형이상학/형이상학Α

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참고[편집]

  1. Plat. Gorgias 448c, Plat. Gorg. 462b-c.
  2. Cf. Plat. Phaedrus 274, Hdt. 2.109.
  3. Aristot. Nic. Eth. 6.1139b 14-1141b 8.
  4. i.e. Metaphysics.
  5. Simon. Fr. 3 (Hiller)
  6. Cf. Solon, Fr. 26 (Hiller); Leutsch and Schneidwin, Paroemiographi, 1.371.
  7. i.e. the fact that the diagonal of a square cannot be rationally expressed in terms of the side.
  8. i.e. δευτέρον ἀμεινόνων("second thoughts are better"). Leutsch and Schneidwin 1.62.
  9. Phys. 2.3, Phys. 2.7
  10. Thales of Miletus, fl. 585 B.C.
  11. That of the Ionian monists, who sought a single material principle of everything.
  12. Cf. Plat. Crat. 402b, Plat. Theaet. 152e, Plat. Theaet. 180c,d.
  13. cf. Hom. Il. 14. 201, Hom. Il. 14.246.
  14. Cf. Hom. Il. 2.755, Hom. Il. 14.271, Hom. Il.15.37.
  15. Hippo of Samos, a medical writer and eclectic philosopher who lived in the latter half of the fifth century B.C. Cf.Aristot. De Anima 405b 2.
  16. The third Milesian monist; fl. circa 545 B.C.
  17. Diogenes of Apollonia, an eclectic philosopher roughly contemporary with Hippo.
  18. A Pythagorean, probably slightly junior to Heraclitus.
  19. Fl. about 500 B.C.
  20. Of Acragas; fl. 450 B.C.
  21. Cf. Empedocles, Fr. 17 (Diels), R.P. 166; Burnet, E.G.P. 108-109.
  22. This is Aristotle's illustration; apparently Anaxagoras did not regard the "elements" as homoeomerous (i.e. composed of parts which are similar to one another and to the whole). Cf. Aristot. De Caelo 302a 28, Aristot. De Gen. et Corr. 314a 24.
  23. Cf. Anaxagoras Fr. 4 (Diels); and see Burnet, E.G.P. 130.
  24. i.e. the Eleatic school.
  25. Founder of the above; fl. about 475.
  26. i.e. in the Δόξα. Parmenides Fr. 8 (Diels); R.P. 121.
  27. Aristotle is probably thinking of Empedocles. Cf. Aristot. Met. 4.8.
  28. Anaxagoras.
  29. Cf. Plat. Phaedo 97b-98b.
  30. A semi-mythical person supposed to have been a preincarnation of Pythagoras.
  31. Probably Aphrodite (so Simplicius, Plutarch).
  32. Hes. Th. 116-20. The quotation is slightly inaccurate.
  33. Empedocles Fr. 17, 26 (Diels); R.P. 166. Cf. Burnet, E.G.P. 108 ff.
  34. Aristot. Phys. 2.3, 7.
  35. Cf. Plat. Phaedo 98b, Plat. Laws 967b; also Aristot. Met. 7.5.
  36. Cf. 3.14.
  37. e.g. Empedocles, Fr. 62 (Diels).
  38. Of Miletus; fl. circa 440 (?) B.C. See Burnet, E.G.P. 171 ff.
  39. Of Abdera; fl. circa 420 B.C. E.G.P loc. cit.
  40. For the probable connection between the Atomists and the Eleatics see E.G.P. 173, 175, and cf. De Gen. et Corr. 324b 35-325a 32.
  41. i.e., of the atoms.
  42. Cf. R.P. 194.
  43. These letters will convey Aristotle's point better to the English reader, but see critical note.
  44. Aristotle seems to have regarded Pythagoras as a legendary person.
  45. Pythagoras himself (fl. 532 B.C.) is said by Aristoxenus (ap. Stobaeus 1.20.1) to have been the first to make a theoretical study of arithmetic.
  46. Cf. Aristot. Met. 14.6ff..
  47. Apparently (cf. infra, Aristot. Met. 1.17) they identified these not only with properties of number but with numbers themselves. Thus justice (properly=squareness)=4, the first square number; soul or mind=1, opportunity=7 (Alexander).
