Our Knowledge of the External World as a Field for Scientific Method in Philosophy

Absolute, 6, 39. Abstraction, principle of, 42, 124 ff. Achilles, Zeno's argument of, 173. Acquaintance, 25, 144. Activity, 224 ff. Allman, 161 n. Analysis, 185, 204, 211, 241. legitimacy of, 150. Anaximander, 3. Antinomies, Kant's, 155 ff. Aquinas, 10. Aristotle, 40, 160 n., 161 ff., 240. Arrow, Zeno's argument of, 173. Assertion, 52. Atomism, logical, 4. Atomists, 160. Belief, 58. primitive and derivative, 69 ff. Bergson, 4, 11, 13, 20 ff., 137, 138, 150, 158, 165, 174, 178, 229 ff. Berkeley, 63, 64, 102. Bolzano, 165. Boole, 40. Bradley, 6, 39, 165. Broad, 172 n. Brochard, 169 n. Burnet, 19 n., 160 n., 161 n., 170 n., 171 ff. Calderon, 95. Cantor, vi, vii, 155, 165, 190, 194, 199. Categories, 38. Causal laws, 109, 212 ff. evidence for, 216 ff. in psychology, 219. Causation, 34 ff., 79, 212 ff. law of, 221. not a priori, 223, 232. Cause, 220, 223. Certainty, degrees of, 67, 68, 212. Change, demands analysis, 151. Cinematograph, 148, 174. Classes, 202. non-existence of, 205 ff. Classical tradition, 3 ff., 58. Complexity, 145, 157 ff. Compulsion, 229, 233 ff. Congruence, 195. Consecutiveness, 134. Conservation, 105. Constituents of facts, 51, 145. Construction v. inference, iv. Contemporaries, initial, 119, 120 n. Continuity, 64, 129 ff., 141 ff., 155 ff. of change, 106, 108, 130 ff. Correlation of mental and physical, 233. Counting, 164, 181, 187 ff., 203. Couturat, 40 n. Dante, 10. Darwin, 4, 11, 23, 30. Data, 65 ff., 211. “hard” and “soft,” 70 ff. Dates, 117. Definition, 204. Descartes, 5, 73, 238. Descriptions, 201, 214. Desire, 227, 235. Determinism, 233. Doubt, 237. Dreams, 85, 93. Duration, 146, 149. Earlier and later, 116. Effect, 220. Eleatics, 19. Empiricism, 37, 222. Enclosure, 114 ff., 120. Enumeration, 202. Euclid, 160, 164. Evellin, 169. Evolutionism, 4, 11 ff. Extension, 146, 149. External world, knowledge of, 63 ff. Fact, 51. atomic, 52. Finalism, 13. Form, logical, 42 ff., 185, 208. Fractions, 132, 179. Free will, 213, 227 ff. Frege, 5, 40, 199 ff. Galileo, 4, 59, 192, 194, 239, 240. Gaye, 169 n., 175, 177. Geometry, 5. Giles, 206 n. Greater and less, 195. Harvard, 4. Hegel, 3, 37 ff., 46, 166. “Here,” 73, 92. Hereditary properties, 195. Hippasos, 163, 237. Hui Tzŭ, 206. Hume, 217, 221. Hypotheses in philosophy, 239. Illusions, 85. Incommensurables, 162 ff., 237. Independence, 73, 74. causal and logical, 74, 75. Indiscernibility, 141, 148. Indivisibles, 160. Induction, 34, 222. mathematical, 195 ff. Inductiveness, 190, 195 ff. Inference, 44, 54. Infinite, vi, 64, 133, 149. historically considered, 155 ff. “true,” 179, 180. positive theory of, 185 ff. Infinitesimals, 135. Instants, 116 ff., 129, 151, 216. defined, 118. Instinct v. Reason, 20 ff. Intellect, 22 ff. Intelligence, how displayed by friends, 93. inadequacy of display, 96. Interpretation, 144. James, 4, 10, 13. Jourdain, 165 n. Jowett, 167. Judgment, 58. Kant, 3, 112, 116, 155 ff., 200. Knowledge about, 144. Language, bad, 82, 135. Laplace, 12. Laws of nature, 218 ff. Leibniz, 13, 40, 87, 186, 191. Logic, 201. analytic not constructive, 8. Aristotelian, 5. and fact, 53. inductive, 34, 222. mathematical, vi, 40 ff. mystical, 46. and philosophy, 8, 33 ff., 239. Logical constants, 208, 213. Mach, 123, 224. Macran, 39 n. Mathematics, 40, 57. Matter, 75, 101 ff. permanence of, 102 ff. Measurement, 164. Memory, 230, 234, 236. Method, deductive, 5. logical-analytic, v, 65, 211, 236 ff. Milhaud, 168 n., 169 n. Mill, 34, 200. Montaigne, 28. Motion, 130, 216. continuous, 133, 136. mathematical theory of, 133. perception of, 137 ff. Zeno's arguments on, 168 ff. Mysticism, 19, 46, 63, 95. Newton, 30, 146. Nietzsche, 10, 11. Noël, 169. Number, cardinal, 131, 186 ff. defined, 199 ff. finite, 160, 190 ff. inductive, 197. infinite, 178, 180, 188 ff., 197. reflexive, 190 ff. Occam, 