1 Metaph. xii. 4.
2 Diog. Laert. Vit. Plat.
3 T. ii. p. 16, c, d. ed. Bekker, t. v. p. 437.
4 See the remarks on this phrase in the next chapter.
5 Hist. Ind. Sc. b. iii. c. ii.
6 This matter is further discussed in the Appendix, Essay A.
7 These matters are further discussed in the Appendix, Essay B.
8 See Appendix, Essay B.
9 Hist. Ind. Sc. b. ii. Additions to 3rd Ed.
10 See these views further discussed in the Appendix, Essay C.
11 Metaph. xii. 4.
12 Hist. Ind. Sc. b. i. c. iii. sect. 2.
13 Analyt. Prior. i. 30.
14 Analyt. Post. i. 18.
15 Analyt. Prior. ii. 23, περι της επαγωγης.
16 Analyt. Post. ii. 19.
17 But the best reading seems to be not ἔν τι but ἔτι: and the clause must be rendered "both to perceive and to retain the perception in the mind." This correction does not disturb the general sense of the passage, that the first principles of science are obtained by finding the One in the Many.
18 Analyt. Post. i. 34.
19 Ibid. ii. 19.
20 Analyt. Prior. ii. 25.
21 See on this subject Appendix, Essay D.
22 See the chapter on Certain Characteristics of Scientific Induction in the Phil. Ind. Sc. or in the Nov. Org. Renov.
23 Phil. Ind. Sc. b. viii. c. i. art. 11, or Hist. Sc. Id. b. viii.
24 B. i. c. xi. sect. 2.
25 B. iii. c. i. sect. 9.
26 De Cælo, ii. 13.
27 Ibid. ii. 10.
28 xii. 8.
29 B. xvi. c. vi.
30 On the Classification of Mammalia, &c.: a Lecture delivered at Cambridge, May 10, 1859, p. 3.
31 B. i. c. xi.
32 History of Scientific Ideas, and Novum Organum Renovatum.
33 The remainder of this chapter is new in the present edition.
34 Hist. of Greece, Part ii. chap. 68.
35 De Antiqua Medicina, c. 20.
36 Lib. i. c. 9.
37 De Elem. i. 6.
38 In former editions I have not done justice to this passage.
39 Hist. Ind. Sc. Addition to Introduction in Third Edition.
40 Lib. i. Fast.
41 Hist. Nat. i. 75.
42 Quæst. Nat. vii. 25.
43 Quæst. Nat. vii. 30, 31.
44 Ibid. iii. 7.
45 Hist. Ind. Sc. b. iii. c. iv. sect. 8.
46 Ibid. b. ix. c. ii.
47 See Hist. Ind. Sc. b. iv. c. i.
48 See the opinion of Aquinas, in Degerando, Hist. Com. des Syst. iv. 499; of Duns Scotus, ibid. iv. 523.
49 Liber Excerptionum, Lib. i. c. i.
50 Tr. Ex. Lib. i. c. vii.
51 Tenneman, viii. 461.
52 Mores Catholici, or Ages of Faith, viii. p. 247.
53 Tenneman, viii. 460.
54 If there were any doubt on this subject, we might refer to the writers who afterwards questioned the supremacy of Aristotle, and who with one voice assert that an infallible authority had been claimed for him. Thus Laurentius Valla: "Quo minus ferendi sunt recentes Peripatetici, qui nullius sectæ hominibus interdicunt libertate ab Aristotele dissentiendi, quasi sophos hic, non philosophus." Pref. in Dial. (Tenneman, ix. 29.) So Ludovicus Vives: "Sunt ex philosophis et ex theologis qui non solum quo Aristoteles pervenit extremum esse aiunt naturæ, sed quâ pervenit eam rectissimam esse omnium et certissimam in natura viam." (Tenneman, ix. 43.) We might urge too, the evasions practised by philosophical Reformers, through fear of the dogmatism to which they had to submit; for example, the protestation of Telesius at the end of the Proem to his work, De Rerum Natura: "Nec tamen, si quid eorum quæ nobis posita sunt, sacris literis, Catholicæve ecclesiæ decretis non cohæreat, tenendum id, quin penitus rejiciendum asseveramus contendimusque. Neque enim humana modo ratio quævis, sed ipse etiam sensus illis posthabendus, et si illis non congruat, abnegandus omnino et ipse etiam est sensus."
