VIII. used in both cases, speaks more accurately, than the LECT. expressions, contained, (or not contained) in of the one, contained, (or not contained) under of the other. In fact, the two quantities and the two quantifications have by logicians been neglected together. This Table, (the principle of which becomes more palpably demonstrative, when the parts of the table are turned into the parts of a circular machine"), exhibits all the mutual relations of the counter quantities.-1o, It represents the classes, as a series of resemblances thought as one, (by a repetition of the same letter in the same series,) but as really distinct, (by separating lines). Thus, A is only A, not A, A, A, &c.; some Animal is not some Animal; one class of Animals is not all, every, or any other; this Animal is not that; Socrates is not Plato; z is not z'. On the other hand, E is E A; and Y is YUOIEA; every lower and higher letter in the series coalescing uninterruptedly into a series of reciprocal subjects and predicates, as shown by the absence of all discriminating lines. Thus, Socrates (z), is Athenian (Y), Greek (U), European (O), Man (I), Mammal (E), Animal (A). Of course the series must be in grammatical and logical harmony. We must not collate notions abstract and notions concrete.-2°, The Table shows the inverse correlation of the two quantities in respect of amount. For example: A, (i.e. A, A, &c.), the highest genus, is represented as having six times the Breadth of Y; whilst Y, (i.e. Y—A), the lowest species, has six times the Depth of A.-3°, The Table manifests all the classes, as in themselves unreal, subjective, ideal; for these are merely fictions or artifices of the a A machine of this kind was constructed by the Author, and used in the class-room to illustrate the doc- LECT. mind, for the convenience of thinking. VIII. Universals only exist in nature, as they cease to be universal in thought; that is, as they are reduced from general and abstract attributes to individual and concrete qualities. A-Y are only truly objective as distributed through z, z, z", &c.; and in that case they are not universals. As Boëthius expresses it:"Omne quod est, eo quod est, singulare est."—4°, The opposition of class to class, through contradictory attributes, is distinguished by lines different from those marking the separation of one part of the same class from another. Thus, Animal, or Sentientlyorganised, (A), is contrasted with Not-animal, or Notsentiently-organised, (A), by lines thicker than those which merely discriminate one animal (A), from another (A)." a See further in Discussions, p. 701 et seq.-ED. LECTURE IX. STOICHEIOLOGY. SECT. II.-OF THE PRODUCTS OF THOUGHT. I. ENNOEMATIC. B. OF CONCEPTS IN SPECIAL.-II. THEIR SUBJECTIVE RELATION-QUALITY. IX. Relation of their sub ject. HAVING Concluded the consideration of the relation LECT. of concepts to their objects,-the relation in which their Quantity is given, I now proceed to consider Concepts to their relation to their conceiving subject the relation in which is given their Quality. This consideration of the quality of concepts does not, in my opinion, belong to the Doctrine of Elements, and ought, in scientific rigour, to be adjourned altogether to the Methodology, as a virtue or perfection of thought. As logicians, however, have generally treated of it likewise under the former doctrine, I shall do so too, and commence with the following paragraph. The Quality consists in Perfection fection. ¶ XXVII. A concept or notion is the unity in Par. XXVII. consciousness of a certain plurality of attributes, of Concepts and it, consequently, supposes the power of think- its logical ing these, both separately and together. But as or Imperthere are many gradations in the consciousness with which the characters of a concept can be thought severally and in conjunction, there will consequently be many gradations in the actual LECT. Par. XXVIII. The two degrees of the logical Perfection and Imperfection of Concepts,their Clearness and Distinctness, and their Obscurity and Indistinct ness. Perfection or Imperfection of a notion. It is this perfection or imperfection which constitutes the logical Quality of a concept." It is thus the greater or smaller degree of consciousness which accompanies the concept and its object, that determines its quality, and according to which it is called logically perfect or logically imperfect. Now there may be distinguished two degrees of this logical perfection, the nature of which is summarily expressed in the following paragraph. ¶ XXVIII. There are two degrees of the logical perfection of concepts,-viz. their Clearness and their Distinctness, and, consequently, two opposite degrees of their corresponding imperfection,―viz. their Obscurity and their Indistinctness. These four qualities express the perfection and imperfection of concepts in extremes; but between these extremes, there lie an indefinite number of intermediate degrees. A concept is said to be clear (clara), when the degree of consciousness is such as enables us to distinguish it as a whole from others; and obscure (obscura), when the degree of consciousness is insufficient to accomplish this. A concept is said to be distinct (distincta, perspicua), when the degree of consciousness is such, as enables us to discriminate from each other the several characters, or constituent parts of which the concept is the sum; and indistinct or confused (indistincta, confusa, imperspicua), when the amount of consciousness requisite for this is a Krug, Logik, § 30. Cf. Esser, Logik, § 45 et seq.-ED. wanting. Confused (confusa) may be employed LECT. as the genus including obscure and indistinct." IX. application pressions obscurity, by reference The expressions clearness and obscurity, and dis- Original tinctness and indistinctness, as applied to concepts, of the exoriginally denote certain modifications of vision; from clearness, vision they were analogically extended to the other &c. senses, to imagination, and finally to thought. It may, therefore, enable us the better to comprehend their secondary application, to consider their primitive. To Leibnitz we owe the precise distinction of concepts into clear and distinct, and from him I borrow the following illustration. In darkness, in the complete Illustrated obscurity of night, we see nothing, there is no per- to vision. ception-no discrimination of objects. As the light dawns, the obscurity diminishes, the deep and uniform sensation of darkness is modified,-we are conscious of a change, we see something, but are still unable to distinguish its features, we know not what it is. As the light increases, the outlines of wholes begin to appear, but still not with a distinctness sufficient to allow us to perceive them completely; but when this is rendered possible, by the rising intensity of the light, we are then said to see clearly. We then recognise mountains, plains, houses, trees, animals, &c., that is, we discriminate these objects as wholes, as unities, from each other. But their parts,—the manifold of which these unities are the sum,-their parts still lose themselves in each other, they are still but a Compare Krug, Logik, 31 et seq. -ED. [Buffier, Logique, § 345 et seq. Kant, Kr. d. r. Vernunft, B. ii. Trans. Dial., art. i. p. 414, 3d ed., 1790.] B See his Meditationes de Cognitione, Veritate, et Ideis, (Opera, ed. Erdmann, p. 79), Nouveaux Essais, L. ii., ch. xxix. The illustration, |