107, 146. One and many, 167, 170. Order, 131. Parmenides, 63, 165 ff., 178. Past and future, 224, 234 ff. Peano, 40. Perspectives, 88 ff., 111. Philoponus, 171 n. Philosophy and ethics, 26 ff. and mathematics, 185 ff. province of, 17, 26, 185, 236. scientific, 11, 16, 18, 29, 236 ff. Physics, 101 ff., 147, 239, 242. descriptive, 224. verifiability of, 81, 110. Place, 86, 90. at and from, 92. Plato, 4, 19, 27, 46, 63, 165 n., 166, 167. Poincaré, 123, 141. Points, 113 ff., 129, 158. definition of, vi, 115. Pragmatism, 11. Prantl, 174. Predictability, 229 ff. Premisses, 211. Probability, 36. Propositions, 52. atomic, 52. general, 55. molecular, 54. Pythagoras, 19, 160 ff., 237. Race-course, Zeno's argument of, 171 ff. Realism, new, 6. Reflexiveness, 190 ff. Relations, 45. asymmetrical, 47. Bradley's reasons against, 6. external, 150. intransitive, 48. multiple, 50. one-one, 203. reality of, 49. symmetrical, 47, 124. transitive, 48, 124. Relativity, 103, 242. Repetitions, 230 ff. Rest, 136. Ritter and Preller, 161 n. Robertson, D. S., 160 n. Rousseau, 20. Royce, 50. Santayana, 46. Scepticism, 66, 67. Seeing double, 86. Self, 73. Sensation, 25, 75, 123. and stimulus, 139. Sense-data, 56, 63, 67, 75, 110, 141, 143, 213. and physics, v, 64, 81, 97, 101 ff., 140. infinitely numerous? 149, 159. Sense-perception, 53. Series, 49. compact, 132, 142, 178. continuous, 131, 132. Sigwart, 187. Simplicius, 170 n. Simultaneity, 116. Space, 73, 88, 103, 112 ff., 130. absolute and relative, 146, 159. antinomies of, 155 ff. perception of, 68. of perspectives, 88 ff. private, 89, 90. of touch and sight, 78, 113. Spencer, 4, 12, 236. Spinoza, 46, 166. Stadium, Zeno's argument of, 134 n., 175 ff. Subject-predicate, 45. Synthesis, 157, 185. Tannery, Paul, 169 n. Teleology, 223. Testimony, 67, 72, 82, 87, 96, 212. Thales, 3. Thing-in-itself, 75, 84. Things, 89 ff., 104 ff., 213. Time, 103, 116 ff., 130, 155 ff., 166, 215. absolute or relative, 146. local, 103. private, 121. Uniformities, 217. Unity, organic, 9. Universal and particular, 39 n. Volition, 223 ff. Whitehead, vi, 207. Wittgenstein, vii, 208 n. Worlds, actual and ideal, 111. possible, 186. private, 88. Zeller, 173. Zeno, 129, 134, 136, 165 ff. PRINTED BY NEILL AND CO., LTD., EDINBURGH. [1] Delivered as Lowell Lectures in Boston, in March and April 1914. [2] London and New York, 1912 (“Home University Library”). [3] The first volume was published at Cambridge in 1910, the second in 1912, and the third in 1913. [4] Appearance and Reality, pp. 32–33. [5] Creative Evolution, English translation, p. 41. [6] Cf. Burnet, Early Greek Philosophy, pp. 85 ff. [7] Introduction to Metaphysics, p. 1. [8] Logic, book iii., chapter iii., § 2. [9] Book iii., chapter xxi., § 3. [10] Or rather a propositional function. [11] The subject of causality and induction will be discussed again in Lecture VIII. [12] See the translation by H. S. Macran, Hegel's Doctrine of Formal Logic, Oxford, 1912. Hegel's argument in this portion of his “Logic” depends throughout upon confusing the “is” of predication, as in “Socrates is mortal,” with the “is” of identity, as in “Socrates is the philosopher who drank the hemlock.” Owing to this confusion, he thinks that “Socrates” and “mortal” must be identical. Seeing that they are different, he does not infer, as others would, that there is a mistake somewhere, but that they exhibit “identity in difference.” Again, Socrates is particular, “mortal” is universal. Therefore, he says, since Socrates is mortal, it follows that the particular is the universal—taking the “is” to be throughout expressive of identity. But to say “the particular is the universal” is self-contradictory. Again Hegel does not suspect a mistake but proceeds to synthesise particular and universal in the individual, or concrete universal. This is an example of how, for want of care at the start, vast and