55 Ages of Faith, viii. 247: to the author of which I am obliged for this quotation.
56 Algazel. See Hist. Ind. Sc. b. iv. c. i.
57 Tenneman, viii. 830.
58 Degerando, iv. 535.
59 Leibnitz's expressions are, (Op. t. vi. p. 16): "Quand j'étais jeune, je prenois quelque a l'Art de Lulle, mais je crus y entrevoir bien des défectuosités, dont j'ai dit quelque chose dans un petit Essai d'écolier intitulé De Arte Combinatoria, publié en 1666, et qui a été réimprimé après malgré moi. Mais comme je ne méprise rien facilement, excepté les arts divinatoires que ne sont que des tromperies toutes pures, j'ai trouvé quelque chose d'estimable encore dans l'Art de Lulle."
60 Works, vii. 296.
61 Fratris Rogeri Bacon, Ordinis Minorum, Opus Majus, ad Clementem Quartum, Pontificem Romanum, ex MS. Codice Dubliniensi cum aliis quibusdam collato, nunc primum edidit S. Jebb, M.D. Londini, 1733.
62 Opus Majus, Præf.
63 Contents of Roger Bacon's Opus Majus.
Part I. On the four causes of human ignorance:—Authority, Custom, Popular Opinion, and the Pride of supposed Knowledge.
Part II. On the source of perfect wisdom in the Sacred Scripture.
Part III. On the Usefulness of Grammar.
Part IV. On the Usefulness of Mathematics.
(1) The necessity of Mathematics in Human Things (published separately as the Specula Mathematica).
(2) The necessity of Mathematics in Divine Things.—1o. This study has occupied holy men: 2o. Geography: 3o. Chronology: 4o. Cycles; the Golden Number, &c.: 5o. Natural Phenomena, as the Rainbow: 6o. Arithmetic: 7o. Music.
(3) The necessity of Mathematics in Ecclesiastical Things. 1o. The Certification of Faith: 2o. The Correction of the Calendar.
(4) The necessity of Mathematics in the State.—1o. Of Climates: 2o. Hydrography: 3o. Geography: 4o. Astrology.
Part V. On Perspective (published separately as Perspectiva).
(1) The organs of vision.
(2) Vision in straight lines.
(3) Vision reflected and refracted.
(4) De multiplicatione specierum (on the propagation of the impressions of light, heat, &c.)
Part VI. On Experimental Science.
64 Op. Maj. p. 1.
65 Ibid. p. 2.
66 Ibid. p. 10.
67 I will give a specimen. Opus Majus, c. viii. p. 35: "These two kinds of philosophers, the Ionic and Italic, ramified through many sects and various successors, till they came to the doctrine of Aristotle, who corrected and changed the propositions of all his predecessors, and attempted to perfect philosophy. In the [Italic] succession, Pythagoras, Archytas Tarentinus and Timæus are most prominently mentioned. But the principal philosophers, as Socrates, Plato, and Aristotle, did not descend from this line, but were Ionics and true Greeks, of whom the first was Thales Milesius.... Socrates, according to Augustine in his 8th book, is related to have been a disciple of Archelaus. This Socrates is called the father of the great philosophers, since he was the master of Plato and Aristotle, from whom all the sects of philosophers descended.... Plato, first learning what Socrates and Greece could teach, made a laborious voyage to Egypt, to Archytas of Tarentum and Timæus, as says Jerome to Paulinus. And this Plato is, according to holy men, preferred to all philosophers, because he has written many excellent things concerning God, and morality, and a future life, which agree with the divine wisdom of God. And Aristotle was born before the death of Socrates, since he was his hearer for three years, as we read in the life of Aristotle.... This Aristotle, being made the master of Alexander the Great, sent two thousand men into all regions of the earth, to search out the nature of things, as Pliny relates in the 8th book of his Naturalia, and composed a thousand books, as we read in his life."
68 Ibid. p. 36.
69 Autonomaticè.
70 Op. Maj. p. 46.
71 See Pref. to Jebb's edition. The passages, there quoted, however, are not extracts from the Opus Majus, but (apparently) from the Opus Minus (MS. Cott. Tib. c. 5.) "Si haberem potestatem supra libros Aristotelis, ego facerem omnes cremari; quia non est nisi temporis amissio studere in illis, et causa erroris, et multiplicatio ignorantiæ ultra id quod valeat explicari.... Vulgus studentum cum capitibus suis non habet unde excitetur ad aliquid dignum, et ideo languet et asininat circa male translata, et tempus et studium amittit in omnibus et expensas."
72 Part ii.
73 Parts iv. v. and vi.
74 Op. Maj. p. 476.
75 Op. Maj. p. 15.
76 Ibid. p. 445, see also p. 448. "Scientiæ aliæ sciunt sua principia invenire per experimenta, sed conclusiones per argumenta facta ex principiis inventis. Si vero debeant habere experientiam conclusionum suarum particularem et completam, tunc oportet quod habeant per adjutorium istius scientiæ nobilis (experimentalis)."