  48. Pythagoras himself is credited with having discovered the ratios of the octave (2 : 1), the fifth (3 : 2) and the fourth (4 : 3). Burnet, E.G.P. 51.
  49. Or "harmony." Cf. Aristot. De Caelo 2.9, and E.G.P. 152.
  50. Earth, sun, moon, five planets, and the sphere of the fixed stars.
  51. i.e. "counter-earth"; a planet revolving round the "central fire" in such a way as to be always in opposition to the earth.
  52. In the lost work On the Pythagoreans; but cf. Aristot. De Caelo 2.13.
  53. See Burnet, E.G.P 143-146.
  54. i.e., as a formal principle. Cf. Ross ad loc.
  55. Either because by addition it makes odd numbers even and even odd (Alexander, Theo Smyrnaeus) or because it was regarded as the principle of both odd and even numbers (Heath).
  56. Zeller attributes the authorship of this theory to Philolaus.
  57. This statement is probably true, but a later addition.
  58. He was generally regarded as a Pythagorean.
  59. The section of Pythagoreans mentioned in 6, and Lacmaeon.
  60. His argument was "Everything that is is one, if 'what is' has one meaning" (πάντα ῞εν, εἰ τὸ ὂν ῝εν σημαίνει, Aristot. Phys. 187a 1); but he probably believed, no less than Melissus, in the material unity of reality. Cf. Melissus Fr. 8 (Diels). It has been suggested, however (by the Rev. C. F. Angus), that he was simply trying to convey in figurative language a conception of absolute existence.
  61. Of Samos; defeated the Athenian fleet in 441 B.C.
  62. Melissus Fr. 8, ll. 32-3, 42-3.
  63. Melissus Fr. 3.
  64. Of Colophon, b. 565 (?) B.C. Criticized and ridiculed most of the views of his day, especially the anthropomorphic conception of the gods. Burnet, E.G.P. 55 ff., esp. 61-62. Cf. Xenophanes Fr. 23 (Diels).
  65. Aristot. Phys. 1.3
  66. Cf. note on Aristot. Met. 3.13.
  67. The Pythagoreans; so called because Pythagoras founded his society at Croton.
  68. i.e., the same number might be the first to which each of several definitions applied; then that number would be each of the concepts so defined.
  69. Compare Aristot. Met. 12.4.2-5.
  70. Cf. Aristot. Met. 4.5.18.
  71. Plat. Crat. 402a (fr. 41 Bywater).
  72. I have translated ἰδέα by Idea and εἶδος by Form wherever Aristotle uses the words with reference to the Platonic theory. Plato apparently uses them indifferently, and so does Aristotle in this particular connection, but he also uses εἶδος in the sense of form in general. For a discussion of the two words see Taylor, Varia Socratica, 178-267, and Gillespie, Classical Quarterly, 6.179-203.
  73. For this interpretation of παρὰ ταῦτα see Ross's note ad loc.
  74. i.e. arithmetical numbers and geometrical figures.
  75. See Aristot. Met. 4.2.19-20, and cf. Aristot. Met. 8.4.4.
  76. ἔξω τῶν πρώτων is very difficult, but it can hardly be a gloss, and no convincing emendation has been suggested. Whatever the statement means, it is probably (as the criticism which follows is certainly) based upon a misunderstanding. From Plat. Parm. 143c, it might be inferred that the Great and Small (the Indeterminate Dyad) played no part in the generation of numbers; but there the numbers are not Ideal, as here they must be. In any case Aristotle is obsessed with the notion that the Dyad is a duplicative principle (Aristot. Met. 13.8.14), which if true would imply that it could generate no odd number. Hence Heinze proposed reading περιττῶν(odd) for πρώτων(which may be right, although the corruption is improbable) and Alexander tried to extract the meaning of "odd" from πρώτων by understanding it as "prime to 2." However, as Ross points out (note ad loc.), we may keep πρώτων in the sense of "prime" if we suppose Aristotle to be referring either (a) to the numbers within the decad (Aristot. Met. 13.8.17) and forgetting 9—the other odd numbers being primes; or (b) to numbers in general, and forgetting the entire class of compound odd numbers. Neither of these alternatives is very satisfactory, but it seems better to keep the traditional text.