imposing systems of philosophy are built upon stupid and trivial confusions, which, but for the almost incredible fact that they are unintentional, one would be tempted to characterise as puns. [13] Cf. Couturat, La Logique de Leibniz, pp. 361, 386. [14] It was often recognised that there was some difference between them, but it was not recognised that the difference is fundamental, and of very great importance. [15] Encyclopædia of the Philosophical Sciences, vol. i. p. 97. [16] This perhaps requires modification in order to include such facts as beliefs and wishes, since such facts apparently contain propositions as components. Such facts, though not strictly atomic, must be supposed included if the statement in the text is to be true. [17] The assumptions made concerning time-relations in the above are as follows:— I. In order to secure that instants form a series, we assume: (a) No event wholly precedes itself. (An “event” is defined as whatever is simultaneous with something or other.) (b) If one event wholly precedes another, and the other wholly precedes a third, then the first wholly precedes the third. (c) If one event wholly precedes another, it is not simultaneous with it. (d) Of two events which are not simultaneous, one must wholly precede the other. II. In order to secure that the initial contemporaries of a given event should form an instant, we assume: (e) An event wholly after some contemporary of a given event is wholly after some initial contemporary of the given event. III. In order to secure that the series of instants shall be compact, we assume: (f) If one event wholly precedes another, there is an event wholly after the one and simultaneous with something wholly before the other. This assumption entails the consequence that if one event covers the whole of a stretch of time immediately preceding another event, then it must have at least one instant in common with the other event; i.e. it is impossible for one event to cease just before another begins. I do not know whether this should be regarded as inadmissible. For a mathematico-logical treatment of the above topics, cf. N. Wilner, “A Contribution to the Theory of Relative Position,” Proc. Camb. Phil. Soc., xvii. 5, pp. 441–449. [18] The above paradox is essentially the same as Zeno's argument of the stadium which will be considered in our next lecture. [19] See next lecture. [20] Monist, July 1912, pp. 337–341. [21] “Le continu mathématique,” Revue de Métaphysique et de Morale, vol. i. p. 29. [22] In what concerns the early Greek philosophers, my knowledge is largely derived from Burnet's valuable work, Early Greek Philosophy (2nd ed., London, 1908). I have also been greatly assisted by Mr D. S. Robertson of Trinity College, who has supplied the deficiencies of my knowledge of Greek, and brought important references to my notice. [23] Cf. Aristotle, Metaphysics, M. 6, 1080b, 18 sqq., and 1083b, 8 sqq. [24] There is some reason to think that the Pythagoreans distinguished between discrete and continuous quantity. G. J. Allman, in his Greek Geometry from Thales to Euclid, says (p. 23): “The Pythagoreans made a fourfold division of mathematical science, attributing one of its parts to the how many, τὸ πόσον, and the other to the how much, τὸ πηλίκον; and they assigned to each of these parts a twofold division. For they said that discrete quantity, or the how many, either subsists by itself or must be considered with relation to some other; but that continued quantity, or the how much, is either stable or in motion. Hence they affirmed that arithmetic contemplates that discrete quantity which subsists by itself, but music that which is related to another; and that geometry considers continued quantity so far as it is immovable; but astronomy (τὴν σφαιρικήν) contemplates continued quantity so far as it is of a self-motive nature. (Proclus, ed. Friedlein, p. 35. As to the distinction between τὸ πηλίκον, continuous, and τὸ πόσον, discrete quantity, see Iambl., in Nicomachi Geraseni Arithmeticam introductionem, ed. Tennulius, p. 148.)” Cf. p. 48. [25] Referred to by Burnet, op. cit., p. 120. [26] iv., 6. 