desk, and not the figure of any other body. But had we only individual abstract notions, what would be our knowledge? We should be cognizant only of qualities viewed apart from their subjects; (and of separate phænomena there exists none in nature); and as these qualities are also separate from each other, we should have no knowledge of their mutual relations.1 Abstract General notions, what and how formed. It is necessary, therefore, that we should form Abstract General notions. This is done when, comparing a number of objects, we seize on their resemblances; when we concentrate our attention on these points of similarity, thus abstracting the mind from a consideration of their differences; and when we give a name to our notion of that circumstance in which they all agree. The general notion is thus one which makes us know a quality, property, power, action, relation; in short, any point of view, under which we recognize a plurality of objects as a unity. It makes us aware of a quality, a point of view, common to many things. It is a notion of resemblance; hence the reason why general names or terms, the signs of general notions, have been called terms of resemblance (termini similitudinis). In this process of generalization, we do not stop short at a first generalization. By a first generalization we have obtained a number of classes of resembling individuals. But these classes we can compare together, observe their similarities, abstract from their differences, and bestow on their common circumstance a common name. On these second classes we can again perform the same operation, and thus ascending the scale of general notions, throwing out of view always a greater number of differences, and seizing always on fewer similarities in the formation of our classes, we arrive at length at the limit of our ascent in the notion of being or existence. Thus placed on the summit of the scale of classes, we descend by a process the reverse of that by which we have ascended; we divide and subdivide the classes, by introducing always more and more characters, and laying always fewer differences aside; the notions become more and more composite, until we at length arrive at the individual. I may here notice that there is a twofold kind of quantity to be considered in notions. It is evident, that in proportion as the class is high, it will, in the first place, contain under it a greater number of classes, and, in the second, will include Twofold quantity in notions, Extension and Comprehension. the smallest complement of attributes. Thus being or existence 1 We should also be overwhelmed with their number. -Jotting. contains under it every class; and yet when we say that a thing exists, we say the very least of it that is possible. On the other hand, an individual, though it contain nothing but itself, involves the largest amount of predication. For example, when I say,this is Richard, I not only affirm of the subject every class from existence down to man, but likewise a number of circumstances proper to Richard as an individual. Now, the former of these quantities, the external, is called the Extension Their designations. of a notion (quantitas ambitus); the latter, the internal quantity, is called its Comprehension or Intension (quantitas complexus). The extension of a notion is, likewise, styled its circuit, region, domain, or sphere (sphæra), also its breadth (λáTOS). On the other hand, the comprehension of a notion is, likewise, called its depth (Bálos). These names we owe to the Greek logi cians.1 The internal and external quantities are in the inverse ratio of each other. The greater the extension, the less the comprehension; the greater the comprehension, the less the extension." Their law. 1 [See Ammonius, In Categ., f. 33. Gr. f. 29. Lat. Brandis, Scholia in Arist., p. 45.] ('A κατηγορίαι καὶ πλάτος ἔχουσι καὶ βάθος, βάθος μὲν τὴν εἰς τὰ μερικώτερα αὐτῶν πρόοδον, πλάτος δὲ τὴν εἰς τὰ πλάγια μετ άστασιν, οἷον ἵνα βάθος μὲν λάβῃς οὕτω τὴν οὐσίαν καὶ τὸ σῶμα καὶ τὸ ἔμψυχον καὶ τὸ ζῷον καὶ οὕτως ἐφεξῆς, πλάτος δέ, ὅταν διέ λῃς τὴν οὐσίαν εἰς σῶμα καὶ ἀσώματον.2 [Cf. Port Royal Logic, p. i. c. vi. p. Eugenios (Aoyin, b. i. c. iv. p. 194 et seq.ED.] 74. LECTURE XXXV. THE ELABORATIVE FACULTY. - GENERALIZATION. - NOMINALISM AND CONCEPTUALISM. Recapitulation. I ENTERED, in my last Lecture, on the discussion of that great cognitive power which I called the Elaborative Faculty, the Faculty of Relations, -the Discursive Faculty,-Comparison, or Judgment; and which corresponds to what the Greek philosophers understood by diavola, when opposed, as a special faculty, to vous. I showed you, that, though a comparison,- a judgment, involved the supposition of two relative terms, still it was an original operation, in fact involved in consciousness, and a condition of every energy of thought. But, besides the primary judgments of existence, — of the existence of the ego and non-ego, and of their existence in contrast to, and in exclusion of, each other, -I showed that this process is involved in perception, external and internal; inasmuch as the recognitions,- that the objects presented to us by the Acquisitive Faculty are many and complex, that one quality is different from another, and that different bundles of qualities are the properties of different things or subjects, are all so many acts of Comparison or Judgment. This being done, I pointed out that a series of operations were to be referred to this faculty, which, by philosophers, had been made the functions of specific powers. Of these operations I enumerated :— 1°, Composition or Synthesis; 2°, Abstraction, Decomposition or Analysis; 3°, Generalization; 4°, Judgment; and 5°, Reasoning. The first of these, -Composition or Synthesis,-which is shown