; LOGIC 271 • progressive division is our surest method, while a correspondingly gradual building up of concepts is equallyproper to the upward process towards the universal. 1 And thus Plato's method, though Aristotle could not accept it as a satisfactory process for deducing definitions, was yet recognised and further worked out <strong>by</strong> him as a means to their discovery. 2 Supposing, then, that we have defined and surveyed the whole field of the knowledge of concepts on this method, we shall obtain a system of ideas such as Plato looked for, 3 carrying us in an unbroken line from the Summa Genera through all the intermediate members down to the lowest species. And since scientific deduction must consist in the specification of causes, and since each specific difference in the upward scale implies the introduction of a new cause, and every added cause creates a corresponding differentia, it results that our logical structure must exactly correspond with the actual sequence and concatenation of causes. Plato never undertook actually to set forth that derivation of everything knowable out of unity, which he saw ahead as the end and goal of science. Aristotle 1 Aristotle includes both, with- the object to be divided; and out further separating them, in lastly (to which Plato devoted the concept of Division. For less attention), that it should this he gives full rules in Anal, not proceed <strong>by</strong> means of deduced Pott. ii. 13, 96, b, 15-97, b, or contingent differences, but <strong>by</strong> 25 ; Top. vi. 5, 6 ; Part. Anvm. the essential ones. Cf. preceding i. 2, 3. Like Plato (Zellbb, note. Ph. d. Gr. pt. i. p. 524 sq.), 2 Two further rules, contained he also considers that the most especially in the sixth book of important thing is that the di- the Topic)—wherehe enumerates vision should be continuous, at length the mistakes made in should omit no intermediate denning—are omitted here, grade, and should totally exhaust 3 See Zell. ibid. p. 525, 588. 272 <strong>ARISTOTLE</strong> considers such a demonstration to be quite impracticable. The highest genera, according to him, are no more capable of being derived from any one higher principle than are the special postulates of each science, 1 They are connected, not <strong>by</strong> any complete community of nature, but only <strong>by</strong> a kind of analogy, 2 and the reason 1 Anal. Post. i. 32, 88, a, 31 sqq., &c. ; vid. supra p. 246. sqq. Aristotle says, in Metaph. xii. 4, 1070, b, 1 {irapa yap t)\v ovtrlav Kal TaAAa refc Karyyopovfieva ovBev %trri koiv&v), that the categories especially can be deduced neither from one another nor from a higher common genus: v. 28, 1024, b, 9 (where the same is said of Form and Matter) ; xi. 9, 1065, b, 8 ; Phys. iii. 1, 200, b, 34 ; De An. i. 6, 410, a, 13 ; Mh. N. i. 4, 1096, a, 19, 23 sqq. ; of. TRENDE- LENBURG, Hist. Beitr. i. 149 sq. The concepts, which one would be most inclined to consider the highest genera, ' Being ' and ' One,' are no ydvri : Metaph. iii. 3, 998, b, 22 ; viii. 6, 1045, b, 5 ; x. 2, 1053, b, 21 ; xi. 1, 1059, b, 27 sq. ; xii. 4, 1070, b. 7 ; Eth. JST. ibid. ; Anal. Post. ii. 7, 92, b, 14 ; Top. iv. 1, 121, a, 16, c. 6, 127, a, 26 sqq. Cf. Trendelenburg, loo. cit. 67 ; Bonitz and Schwegler on Metaph. iii. 3 (more on p. 276 infra'). Therefore the principle ' that eventually everything is contained in a single highest concept as in a common genus,' which Strumpell, Gesch. d. theor. Phil. d. Gr. p. 193, gives as an assertion of Aristotle, is not really Aristotelian. 2 In Metaph. v. 6, 1016, b, 31, four kinds of Unity are distinguished (somewhat different is the other fourfold enumeration in Metaph. x. 1, in which the unity of analogy does not occur) : the unity of number, of species, of genus, and of analogy. Each of these unities includes in it the subsequent unities (i.e. that which in number is one is also one in species, &c.) ; but not vive versa. Hence the unity of Analogy can occur even in those things which belong to no common genus (cf. Part. An. i. 5, 645, b, 26 : t& ficv yap exavat to Kotvbv Kar avahoylav, ra Se Kara yevos, Ta Sh /car' elSos). It occurs in everything Sera £%« us fiAAo vpbs SAAo. It consists in identity of relation (io-oV»js \6yav~), and hence supposes at least four members {Eth. N. v. 6, 1131, a, 31). Its formula is : &s touto iv tovtu % irpbs touto, to*8' ev T tV abri]v %x ov 5vvaii.iv, ibid. i. 4, 644, b, 11 ii. 6, 652, a, 3), and in fact in all categories {Metaph. xiv. 6, 1093, b, 18). Besi8es those in the passages just mentioned, other instances are given in De Part.
: : LOGIC 273 why the sciences are not all one, is just because each class of actual existences has its own peculiar sort of knowledge which applies to it. 1 If it be true that among the sciences we find one which is a science of first principles—the ' First Philosophy '—we must not expect it to develop its subject-matter out of any single principle of being. On the contrary, we shall find it necessary, before proceeding to any further researches, that we should inquire into all the most general points of view from which the world of actual existence can be considered, or, in other words, enumerate the highest generic concepts themselves. This it is with which the doctrine of the Categories is concerned, and these form accordingly the true connecting link, in Aristotle's philosophic system, between Logic and Metaphysics. Anvrn., Anal. Pri. i. 46, 61, b, 22, and Bliet. iii. 6 fin. That which cannot be deduced from any other thing (the highest principles), must be explained <strong>by</strong> analogy, as, for example, the concepts of Matter, of T?orm, &c. ; cf . Metaph. ix. 6 (vid. sup. p. 269, n. 1); xii. 4, 1070, b, 16 sqq., and Phys. i. 7, 1 91 , a, 7. This is the account given <strong>by</strong> Trendelenburg in his Hist, lieitr. i. 151 sqq. Analogy ' is of special importance ' to Aristotle in his study of Natural History; see thereon infra, and cf. Meter, Arist. Thierhunde, 334 sqq. 1 Anal. Post. i. 28 init. : p-la ft eiriar'tjfjir] effrlv t) lv6s yevovs . . . eTe'pct 8' imffT^liri tffr\v irepas, 'ifftap at apxal fifo' e/c ruf aiiruv pA\& erepai etc tuv erepav. Metaph. iii. 2, 997, a, 21 : irep* oSv t
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