77 Op. Maj. p. 60.
78 Ibid. p. 64.
79 "Veritates magnificas in terminis aliarum scientiarum in quas per nullam viam possunt illæ scientiæ, hæc sola scientiarum domina speculativarum, potest dare." Op. Maj. p. 465.
80 One of the ingredients of a preparation here mentioned, is the flesh of a dragon, which it appears is used as food by the Ethiopians. The mode of preparing this food cannot fail to amuse the reader. "Where there are good flying dragons, by the art which they possess, they draw them out of their dens, and have bridles and saddles in readiness, and they ride upon them, and make them bound about in the air in a violent manner, that the hardness and toughness of the flesh may be reduced, as boars are hunted and bulls are baited before they are killed for eating." Op. Maj. p. 470.
81 Op. Maj. p. 473.
82 Quoted by Jebb, Pref. to Op. Maj.
83 Mosheim, Hist. iii. 161.
84 Op. Maj. p. 57.
85 Mosheim, iii. 161.
86 Gratian published the Decretals in the twelfth century; and the Canon and Civil Law became a regular study in the universities soon afterwards.
87 Tenneman, ix. 4.
88 Tenneman, ix. 25.
89 "Jam nobis manifestum est terram istam in veritate moveri," &c.—De Doctâ Ignorantiâ, lib. ii. c. xii.
90 De Doct. Ignor. lib. i. c. i.
91 De Conjecturis, lib. i. c. iii. iv.
92 Born in 1433.
93 Born 1529, died 1597.
94 Aristoteles Exotericus, p. 50.
95 Tiraboschi, t. vii. pt. ii. p. 411.
96 "Franciscus Patricius, novam veram integram de universis conditurus philosophiam, sequentia uti verissima prænuntiare est ausus. Prænunciata ordine persecutus, divinis oraculis, geometricis rationibus, clarissimisque experimentis comprobavit.
Ante primum nihil,
Post primum omnia,
A principio omnia," &c.
His other works are Panaugia, Pancosmia, Dissertations Peripateticæ.
97 Tiraboschi, t. vii. pt. ii. p. 411.
98 Dissert. Perip. t. ii. lib. v. sub fin.
99 Tenneman, ix. 148.
100 Tenneman, ix. 167.
101 Ibid. 158.
102 Agrippa, De Occult. Phil. lib. i. c. l.
103 Written in 1526.
104 Philip Aurelius Theophrastus Bombastus von Hohenheim, also called Paracelsus Eremita, born at Einsiedlen in Switzerland, in 1493.
105 Hist. Sc. Id. b. ix. c. 2. sect. 1. The Mystical School of Biology.
106 Tenneman, ix. 221.
107 Tenneman, ix. 265.
108 Bernardini Telesii Consentini De Rerum Natura juxta propria Principia.
109 I take this account from Tenneman: this Proem was omitted in subsequent editions of Telesius, and is not in the one which I have consulted. Tenneman, Gesch. d. Phil. ix. 280.
110 Proem.
111 "De Principiis atque Originibus secundum fabulas Cupidinis et Cœli: sive Parmenidis et Telesii et præcipuè Democriti Philosophia tractata in Fabula de Cupidine."
112 "Talia sunt qualia possunt esse ea quæ ab intellectu sibi permisso, nec ab experimentis continenter et gradatim sublevato, profecta videntur."
113 Thom. Campanella de Libris propriis, as quoted in Tenneman, ix. 291.
114 Economisti Italiani, t. i. p. xxxiii.
115 Tenneman, ix. 305.
116 Hist. Ind. Sc. b. xvi. c. iii. sect. 2.
117 Ibid. b. xvii. c. ii. sect. 1.
118 Quæst. Peripat. i. 1.
119 Tenneman, ix. 108.
120 Hist. Ind. Sc. b. v. c. iii. sect. 2.
121 Tenneman, ix. 420. "Quæcunque ab Aristotele dicta essent commenticia esse." Freigius, Vita Petri Rami, p. 10.
122 Rami, Animadv. Aristot. i. iv.
123 See Hist. Ind. Sc. b. iv. c. iv. sect. 4.
124 Tenneman, ix. 230.
125 Ibid. 108.
126 Tenneman, ix. 246.
127 Melancthon, De Anima, p. 207, quoted in Tenneman, ix. 121.
128 His works have never been published, and exist in manuscript in the library of the Institute at Paris. Some extracts were published by Venturi, Essai sur les Ouvrages de Leonard da Vinci. Paris, 1797.
129 Leonardo died in 1520, at the age of 78.
130 Paul III. in 1543.
131 Hist. Ind. Sc. b. v. c. ii.
132 Born 1537, died 1619.
133 Hist. Ind. Sc. b. xvii. c. ii. sect. 1.
134 Fabricius, De Motu Locali, p. 182.
135 p. 199.