  77. For a similar use of the word ἐκμαγεῖον cf. Plat. Tim. 50c.
  78. Aristotle's objection is that it is unreasonable that a single operation of the formal upon the material principle should result in more than one product; i.e. that the material principle should be in itself duplicative.
  79. Plato refers several times in the dialogues to an efficient cause (e.g. the Demiurgus,Plat. Soph. 265b-d, Plat. Tim. 28c ff.) and a final cause (e.g. Plat. Phil. 20d, 53e, Plat. Tim. 29d ff.); but Aristotle does not seem to take these allusions seriously.
  80. Cf. Plat. Phil. 25e-26b.
  81. Aristot. Met. 3.17; 4.3.
  82. Aristot. Phys. 2.3
  83. See note on Aristot. Met. 5.15.
  84. The various references in Aristotle to material principles intermediate between certain pairs of "elements" have been generally regarded as applying to Anaximander's ἄπειρον or Indeterminate; but the references are so vague (cf. Aristot. Met. 7.6, Aristot. Phys.187a 14, 189b 3, 203a 18) that it seems better to connect them with later and minor members of the Milesian school. Cf. Ross's note ad loc.
  85. Cf. Aristot. Met. 3.17.
  86. Cf. Aristot. Met. 3.5, 8.
  87. Cf. Aristot. Met. 4.1.
  88. Cf. Aristot. Met. 7.3 n.
  89. Aristot. De Caelo, 3.7; Aristot. De Gen. et Corr. 2.6.
  90. Cf. Aristot. Met. 4.6.
  91. Mind, and the "mixture" of homoeomerous particles.
  92. Anaxagoras. Fr. 12 (Diels).
  93. Aristot. Met. 1.8.17.
  94. Aristotle uses the word μέγεθος both of magnitude in general and of spatial magnitude or extension. Here the meaning seems to be the former. Numbers obviously have magnitude, and might be regarded as causing it; but (except on the Number-Atomism theory,) they are no more the cause of extension than that of gravity.
  95. i.e., how can number be both reality and the cause of reality?
  96. The point seems to be this. The Pythagoreans say that Opinion is a number, 3 (or 2, according to another version), and is located in a certain region of the universe because that region is proper to a corporeal magnitude composed of the number 3 (air was so composed according to Syrianus). Are we to understand, says Aristotle, that the abstract number identified with Opinion is the same as the concrete number of which air consists? The difficulty is probably due to an attempt to combine two different Pythagorean views of number.
  97. For a discussion of the Ideal theory and Aristotle's conception of it see Introduction; and with the whole contents of Aristot. Met. 9.1-15 cf. Aristot. Met. 13.4.6-5.
  98. An Idea which represents their common denominator.
  99. The heavenly bodies.
  100. Aristotle is here speaking as a Platonist. Contrast the language of Aristot. Met. 13.4.7ff., and see Introduction.
  101. Scientific knowledge must have a permanent object (cf. Aristot. Met. 1.4.2.
  102. Including artificial products; cf. Aristot. Met. 1.15.
  103. The fact that several particulars can have a common quality or nature implies a single Idea of which they all partake (Plat. Rep. 596a).
  104. The theory always admitted Ideas of perishable things, e.g. "man." The objection here is that if the memory of dead men establishes the Idea of "man," the memory of a dead individual establishes an Idea of that (perishable) individual.
  105. Plat. Phaedo 74a-77a, Plat. Rep. 479a-480a.
  106. Several arguments bore this name. Here the reference is probably to the following: If X is a man because he resembles the Idea of Man, there must be a third "man" in whom the humanity of these two is united. Cf.Plat. Parm. 132a-133a.
  107. The Indeterminate Dyad, being to Aristotle a glorified 2, falls under the Idea of Number, which is therefore prior to it.
  108. This seems to be a development of the same objection. Number, which is relative, becomes prior to the supposedly self-subsistent Dyad.
  109. Sensible double things are not eternal; therefore they do not, in the proper sense of "participation," participate in the Idea of Doubleness qua having the accidental attribute "eternal." Therefore Ideas, qua participated in, are not attributes but substances.
  110. i.e. pairs of sensible objects.
  111. i.e. mathematical 2s.
