Part 21

[87] [Greek: Epiphora]. [Greek: Epi] = "in" as in [Greek: epagôgê], inductio, and [Greek: -phora] = -ferentia, as in [Greek: diaphora], dif_ferentia_.

[88] Diog. Laërt. x. 33 seq.; Sext. Emp. Adv. Math. vii. 211.

[89] Diog. Laërt. x. 87; cf. Lucretius, vi. 703 sq., v. 526 sqq. (ed. Munro).

[90] Sextus Empiricus, _Pyrrhon. Hypotyp._ ii. 195, 196.

[91] Sextus, _op. cit._ ii. 204.

[92] _Op. cit._ iii. 17 sqq., and especially 28.

[93] The point is raised by Aristotle, 95A.

[94] See Jourdain, _Recherches critiques sur l'âge et l'origine des traductions latines d'Aristote_ (1843).

[95] See E. Cassirer, _Das Erkenntnisproblem_, i. 134 seq., and the justificatory excerpts, pp. 539 sqq.

[96] See Riehl in _Vierteljahrschr. f. wiss. Philos._ (1893).

[97] Bacon, _Novum Organum_, ii. 22, 23; cf. also Aristotle, _Topics_ i. 12. 13, ii. 10. 11 (Stewart, ad _Nic. Eth._ 1139b 27) and Sextus Empiricus, _Pyrr. Hypot._ iii. 15.

[98] Bacon's _Works_, ed. Ellis and Spedding, iii. 164-165.

[99] A notable formula of Bacon's _Novum Organum_ ii. 4 § 3 turns out, _Valerius Terminus_, cap. 11, to come from Aristotle, _Post. An._ i. 4 _via_ Ramus. See Ellis in Bacon's _Works_, iii. 203 sqq.

[100] _De Civitate Dei_, xi. 26. "Certum est me esse, si fallor."

[101] Cf. Plato, _Republic_, 381E seq.

[102] _Elementa Philosophiæ_, i. 3. 20, i. 6. 17 seq.

[103] Hobbes, _Elementa Philosophiæ_, i. 1. 5.

[104] _Id. ib._ i. 6. 16.

[105] _Id. ib._ i. 4. 8; cf. Locke's _Essay of Human Understanding_, iv. 17.

[106] _Id. Leviathan_, i. 3.

[107] _Id. Elem. Philos._ i. 6. 10.

[108] Condillac, _Langue des Calculs_, p. 7.

[109] Locke, _Essay_, iii. 3.

[110] _Id. ib._ iv. 17.

[111] _Loc. cit._ § 8.

[112] _Id. ib._ iv. 4, §§ 6 sqq.

[113] Berkeley, _Of the Principles of Human Knowledge_, § 142.

[114] Hume, _Treatise of Human Nature_, i. 1. 7 (from Berkeley, _op. cit._, introd., §§ 15-16).

[115] _Essay_, iv. 17, § 3.

[116] Hume, _Treatise of Human Nature_, i. 3. 15.

[117] Mill, _Examination of Sir William Hamilton's Philosophy_, cap. 17.

[118] Cf. Mill, _Autobiography_, p. 159. "I grappled at once with the problem of Induction, postponing that of Reasoning." _Ib._ p. 182 (when he is preoccupied with syllogism), "I could make nothing satisfactory of Induction at this time."

[119] _Autobiography_, p. 181.

[120] The insight, for instance, of F. H. Bradley's criticism, _Principles of Logic_, II. ii. 3, is somewhat dimmed by a lack of sympathy due to extreme difference in the point of view adopted.

[121] Bacon, _Novum organum_, i. 100.

[122] Russell's _Philosophy of Leibnitz_, capp. 1-5.

[123] See especially remarks on the letter of M. Arnauld (Gerhardt's edition of the philosophical works, ii. 37 sqq.).

[124] Gerhardt, vi. 612, quoted by Russell, _loc. cit._, p. 19.

[125] Ibid., ii. 62, Russell, p. 33.

[126] Spinoza, ed. van Vloten and Land, i. 46 (_Ethica_, i. 11).

[127] _Nouveaux essais_, iv. 2 § 9, 17 § 4 (Gerhardt v. 351, 460).

[128] _Critique of Judgment_, Introd. § 2, _ad. fin._ (_Werke_, Berlin Academy edition, vol. v. p. 176, l. 10).

[129] _Kant's Introduction to Logic and his Essay on the Mistaken Subtlety of the Four Figures_, trans. T. K. Abbott (1885).