136 Speculationum Liber, p. 195.
137 Ibid. p. 169.
138 Gulielmi Gilberti, Colcestriensis, Medici Londinensis, De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure, Physiologia Nova, plurimis et Argumentis et Experimentis demonstrata.
139 Hist. Ind. Sc. b. xii. c. i.
140 Pref.
141 De Magnete, lib. vi. c. 3, 4.
142 Nov. Org. b. i.
143 B. i. Aph. 64.
144 Vol. ix. 185.
145 De Magnete, p. 60.
146 B. iii. c. 4.
147 Nov. Org. b. ii. Aph. 48.
148 Drinkwater's Life of Galileo, p. 18.
149 Life of Galileo, p. 9.
150 Hist. Ind. Sc. b. vi. c. ii. sect. 5.
151 Life of Galileo, p. 29.
152 Ibid. p. 33.
153 Il Saggiatore, ii. 247.
154 Il Saggiatore, ii. 200.
155 Ibid. i. 501.
156 Hist. Ind. Sc. b. vi. c. ii. sect. 2.
157 Hist. Ind. Sc. b. vi. c. ii. sect. 4.
158 Ibid. b. v. c. iv. sect. 1.
159 De Stell. Mart. p. iv. c. 51 (1609); Drinkwater's Kepler, p. 33.
160 Published 1604. Hist. Ind. Sc. b. ix. c. ii.
161 Hist. Ind. Sc. b. v. c. iv. sect. i.
162 Hist. Ind. Sc. b. vii. c. vi. sect 1.
163 De Stell. Mart. p. 11. c. 19.
164 Hist. Ind. Sc. b. ii. c. iv. sect. 6.
165 Ibid. sect. 8.
166 Montucla, i. 566.
167 De Augm. lib. iv. c. 1.
168 And in other passages: thus, "Ego enim buccinator tantum pugnam non ineo." Nov. Org. lib. iv. c. i.
169 Lib. 1. Aphor. 78 et seq.
170 Aug. Sc. Lib. iii. c. 4. p. 194. So in other places, as Nov. Org. i. Aph. 104. "De scientiis tum demum bene sperandum est quando per scalam veram et per gradus continuos, et non intermissos aut hiulcos a particularibus ascendetur ad axiomata minora, et deinde ad media, alia aliis superiora, et postremo demum ad generalissima."
171 Nov. Org. 1. Aph. 22.
172 Ib. Aph. 20.
173 1 Ax. 15.
174 Nov. Org. lib. ii. Aph. 19.
175 Inst. Mag. par. iii. (vol. viii. p. 244).
176 Hist. Ind. Sc. b. x. c. i.
177 Ib. c. iv.
178 Nov. Org. lib. i. Aph. 61.
179 Nov. Org. lib. ii. Aph. 10.
180 Aph. 11.
181 Aph. 15, p. 105.
182 Page 110.
183 Herschel, On the Study of Nat. Phil. Art. 192.
184 Nov. Org. lib. i. Aph. 40.
185 Nov. Org. lib. i. Ax. 103.
186 Edinb. Rev. No. cxxxii. p. 65.
187 Ib.
188 Pref. to the Nat. Hist. i. 243.
189 Nov. Org. lib. i. Aph. 19.
190 Ibid. lib. i. Aph. 20.
191 Aph. 27.
192 Ib. 28.
193 Aph. 104. So Aph. 105. "In constituendo axiomate forma inductionis alia quam adhuc in usu fuit excogitanda est," &c.
194 Ep. ad P. Fulgentium. Op. x. 330.
195 Nov. Org. i. Aph. 113.
196 See the motto to Kant's Kritik der Reinen Vernunft.
197 Œuvres Philosophiques de Bacon, &c. par M. N. Bouillet, 3 Tomes.
Examen de la Philosophie de Bacon (Œuvres Posthumes du Comte J. de Maistre).
Bacon, sa Vie, son Temps, sa Philosophie, par Charles de Remusat.
Histoire de la Vie et des Ouvrages de François Bacon, par J. B. de Vaugelles.
Franz Baco von Verulam, von Kuno Fischer.
The Works of Francis Bacon, collected and edited by James Spedding, Robert Leslie Ellis, and Douglas Denon Heath.