  112. The argument of 7-8 is: Ideas are substances. The common name which an idea shares with its particulars must mean the same of both; otherwise "participation" is merely homonymy. But as applied to Ideas it denotes substance; therefore particulars must be substances.
  113. This objection, like the next, is chiefly directed against the transcendence of the Ideas. It is anticipated by Plato in Plat. Parm. 134d.
  114. Anaxagoras Fr. 12ad fin.
  115. See note on Aristot. Met. 12.8.9. Apparently he was a Platonist who regarded the Ideas as immanent in particulars.
  116. Plato says "the Demiurgus"?Plat. Tim. 28c, Plat. Tim. 29a.
  117. Why this consequence is objectionable is not quite clear. Perhaps it is on the ground that to "account for appearances" in this way is not economical.
  118. The species will be the "pattern" of individuals, and the genus of the species.
  119. Cf. Aristot. Met. 1.10.
  120. Plat. Phaedo 100d.
  121. The point, which is not very clearly expressed, is that the Ideas will not be pure numerical expressions or ratios, but will have a substrate just as particulars have.
  122. That the words in brackets give the approximate sense seems clear from Aristot. Met. 13.6.2-3, Aristot. Met. 13.7.15; but it is difficult to get it out of the Greek.
  123. Cf. vi. 4.
  124. i.e., if 2 is derived from a prior 2 (the Indeterminate Dyad; Aristotle always regards this as a number 2), and at the same time consists of two units or 1s, 2 will be prior both to itself and to 1.
  125. In the Aristot. De Gen. et Corr. 320b 23Aristotle says that there is not.
  126. This last sentence shows that in what goes before A. has been regarding the Platonic One as a unit. If this is so, he says, substance cannot be composed of it. If on the other hand the One is something different from the unit, they ought to make this clear.
  127. The lines, planes, and solids here discussed are probably the Ideal lines, etc., which are immediately posterior to the Idea-Numbers. Cf. 30, Aristot. Met. 13.6.10, Aristot. Met. 13.9.2, and see Introduction.
  128. Lines, planes, and solids are generated from varieties of the Great and Small, but points cannot be, having no magnitude; how, then, can the latter be present in the former?
  129. That Plato denied the existence of the point and asserted that of indivisible lines is not directly stated elsewhere, but the same views are ascribed to Xenocrates, and were attacked in the treatise Xenocrates De lineis insecabilibus. See Ross ad loc.
  130. Sc. if the point is the limit of the line.
  131. Cf. Aristot. Met. 7.5 and Aristot. Met. 1.9.
  132. Aristot. Met. 1.12.
  133. The final cause. Cf. Aristot. Met. 1.6.9-10.
  134. e.g. Speusippus, for whom see Aristot. Met. 7.2.4.
  135. Cf. Plat. Rep.531c-d
  136. Cf. iv. 10.
  137. The word ἔκθεσις has various technical meanings. The process referred to here apparently consisted in taking, e.g., particular men, and reducing them with reference to their common nature to a single unit or universal, "man"; then taking "man," "horse," "dog," etc. and treating them in the same way, until a unit is reached which embraces everything (Alexander).
  138. Probably those of relative or negative terms. Cf. Aristot. Met. 1.3.
  139. See note on Aristot. Met. 1.23.
  140. e.g. Plato's Dialectic.
  141. Cf. the doctrine of ἀνάμνησις (recollection), Plat. Meno 81c, Plat. Phaedo 72e.
  142. στοιχεῖον means both "an element" and "a letter of the alphabet"; hence letters are often used as analogues of the material elements. The point here is: Is Z or rather the Greek ζ) a στοιχεῖον, or is it further analyzable? Since this can be disputed, we must expect differences of opinion about the elements in general.
  143. Peculiar to them as sounds, not as individual sounds. If sights and sounds had the same elements, sight, which knows those elements as composing sights, would know them as composing sounds; i.e., we could see sounds.
  144. Aristot. Phys. 2.3, 7.
  145. Empedocles Fr. 96, 98 (Diels), Ritter and Preller 175. Aristotle says that Empedocles had some idea of the essence or formal cause, but did not apply it generally.
  146. The reference is to Book 3. See Introduction.
  147. Simonides of Ceos