213b, 22; H. Ritter and L. Preller, Historia Philosophiæ Græcæ, 8th ed., Gotha, 1898, p. 75 (this work will be referred to in future as “R. P.”). [27] The Pythagorean proof is roughly as follows. If possible, let the ratio of the diagonal to the side of a square be m/n, where m and n are whole numbers having no common factor. Then we must have m2 = 2n2. Now the square of an odd number is odd, but m2, being equal to 2n2, is even. Hence m must be even. But the square of an even number divides by 4, therefore n2, which is half of m2, must be even. Therefore n must be even. But, since m is even, and m and n have no common factor, n must be odd. Thus n must be both odd and even, which is impossible; and therefore the diagonal and the side cannot have a rational ratio. [28] In regard to Zeno and the Pythagoreans, I have derived much valuable information and criticism from Mr P. E. B. Jourdain. [29] So Plato makes Zeno say in the Parmenides, apropos of his philosophy as a whole; and all internal and external evidence supports this view. [30] “With Parmenides,” Hegel says, “philosophising proper began.” Werke (edition of 1840), vol. xiii. p. 274. [31] Parmenides, 128 A–D. [32] This interpretation is combated by Milhaud, Les philosophes-géomètres de la Grèce, p. 140 n., but his reasons do not seem to me convincing. All the interpretations in what follows are open to question, but all have the support of reputable authorities. [33] Physics, vi. 9. 2396 (R.P. 136–139). [34] Cf. Gaston Milhaud, Les philosophes-géomètres de la Grèce, p. 140 n.; Paul Tannery, Pour l'histoire de la science hellène, p. 249; Burnet, op. cit., p. 362. [35] Cf. R. K. Gaye, “On Aristotle, Physics, Z ix.” Journal of Philology, vol. xxxi., esp. p. 111. Also Moritz Cantor, Vorlesungen über Geschichte der Mathematik, 1st ed., vol. i., 1880, p. 168, who, however, subsequently adopted Paul Tannery's opinion, Vorlesungen, 3rd ed. (vol. i. p. 200). [36] “Le mouvement et les partisans des indivisibles,” Revue de Métaphysique et de Morale, vol. i. pp. 382–395. [37] “Le mouvement et les arguments de Zénon d'Élée,” Revue de Métaphysique et de Morale, vol. i. pp. 107–125. [38] Cf. M. Brochard, “Les prétendus sophismes de Zénon d'Élée,” Revue de Métaphysique et de Morale, vol. i. pp. 209–215. [39] Simplicius, Phys., 140, 28 D (R.P. 133); Burnet, op. cit., pp. 364–365. [40] Op. cit., p. 367. [41] Aristotle's words are: “The first is the one on the non-existence of motion on the ground that what is moved must always attain the middle point sooner than the end-point, on which we gave our opinion in the earlier part of our discourse.” Phys., vi. 9. 939B (R.P. 136). Aristotle seems to refer to Phys., vi. 2. 223AB [R.P. 136A]: “All space is continuous, for time and space are divided into the same and equal divisions…. Wherefore also Zeno's argument is fallacious, that it is impossible to go through an infinite collection or to touch an infinite collection one by one in a finite time. For there are two senses in which the term ‘infinite’ is applied both to length and to time, and in fact to all continuous things, either in regard to divisibility, or in regard to the ends. Now it is not possible to touch things infinite in regard to number in a finite time, but it is possible to touch things infinite in regard to divisibility: for time itself also is infinite in this sense. So that in fact we go through an infinite, [space] in an infinite [time] and not in a finite [time], and we touch infinite things with infinite things, not with finite things.” Philoponus, a sixth-century commentator (R.P. 136A, Exc. Paris Philop. in Arist.