198 Note to Aph. xviii.
199 Pref. to the Parasceue, Vol. i. p. 382.
200 Anatomical Exercitations concerning the Generation of Living Creatures, 1653. Preface.
201 He used similar expressions in conversation. George Ent, who edited his Generation of Animals, visited him, "at that time residing not far from the city; and found him very intent upon the perscrutation of nature's works, and with a countenance as cheerful, as mind unperturbed; Democritus-like, chiefly searching into the cause of natural things." In the course of conversation the writer said, "It hath always been your choice about the secrets of Nature, to consult Nature herself." "'Tis true," replied he; "and I have constantly been of opinion that from thence we might acquire not only the knowledge of those less considerable secrets of Nature, but even a certain admiration of that Supreme Essence, the Creator. And though I have ever been ready to acknowledge, that many things have been discovered by learned men of former times; yet do I still believe that the number of those which remain yet concealed in the darkness of impervestigable Nature is much greater. Nay, I cannot forbear to wonder, and sometimes smile at those, who persuade themselves, that all things were so consummately and absolutely delivered by Aristotle, Galen, or some other great name, as that nothing was left to the superaddition of any that succeeded."
202 Lib. i. c. 2, 3.
203 Anal. Post. ii.
204 Pars iii. p. 45.
205 See Hist. Ind. Sc. b. vi. c. ii.
206 Cap. i. ii.
207 Hist. Ind. Sc. b. ix. c. ii.
208 Meteorum, c. viii. p. 187.
209 Mackintosh, Dissertation on Ethical Science.
210 Hist. Ind. Sc. b. vii. c. i.
211 Castelli, Torricelli, Viviani, Baliani, Gassendi, Mersenne, Borelli, Cavalleri.
212 De Plenitudine Mundi, in qua defenditur Cartesiana Philosophia contra sententias Francisci Baconi, Th. Hobbii et Sethi Wardi.
213 Bacon's Works, vol. ii. 111.
214 Hist. Ind. Sc. b. vii. c. i.
215 Nov. Org. lib. ii. Aph. 2.
216 Ib. lib. ii. Aph. 45.
217 Optics, qu. 31, near the end.
218 Qu. 28.
219 Hist. Ind. Sc. b. v. and b. vii.
220 Optics, qu. 31.
221 History of Ideas, b. iii. c. x.
222 Ibid. b. iii. c. ix. x. xi.
223 Opticks, qu. 31.
224 Nov. Org. l. ii. Aph. 2. "Licet enim in natura nihil existet præter corpora individua, edentia actus puros individuos ex lege; in doctrinis tamen illa ipsa lex, ejusque inquisitio, et inventio, et explicatio, pro fundamento est tam ad sciendum quam ad operandum. Eam autem legem, ejusque paragraphos, formarum nomine intelligimus; præsertim cum hoc vocabulum invaluerit, et familiariter occurrat."
Aph. 17. "Eadem res est forma calidi vel forma luminis, et lex calidi aut lex luminis."
225 Essay, b. xi. c. iv. sect. 3.
226 Ibid. c. xiii. sect. 22.
227 History of Ideas, b. iii. c. iii. Modern Opinions respecting the Idea of Cause.
228 Ibid. b. i. c. iv.
229 Langue des Calculs, p. 1.
230 Grammaire, p. xxxvi.
231 Since the selection and construction of terms is thus a matter of so much consequence in the formation of science, it is proper that systematic rules, founded upon sound principles, should be laid down for the performance of this operation. Some such rules are accordingly suggested in b. iv. of the Nov. Org. Ren.
232 Disc. Prélim. p. viii.
233 Helvetius Sur l'Homme, c. xxiii.
234 P. xiii.
235 See Mr.Sharpe's Essays.
236 Price's Essays, p. 16.
237 P. 18.
238 Reid, Essays on the Powers of the Human Mind, iii. 31.
239 Stewart, Outlines of Moral Phil. p. 138.
240 Whately, Polit. Econ. p. 76.
241 Cousin, Fragmens Philosophiques, i. 53.
242 Ibid. i. 67.
243 See also the vigorous critique of Locke's Essay, by Lemaistre, Soirées de St. Petersbourg.
244 Ampère, Essai, p. 210.
245 Kritik der Reinen Vernunft, Pref. p. xv.
246 The sensational system never acquired in Germany the ascendancy which it obtained in England and France; but I am compelled here to pass over the history of philosophy in Germany, except so far as it affects ourselves.
247 i. p. 14.
248 i. p. 7.
249 Hist. Ind. Sc. b. xi. c. vii.
250 P. 15.
251 P. 16.
252 M. Comte's statement is so entirely at variance with the fact that I must quote it here. (Phil. Pos. vol. i. p. 705.)
"Le second théorème général de dynamique consiste dans le célèbre et important principe des aires, dont le première idée est due à Kepler, qui découvrit et démontra forte simplement cette propriété pour le cas du mouvement d'une molecule unique, ou en d'autres terms, d'un corps dont tous les points se meuvent identiquement. Kepler établit, par les considérations les plus élémentaires, qui si la force accélératrice totale dont une molecule est animée tend constamment vers un point fixé, le rayon vecteur du mobile décrit autour de ce point des aires égales en temps egaux, de telle sorte que l'aire décrite au bout d'un temps quelconque croît proportionellement à ce temps. Il fit voir en outre que réciproquement, si une semblable relation a été vérifiée dans le mouvement d'un corps par rapport à un certain point, c'est une preuve suffisante de l'action sur le corps d'un force dirigée sans cesse vers ce point."