[130] _Loc. cit._, p. 11.

[131] Or antitheses. Kant follows, for example, a different line of cleavage between form and content from that developed between thought and the "given." And these are not his only unresolved dualities, even in the _Critique of Pure Reason_. For the logical inquiry, however, it is permissible to ignore or reduce these differences.

The determination too of the sense in which Kant's theory of knowledge involves an unresolved antithesis is for the logical purpose necessary so far only as it throws light upon his logic and his influence upon logical developments. Historically the question of the extent to which writers adopted the dualistic interpretation or one that had the like consequences is of greater importance.

It may be said summarily that Kant holds the antithesis between thought and "the given" to be unresolved and within the limits of theory of knowledge irreducible. The dove of thought falls lifeless if the resistant atmosphere of "the given" be withdrawn (_Critique of Pure Reason_, ed. 2 Introd. Kant's _Werke_, ed. of the Prussian Academy, vol. iii. p. 32, ll. 10 sqq.). Nevertheless the thing-in-itself is a problematic conception and of a limiting or negative use merely. He "had woven," according to an often quoted phrase of Goethe, "a certain sly element of irony into his method; ... he pointed as it were with a side gesture beyond the limits which he himself had drawn." Thus (_loc. cit._ p. 46, ll. 8, 9) he declares that "there are two lineages united in human knowledge, which perhaps spring from a common stock, though to us unknown--namely sense and understanding." Some indication of the way in which he would hypothetically and speculatively mitigate the antithesis is perhaps afforded by the reflection that the distinction of the mental and what appears as material is an external distinction in which the one appears outside to the other. "Yet what as thing-in-itself lies back of the phenomenon may perhaps not be so wholly disparate after all" (ib. p. 278, ll. 26 sqq.).

[132] _Critique of Judgment_, Introd. § 2 (_Werke_, v., 276 ll. 9 sqq.); cf. Bernard's "Prolegomena" to his translation of this, (pp. xxxviii. sqq.).

[133] _Die Logik, insbesondere die Analytik_ (Schleswig, 1825). August Detlev Christian Twesten (1789-1876), a Protestant theologian, succeeded Schleiermacher as professor in Berlin in 1835.

[134] See _Sir William Hamilton: The Philosophy of Perception_, by J. Hutchison Stirling.

[135] _Hauptpunkte der Logik_, 1808 (_Werke_, ed. Hartenstein, i. 465 sqq.), and specially _Lehrbuch der Einleitung in die Philosophie_ (1813), and subsequently §§ 34 sqq. (_Werke_, i. 77 sqq.).

[136] See Ueberweg, _System of Logic and History of Logical Doctrines_, § 34.

[137] _Drei Bücher der Logik_, 1874 (E.T., 1884). The Book on Pure Logic follows in essentials the line of thought of an earlier work (1843).

[138] _Logic_, Eng. trans. 35 _ad. fin._

[139] _Logic_, Introd. § ix.

[140] For whom see Höffding, _History of Modern Philosophy_, Eng. trans., vol. ii. pp. 122 sqq.; invaluable for the logical methods of modern philosophers.

[141] _Wissenschaft der Logik_ (1812-1816), in course of revision at Hegel's death in 1831 (_Werke_, vols. iii.-v.), and _Encyklopädie der philosophischen Wissenschaften_, i.; _Die Logik_ (1817; 3rd ed., 1830); _Werke_, vol. vi., Eng. trans., Wallace (2nd ed., 1892).

[142] _The Principles of Logic_ (1883).

[143] _Logic, or The Morphology of Thought_ (2 vols., 1888).

[144] _Logic_, Pref. pp. 6 seq.

[145] _Id._ vol. ii. p. 4.

[146] _Logik_ (1873, 1889), Eng. trans. ii. 17.

[147] _Op. cit._ ii. 289.

[148] _Introd. to Logic._, trans. Abbott, p. 10.

[149] _Ueber Annahmen_ (1902, &c.)

[150] _Logik_ (1880, and in later editions).

[151] Yet see _Studies in Logic_, by John Dewey and others (1903).

