LECT. under Ex tension, are regulated,viz. of Homogeneity and Heterogeneity. Explication. tion and tion. Law of only in soever may be any two concepts, they both still stand subordinated under some higher concept; in other words, things the most dissimilar must, in certain respects, be similar. The other, the law of Heterogeneity (principium Heterogeneitatis), is,―That every concept contains other concepts under it; and, therefore, when divided proximately, we descend always to other concepts, but never to individuals; in other words, things the most homogeneous, similar,-must, in certain respects, be heterogeneous, dissimilar. Of these two laws, the former, as the principle which Generifica enables, and in fact compels, us to rise from species to Specifica genus, is that which determines the process of Generification; and the latter, as the principle which enables, and in fact compels, us to find always species under a genus, is that which regulates the process of Specification. The second of these laws, it is evident, is only neity true true ideally, only true in theory. The infinite divisibility of concepts, like the infinite divisibility of space and time, exists only in speculation. And that it is theoretically valid, will be manifest, if we take two similar concepts, that is, two concepts with a small difference let us then clearly represent to ourselves this difference, and we shall find that how small soever it may be, we can always conceive it still less, without being nothing, that is, we can divide it ad infinitum ; but as each of these infinitesimally diverging differences affords always the condition of new species, it is evident that we can never end, that is, reach the individual, except per saltum." There is another law, which Kant promulgates in a Cf. Krug, Logik, § 45, p. 135, and pp. 136, 137.-ED. XI. Law of Lo nity. the Critique of Pure Reason," and which may be called LECT. the law of Logical Affinity, or the law of Logical Continuity. It is this,-That no two co-ordinate species gical Affitouch so closely on each other, but that we can conceive other or others intermediate. Thus man and orang-outang, elephant and rhinoceros, are proximate species, but still how great is the difference between them, and how many species can we not imagine to ourselves as possibly interjacent ? This law I have, however, thrown out of account, Grounds on as not universally true. For it breaks down when law must be Thus we apply it to mathematical classifications. a P. 510, ed. Rosenkranz. Cf. 102, 103. [Compare Fries, Logik, 8 Bachmann, [Logik, § 61, pp. which this rejected. XII. Reciprocal LECTURE XII. STOICHEIOLOGY. SECT. II.-OF THE PRODUCTS OF THOUGHT. I. ENNOEMATIC. III. RECIPROCAL RELATIONS OF CONCEPTS. B. QUANTITY OF COMPREHENSION. LECT. HAVING now concluded the consideration of the Reciprocal Relation of Concepts as determined by the Relation of quantity of Extension, I proceed to treat of that Compre- relation as regulated by the counter quantity of Comprehension. On this take the following paragraph: notions in hension. Par. XLI. Identical and Different notions. ¶ XLI. When two or more concepts are compared together according to their Comprehension, they either coincide or they do not; that is, they either do or do not comprise the same characters. Notions are thus divided into Identical and Different, (conceptus identici et diversi). The Identical are either absolutely or relatively the same. Of notions Absolutely Identical there are actually none; notions Relatively Identical are called, likewise, Similar or Cognate, (notiones similes, affines, cognatæ); and if the common attributes, by which they are allied, XII. be proximate and necessary, they are called Re- LECT. ciprocating or Convertible, (notiones reciproca, convertibiles.)" tion. notions im In explanation of this paragraph, it is only neces- Explicasary to say a word in regard to notions absolutely Absolutely Identical. That such are impossible is manifest. Identical "For, it being assumed that such exist, as absolutely possible. identical they necessarily have no differences by which they can be distinguished: but what are indiscernible can be known, neither as two concepts, nor as two identical concepts; because we are, ex hypothesi, unable to discriminate the one from the other. They are, therefore, to us as one. Notions absolutely identical can only be admitted, if, abstracting our view altogether from the concepts, we denominate those notions. identical, which have reference to one and the same object, and which are conceived either by different minds, or by the same mind, but at different times. Their difference is, therefore, one not intrinsic and necessary, but only extrinsic and contingent. Taken in this sense, Absolutely Identical notions will be only a less correct expression for Reciprocating or Convertible notions." B ¶ XLII. Considered under their Comprehen- Par. XLII. Opposition sion, concepts, again, in relation to each other, are of Concepts. said to be either Congruent or Agreeing, inasmuch as they may be connected in thought; or Conflictive, inasmuch as they cannot. The confliction constitutes the Opposition of notions, (Tò ἀντικεῖσθαι, oppositio). This is twofold ;—1o, a [Esser, Logik, § 36.] Krug, Logik, § 37, and Anm. i.— B [Esser, Logik, § 36, p. 79.] Cf. ED. LECT. Explication. Agreement, and Conflic tion. Immediate or Contradictory Opposition, called All "Identity is not to be confounded with Agreement Identity and or Congruence, nor Diversity with Confliction. Diversity identical concepts are, indeed, congruent; but all congruent notions are not identical. Thus, learning and virtue, beauty and riches, magnanimity and stature, are congruent notions, inasmuch as, in thinking a thing, they can easily be combined in the notion we form of it, although in themselves very different from each other. In like manner, all conflictive notions are diverse or different notions, for unless different, they could not be mutually conflictive. But, on the other hand, all different concepts are not conflictive; but those only whose difference is so great that each involves the negation of the other; as, for example, virtue and vice, beauty and deformity, wealth and poverty. Thus these notions are by pre-eminence — κατ' ἐξοχὴν - Kaт' ¿§oxǹv — said to be opposed, although it is true, that in thinking we can oppose, or place in antithesis, not only different, but even identical, concepts." "To speak now of the distinction of Contradictory a [Cf. Drobisch, Logik, p. 17, § 25 seq.] |