There is not a trace of the above propositions in the work De Stellâ Martis, which contains Kepler's discovery of his law, nor, I am convinced, in any other of Kepler's works. He is everywhere constant to his conceptions of the magnetic virtue residing in the sun, by means of which the sun, revolving on his axis, carries the planets round with him. M. Comte's statement so exactly expresses Newton's propositions, that one is led to suspect some extraordinary mistake, by which what should have been said of the one was transferred to the other.
253 Vol. ii. p. 433.
254 Vol. ii. 640.
255 I venture to offer this problem;—to express the laws of the phenomena of diffraction without the hypothesis of undulations;—as a challenge to any one who holds such hypothesis to be unphilosophical.
256 ii. p. 641.
257 ii. p. 673.
258 Hist. Ind. Sc. ii. 489, b. x. c. i.
259 ii. p. 561.
260 i. 50.
261 i. 41.
262 ii. 433.
263 Phil. Pos. ii. 392-398.
264 [A System of Logic, Ratiocinative and Inductive, being a connected view of the Principles of Evidence, and of the Methods of Scientific Investigation. By John Stuart Mill.]
265 These Remarks were published in 1849, under the title Of Induction, with especial reference to Mr. J. S. Mill's System of Logic.
266 My references are throughout (except when otherwise expressed) to the volume and the page of Mr. Mill's first edition of his Logic.
267 On this subject see an Essay On the Transformation of Hypotheses, given in the Appendix.
268 B. vii. c. iii. sect. 3.
269 B. iii. c. ix. art. 7.
270 B. i. c. iii.
271 B. iii. c. viii.
272 Discourse, Art. 192.
273 B. xi. c. xi.
274 Phil. b. xiii. c. ix. art. 7.
275 B. xiii. c. viii.
276 Given also in the Phil. Ind. Sc. b. xiii. c. vii. sect. 17.
277 Ibid. b. vi. c. iv.
278 See Hist. Ind. Sc. b. xii. note D, in the second edition.
279 There are some points in my doctrines on the subject of the Classificatory Sciences to which Mr. Mill objects, (ii. 314, &c.), but there is nothing which I think it necessary to remark here, except one point. After speaking of Classification of organized beings in general, Mr. Mill notices (ii. 321) as an additional subject, the arrangement of natural groups into a Natural Series; and he says, that "all who have attempted a theory of natural arrangement, including among the rest Mr. Whewell, have stopped short of this: all except M. Comte." On this I have to observe, that I stopped short of, or rather passed by, the doctrine of a Series of organized beings, because I thought it bad and narrow philosophy: and that I sufficiently indicated that I did this. In the History (b. xvi. c. vi.) I have spoken of the doctrine of Circular Progression propounded by Mr. Macleay, and have said, "so far as this view negatives a mere linear progression in nature, which would place each genus in contact with the preceding and succeeding ones, and so far as it requires us to attend to the more varied and ramified resemblances, there can be no doubt that it is supported by the result of all the attempts to form natural systems." And with regard to the difference between Cuvier and M. de Blainville, to which Mr. Mill refers (ii. 321), I certainly cannot think that M. Comte's suffrage can add any weight to the opinion of either of those great naturalists.
280 Hist. Ind. Sc. b. x. note (VA) in the second edition.
281 B. xi. c. v. art. 11.
282 I have given elsewhere (see last chapter) reasons why I cannot assign to M. Comte's Philosophie Positive any great value as a contribution to the philosophy of science. In this judgment I conceive that I am supported by the best philosophers of our time. M. Comte owes, I think, much of the notice which has been given to him to his including, as Mr. Mill does, the science of society and of human nature in his scheme, and to his boldness in dealing with these. He appears to have been received with deference as a mathematician: but Sir John Herschel has shown that a supposed astronomical discovery of his is a mere assumption. I conceive that I have shown that his representation of the history of science is erroneous, both in its details and in its generalities. His distinction of the three stages of sciences, the theological, metaphysical, and positive, is not at all supported by the facts of scientific history. Real discoveries always involve what he calls metaphysics; and the doctrine of final causes in physiology, the main element of science which can properly be called theological, is retained at the end, as well as the beginning of the science, by all except a peculiar school.
283 I have also, in the same place, given the Inductive Pyramid for the science of Optics. These Pyramids are necessarily inverted in their form, in order that, in reading in the ordinary way, we may proceed to the vertex. Phil. Ind. Sc. b. xi. c. vi.