in the formation of Complex or Collective notions, I stated to you was the result of an act of comparison. For a complex notion (I gave you as examples an army, a forest, a town) being only the repetition of notions absolutely similar, this similarity could be ascertained only by comparison. In speaking of this process, I explained the support afforded in it to the mind by language. I then recalled to you what was meant by abstraction. Abstraction is no positive act; it is merely the negation of attention. We can fully attend only to a single thing at a time; and attention, therefore, concentrated on one object or one quality of an object, necessarily more or less abstracts our consciousness from others. Abstraction from, and attention to, are thus correlative terms, the one being merely the negation of the other. I noticed the improper use of the term abstraction by many philosophers, in applying it to that on which attention is converged. This we may indeed be said to prescind, but not to abstract. Thus let A, B, C, be three qualities of an object. We prescind A, in abstracting it from B and C; but we cannot, without impropriety, simply say that we abstract A. Thus by attending to one object to the abstraction from all others, we, in a certain sort, decompose or analyze the complex materials presented to us by Perception and Self-consciousness. This analysis or decomposition is of two kinds. In the first place, by concentrating attention on one integrant part of an object, we, as it were, withdraw or abstract it from the others. For example, we can consider the head of an animal to the exclusion of the other members. This may be called Partial or Concrete Abstraction. The process here noticed has, however, been overlooked by philosophers, insomuch that they have opposed the terms concrete and abstract as exclusive contraries. In the second place, we can rivet our attention on some particular mode of a thing, as its smell, its color, its figure, its motion, its size, etc., and abstract it from the others. This may be called Modal Abstraction. The abstraction we have been now speaking of is performed on individual objects, and is consequently particular. There is nothing necessarily connected with Generalization in Abstraction. Generalization is indeed dependent on abstraction, which it supposes; but abstraction does not involve generalization. I remark this, because you will frequently find the terms abstract and general applied to notions, used as convertible. Nothing, however, can be more incorrect. "A person," says Mr. Stewart, "who had never seen but one rose, might yet have been able to consider its color apart from its other qualities; and, therefore, there may be such 1 [Cf. Kant, De Mundi Sensibilis Forma [ 6. Biran. [Examen des Leçons de M. Laromiguière, 3, Nouvelles Considerat. p. 194.- ED.] Bilfinger, Dilucidationes, § 262.] 2 [On Precision, and its various kinds, see Derodon, Logica, pars ii. c. vi. 11. Opera, p. 233, ed. 1668; and Chauvin, Lex. v. Præcisio (Præscisio).] a thing as an idea which is at once abstract and particular. After having perceived this quality as belonging to a variety of individ uals, we can consider it without reference to any of them, and thus form the notion of redness or whiteness in general, which may be called a general abstract idea. The words abstract and general, therefore, when applied to ideas, are as completely distinct from each other as any two words to be found in the language." I showed that abstraction implied comparison and judgment; for attention supposes preference, preference is a judgment, and a judgment is the issue of comparison. I then proceeded to the process of Generalization, which is still more obtrusively comparison, and nothing but comparison. Generalization is the process through which we obtain what are called general or universal notions. A general notion is nothing but the abstract notion of a circumstance in which a number of individual objects are found to agree, that is, to resemble each other. In so far as two objects resemble each other, the notion we have of them is identical, and, therefore, to us the objects may be considered as the same. Accordingly, having discovered the circumstance in which objects agree, we arrange them by this common circumstance into classes, to which we also usually give a common name. I explained how, in the prosecution of this operation, commencing with individual objects, we generalized these into a lowest class. Having found a number of such lowest classes, we then compare these again together, as we had originally compared individuals; we abstract their points of resemblance, and by these points generalize them into a higher class. The same process we perform upon these higher classes; and thus proceed, generalizing class from classes, until we are at last arrested in the one highest class, that of being. Thus we find Peter, Paul, Timothy, etc., all agree in certain common attributes, and which distinguish them. from other animated beings. We accordingly collect them into a class, which we call man. In like manner, out of the other animated beings which we exclude from man, we form the classes, horse, dog, ox, etc. These and man form so many lowest classes or species. But these species, though differing in certain respects, all agree in others. Abstracting from their diversities, we attend only to their resemblances; and as all manifesting life, sense, feeling, etc. this resemblance gives us a class, on which we bestow the name animal. Animal, or living sentient existences, we then compare with lifeless existences, and thus going on 1 Elements, vol. i. c. iv. § 1. Works, vol. ii. p. 165.-ED.] So Whately, [Logic, b. i. § 6, p. 49; b. ii. c. v. § 1, p. 122 (8th edit). - ED.] |