Anal. Post. bk. ii, ch. v), and teaches that its chief use is to test definitions when obtained. Among the later Peripatetics the method was more esteemed. Modern logicians have drawn chiefly from Boethius's work De Divisione. Cf. Cic. Top. ch. vi, and Quintil. v, 10. See also Kant's Logic, § 113; and Trend, Elem. § 58. 10. The Federal domain consists of states and territories; the states, of Northern, Southern, etc.; and each state is divided into counties. 11. The elements of a truc civilization are, a wise and just polity, a general intelligence, and an aesthetic culture. 12. Job's family contained sons and daughters. Job's children were sons and daughters. The sons of Zebedee were James and John. 13. The fine arts are drawing, painting, sculpture, architecture, poetry, and photography. 14. Wealth naturally divides itself into three portions-1st. That which is reserved for immediate consumption, and of which the characteristic is that it affords no revenue or profit; 2d. The fixed capital, which affords profit without circulating or changing masters; 3d. The circulating capital, which affords a profit only by circulating.-A. Smith. 15. Profits are divided into interest, insurance, and wages of superintendence.-Mill. 16. The origin of colonies is to be traced either to the necessity for frontier garrisons, as among the Romans, or to the poverty or discontent of the inhabitants of the mother-country, as among the Greeks. 17. Divide and subdivide Triangle so as to include the scalene, the right-angled, the equiangular, the obtuse-angled, and the isosceles. 18. Make several divisions of Citizens, stating the principle in each, into these given species: Laity, aliens, naturalized, peers, clergy, baronets, native, commons. 19. Divide Man on the principle of age, sex, family relations, color, stature, riches, rank, education, occupation, and disposition. 20. Are Books or is A Library divided into folios, quartos, octavos, and duodecimos? 21. Is the distinction of The Ten Virgins into five wise and five foolish a logical division or a partition? 22. Divide and subdivide the Officers of the United States Government with reference to their official functions. 23. Divide and subdivide War on any designated principle. 24. Divide and subdivide Pleasures on the ground of their effect on the mind and character. 25. Give the divisions and subdivisions of Topic iv, on Relation. VII. COMPLETE SYSTEM. § 1. In concluding this general division of Logic treating of the Concept, it is needful to gather up into one some of the results obtained, and this will give occasion to remark a few additional points. The notion of a series of related concepts has been anticipated, especially under the last topic. We proceed to examine the form of such a series when it is evolved into a complete system. As preliminary, and at the risk of some repetition, we will present and remark upon the following scheme of the two quantities: The most obvious point here illustrated is the law of thought that as intension increases, extension diminishes, and vice versa; that the maximum of either one is the minimum of the other; that these two quantities of thought are in inverse ratio. In ascending the series we think out marks and think in things in the same act. For each mark thrown out, a concept is brought in. Now this act, on the intensive side, this thinking out marks, is abstraction; for in it we draw away a complement of marks, and thus abstract these from at least one other which passes out of consciousness. Thus, we first abstract existing, living, sentient, from rational; then existing, living, from sentient; then existing from living. On the side of extension there is, for each abstraction, a generalization. In thinking out rational, we think in brutes, i. e., the marks existing, living, sentient, are generalized as belonging to brutes in common with men; and these two classes of things are united in the more general or generic class which we term animal. Hence, generalization is also generification. It follows that abstraction and generalization are what might be called directly parallel correlatives; directly parallel, as moving in the same direction in the different quantities. In descending the series, we think in marks and think out things in the same act. This act, on the intensive side, is determination, because the bringing in a mark, while it narrows down and fixes specifically or definitely the limit of a smaller class of things, also attains a fuller, deeper knowledge of them. Determination, which in the scheme descends, is the inverse correlative of abstraction, which ascends. On the side of extension, there is for each determination a specialization. In thinking in sentient, into existing, living, we think out plants, i. c., the notion organism is specialized into animal by excluding vegetation, and we have established a subordinate, special, or specific class, animal. Hence specialization is also specification. Specialization, which descends, is the inverse correlative of generalization, which ascends. Finally, determination and specialization may also be called directly parallel, or, simply, parallel correlatives. It should also be observed that on the one side abstraction is analysis, and determination synthesis; while, on the other side, the order is reversed, specialization is analysis, and generalization is synthesis. Hence the movement that is analysis in one quantity of thought, is synthesis in the other. The neglect of this distinction by logical. authors has led to much confusion in the use of these terms. § 2. The isagogue of Porphyry to the Categories of Aristotle, written in the third century, was designed as a detailed explanation of the relations of genera and species. From its doctrine subsequent logicians constructed a scheme which, because of the form it presented, was called by the Latins the tree of Porphyry (arbor Porpyriana), and by the Greeks the ladder (λipa).' It exhibits a hierarchy of concepts representing a complete system. The following scheme presents the device in a modified form, with the same matter already used: 1 For a delineation of it, as given by Thomas Aquinas, see Mansel's Aldrich, p. 32. The isagogue will be found appended to Owen's translation of the Organon of Aristotle (Bohn's ed.); and also prefixed to St. Hilaire's Logique D'Aristote, tradulte (Paris, 1844). The doctrine of the isagogue is drawn largely from the writings, and sometimes is expressed in almost the very words, of Plato. § 3. It is evident that the mind, rising from individuals to classes, and by successive generalizations forming wider and wider classes or genera, at each step diminishing the marks connoted, at last must reach a notion of widest generality, connoting but one mark, above which, of course, it cannot rise; and the process necessarily ceases. This highest, widest notion is called the “summum genus," and is defined as the genus that cannot become a species. It is represented in the above scheme by Being or Thing, containing in it only the notion existing, and containing under it all things. This is a simple notion and cannot be defined, not being referable to a genus. The Aristotelian logicians consider the summa genera as fixed by nature, and ten in number, corresponding to the ten Categories or Predicaments of Aristotle. By the Categories, Aristotle means, metaphysically, a classification a posteriori of the modes of objective or real existence; logically, a classification of the most general terms that can be predicated of any subject whatever. They are as follows, illustrated by his own examples: 1. Substance; it is a man, a horse, etc. 2. Quantity; it is two cubits long, three cubits, etc. 3. Quality; it is white, grammatical, etc. 4. Relation;-it is double, half as large, greater, etc. 5. Action; it cuts, burns, etc. 6. Passion; it is cut, is burned, etc. 7. Place; it is in the Agora, in the Lyceum, etc. 8. Time; it is to-day, was yesterday, last year, etc. 9. Posture; it is reclining, seated, etc. 10. Possession; it is having shoes, armor, etc. Everything that can be spoken of or thought of comes under one or the other of these Categories; in other words, whatever can be a subject of predication is in one or the other of these Predicaments. Each is, therefore, the highest generalization of a series of notions, each a summum genus. Aristotle, in his logical writings, whatever place they may hold in his metaphysics, evidently intends the Categories to be an enumeration of the widest notions signified by single terms. They have excited a world of discussion, been sharply criticised, banished repeatedly to metaphysics, and as often recalled to Logic. Kant objects to them: 1st. That the analysis is not made on any one principle; 2d. That the enumeration is incomplete; 3d. 2 Categoria, ch. iv. See also Topica, i, 9; and Metaphysica, iv, 7. |