284 Cosmos, vol. ii. note 35.
285 The reader will probably recollect that as Induction means the inference of general propositions from particular cases, Deduction means the inference by the application of general propositions to particular cases, and by combining such applications; as when from the most general principles of Geometry or of Mechanics, we prove some less general theorem; for instance, the number of the possible regular solids, or the principle of vis viva.
286 B. vi. c. v.
287 c. vi.
288 Hist. b. vi. c. vi. sect. 13.
289 Hist. Ind. Sc. b. viii.
290 Reprinted in the Appendix to this volume.
291 Phil. Pos. t. iv. p. 264.
292 Logic, b. vi. c. 3.
293 Jones, On Rent, 1833.
294 Literary Remains, 1859.
295 The substance of this and the next chapter was printed as a communication to the Cambridge Phil. Soc. in 1840.
296 Or in the earlier editions, in the Philosophy of the Inductive Sciences.
297 Phil. of Biol. c. v.
298 Hist. Ind. Sc. b. ix. c. iii.
299 Ibid. b. vii. c. ii.
300 Sir W. Hamilton's Note on the Philosophy of the Unconditioned.
301 Werenfels in Mr. Mansel's Bampton Lectures, lect. ii. Note 15.
302 Scholium Generale at the end of the Principia.
303 B. iv. c. i.
304 Reid's Works, Supplementary Dissertation D.
305 Hist. Sc. Id. b. iii.
306 Hist. Sc. Id. b. vi. c. iii.
307 The remarks contained in this chapter have for the most part been already printed and circulated in a Letter to the Author of Prolegomena Logica, 1852.
308 Biographical History of Philosophy, 1846. In a more recent edition the author of this work has modified his expressions, but still employs himself in arguing against Dr. Whewell, in order to overthrow Kant. So far as his arguments affect my philosophy, they are, as I conceive, answered in the various expositions which I have given of that philosophy.
309 B. ii. The Philosophy of the Pure Sciences. Chap. ii. Of the Idea of Space. Chap. iii. Of some peculiarities of the Idea of Space. Chap. vii. Of the Idea of Time. Chap. viii. Of some peculiarities of the Idea of Time.
310 Prolegomena Logica, by H. L. Mansel, M.A. 1851.
311 Logic, i p. 273, 3rd edit.
312 No. 193, p. 29.
313 Prol. Log. p. 123.
314 See Phil. Ind. Sc. b. vi. c. iii.
315 Kant.
316 Republished as The History of Scientific Ideas.
317 Given in the Novum Organon Renovatum.
318 Nov. Org. Ren. Aph. cv.
319 Hist. Sc. Id. b. ix. c. vi.
320 Hist. Ind. Sc. b. xviii. c. vi. sect. 5
321 P. 116. "No amount of human knowledge can be adequate which does not solve the phenomena of these absolute certainties."
322 Prof. Butler, Lect. ix. Second Series, p. 136, appears to think that Plato had sufficient grounds (of a theological kind) for the assumption of such Ideas; but I see no trace of them.
323 I am aware that this translation is different from the common translation. It appears to me to be consistent with the habit of the Greek language. It slightly leans in favour of my view; but I do not conceive that the argument would be perceptibly weaker, if the common interpretation were adopted.
324 In the First Alcibiades, Pythodorus is mentioned as having paid 100 minæ to Zeno for his instructions (119 A).
325 P. 183 e.
326 Deip. xi. c. 15, p. 105.
327 Accedit et illud quod naturalis philosophia in iis ipsis viris, qui ei incubuerunt, vacantem et integrum hominem, præsertim his recentioribus temporibus, vix nacta sit; nisi forte quis monachi alicujus in cellula, aut nobilis in villula lucubrantis, exemplum adduxerit; sed facta est demum naturalis philosophia instar transitus cujusdam et pontisternii ad alia. Atque magna ista scientiarum mater ad officia ancillæ detrusa est; quæ medicinæ aut mathematicis operibus ministrat, et rursus quæ adolescentium immatura ingenia lavat et imbuat velut tinctura quadam prima, ut aliam postea felicius et commodius excipiant.
328 μεταξὺ οἰκονομίας καὶ χρεματισμοῦ, between house-keeping and money-getting.
329 τὸ περὶ τοὺς λόγους.
330 The Sciences are to draw the mind from that which grows and perishes to that which really is: μάθημα ψυχῆς ὁλκὸν ἀπὸ τοῦ γιγνομένου ἐπι τὸ ὅν.
331 ἐπὶ θέαν τῆς τῶν ἀριθμῶν φύσεως.
332 τῇ νοηήσει αὐτῇ.
333 He adds "and for the sake of war;" this point I have passed by. Plato does not really ascribe much weight to this use of Science, as we see in what he says of Geometry and Astronomy.
334 ἀρθῶς ἕχει ἑξῆς μετὰ δευτέραν αὕξην τρίτην λαμβάνειν, ἕστι δέ που τοῦτο περὶ τὴν τῶν κύβων αύξην καὶ τὸ βάθους μέτεχον.
335 ἀντίστροφον αὐτοῦ.
336 πρὸς ἐναρμόνιον φορὰν ὦτα παγῆναι.
337 πυκνώματα ἄ ττα.
338 τίνες ξύμφωνοι ἀριθμοὶ, &c.
339 Η καὶ διαλεκτικὸν καλεῖς τὸν λόγον ἐκάστου λαμβάνοντα τῆς οὐσίας; (§ 14).
340 ὥσπερ θριγγὸς τοῖς μαθήμασιν ἡ διαλεκτικὴ ἦμιν ἐπάνω κεῖσθαι. (§ 14).]
341 Pol. vi. § 19.
342 He adds, "This oraton, this visible world, I will not say has any connexion with ouranon, heaven, that I may not be accused of playing upon words."
343 It is plain that Plato, by Hypotheses, in this place, means the usual foundations of Arithmetic and Geometry; namely, Definitions and Postulates. He says that "the arithmeticians and geometers take as hypotheses (hυποθεμενοι) odd and even, and the three kinds of angles (right, acute, and obtuse); and figures, (as a triangle, a square,) and the like." I say his "hypotheses" are the Definitions and Postulates, not the Axioms: for the Axioms of Arithmetic and Geometry belong to the Higher Faculty, which ascends to First Principles. But this Faculty operates rather in using these axioms than in enunciating them. It knows them implicitly rather than expresses them explicitly.
344 διάνοιαν άλλ' οὐ νοῦν.
345 The Diagram, as here described, would be this:
| Intelligible World. | Visible World. | ||
| Intuition. | Conception. | Things. | Images. |
Plato supposes the whole, and each of the two parts, to be divided in the same ratio, in order that the analogy of the division in each case may be represented.
346 The four segments might be as 4: 2: 2: 1; or as 9: 6: 6: 4; or generally, as a: ar: ar: ar2.
348 τῇ τοῦ διαλέγεσθαι δυνόμει.
349 This term occurs in other parts of Aristotle. See the additional Note.
350 Mr. Owen, to whom I am indebted for the physiological part of this criticism, tells me, "All mammalia have bile, the carnivora in greater proportion than the herbivora: the gall-bladder is a comparatively unimportant accessory to the biliary apparatus; adjusting it to certain modifications of stomach and intestine: there is no relation between natural longevity and bile. Neither has the presence or absence of the gall-bladder any connexion with age. Man and the elephant are perhaps for their size the longest lived animals, and the latest at coming to maturity: one has the gall-bladder, and the other not."
351 Hist. Sc. Ind. b. iii.
352 These remarks were written in 1841. The accompanying Memoir contains a further discussion of this problem.
353 Cartes. Princip. iv. 23.
354 Jac. Bernoulli, Nouvelles Pensées sur le Système de M. Descartes, op. t. i. p. 239 (1686).
355 De la Cause de la Pesanteur (1689), p. 135.
356 Journal des Savans, 1703. Mém. Acad. Par. 1709.
Bulfinger, in 1726 (Acad. Petrop.), conceived that by making a sphere revolve at the same time about two axes at right angles to each other, every particle would describe a great circle; but this is not so.
357 Acad. Par. 1714, Hist. p. 106.
358 Acad. Par. 1733.
359 Acad. Sc. 1709. If we abandon the clear principles of mechanics, the writer says, "toute la lumière que nous pouvons avoir est éteinte, et nous voilà replongés de nouveau dans les anciennes ténèbres du Peripatetisme, dont le Ciel nous veuille preserver!"
It was also objected to the Newtonian system, that it did not account for the remarkable facts, that all the motions of the primary planets, all the motions of the satellites, and all the motions of rotation, including that of the sun, are in the same direction, and nearly in the same plane; facts which have been urged by Laplace as so strongly recommending the Nebular Hypothesis; and that hypothesis is, in truth, a hypothesis of vortices respecting the origin of the system of the world.
360 Nouvelle Physique Céleste, Op. t. iii. p. 163.
The deviation of the orbits of the planets from the plane of the sun's equator was of course a difficulty in the system which supposed that they were carried round by the vortices which the sun's rotation caused, or at least rendered evident. Bernoulli's explanation consists in supposing the planets to have a sort of leeway (dérive des vaisseaux) in the stream of the vortex.
361 See Hist. Sc. Ideas, b. iii. c. ix. Art. 7.
362 See Mill's Logic, vol. i. p. 311, 2nd ed.
363 These letters refer to passages in the Translation annexed to this Memoir.