LOGOCYCLIC CURVE, STROPHOID or FOLIATE, a cubic curve generated by increasing or diminishing the radius vector of a variable point Q on a straight line AB by the distance QC of the point from the foot of the perpendicular drawn from the origin to the fixed line. The polar equation is r cos[theta] = a(1 ± sin[theta]), the upper sign referring to the case when the vector is increased, the lower when it is diminished. Both branches are included in the Cartesian equation (x² + y²)(2a - x) = a²x, where a is the distance of the line from the origin. If we take for axes the fixed line and the perpendicular through the initial point, the equation takes the form y [root](a - x) = x [root](a + x). The curve resembles the folium of Descartes, and has a node between x = 0, x = a, and two branches asymptotic to the line x = 2a.

[Illustration.]

LOGOGRAPHI ([Greek: logos], [Greek: graphô], writers of prose histories or tales), the name given by modern scholars to the Greek historiographers before Herodotus.[1] Thucydides, however, applies the term to all his own predecessors, and it is therefore usual to make a distinction between the older and the younger logographers. Their representatives, with one exception, came from Ionia and its islands, which from their position were most favourably situated for the acquisition of knowledge concerning the distant countries of East and West. They wrote in the Ionic dialect, in what was called the unperiodic style, and preserved the poetic character of their epic model. Their criticism amounts to nothing more than a crude attempt to rationalize the current legends and traditions connected with the founding of cities, the genealogies of ruling families, and the manners and customs of individual peoples. Of scientific criticism there is no trace whatever. The first of these historians was probably Cadmus of Miletus (who lived, if at all, in the early part of the 6th century), the earliest writer of prose, author of a work on the founding of his native city and the colonization of Ionia (so Suïdas); Pherecydes of Leros, who died about 400, is generally considered the last. Mention may also be made of the following: Hecataeus of Miletus (550-476); Acusilaus of Argos,[2] who paraphrased in prose (correcting the tradition where it seemed necessary) the genealogical works of Hesiod in the Ionic dialect; he confined his attention to the prehistoric period, and made no attempt at a real history; Charon of Lampsacus (c. 450), author of histories of Persia, Libya, and Ethiopia, of annals ([Greek: hôroi]) of his native town with lists of the prytaneis and archons, and of the chronicles of Lacedaemonian kings; Xanthus of Sardis in Lydia (c. 450), author of a history of Lydia, one of the chief authorities used by Nicolaus of Damascus (_fl._ during the time of Augustus); Hellanicus of Mytilene; Stesimbrotus of Thasos, opponent of Pericles and reputed author of a political pamphlet on Themistocles, Thucydides and Pericles; Hippys and Glaucus, both of Rhegium, the first the author of histories of Italy and Sicily, the second of a treatise on ancient poets and musicians, used by Harpocration and Plutarch; Damastes of Sigeum, pupil of Hellanicus, author of genealogies of the combatants before Troy (an ethnographic and statistical list), of short treatises on poets, sophists, and geographical subjects.

On the early Greek historians, see G. Busolt, _Griechische Geschichte_ (1893), i. 147-153; C. Wachsmuth, _Einleitung in das Studium der alten Geschichte_ (1895); A. Schäfer, _Abriss der Quellenkunde der griechischen und römischen Geschichte_ (ed. H. Nissen, 1889); J. B. Bury, _Ancient Greek Historians_ (1909), lecture i.; histories of Greek literature by Müller-Donaldson (ch. 18) and W. Mure (bk. iv. ch. 3), where the little that is known concerning the life and writings of the logographers is exhaustively discussed. The fragments will be found, with Latin notes, translation, prolegomena, and copious indexes, in C. W. Müller's _Fragmenta historicorum Graecorum_ (1841-1870).

See also GREECE: _History, Ancient_ (section, "Authorities").

FOOTNOTES:

[1] The word is also used of the writers of speeches for the use of the contending parties in the law courts, who were forbidden to employ advocates.

[2] There is some doubt as to whether this Acusilaus was of Peloponnesian or Boeotian Argos. Possibly there were two of the name. For an example of the method of Acusilaus see Bury, _op. cit._ p. 19.

LOGOS [Greek: logos], a common term in ancient philosophy and theology. It expresses the idea of an immanent reason in the world, and, under various modifications, is met with in Indian, Egyptian and Persian systems of thought. But the idea was developed mainly in Hellenic and Hebrew philosophy, and we may distinguish the following stages:

1. _The Hellenic Logos._--To the Greek mind, which saw in the world a [Greek: kosmos] (ordered whole), it was natural to regard the world as the product of reason, and reason as the ruling principle in the world. So we find a Logos doctrine more or less prominent from the dawn of Hellenic thought to its eclipse. It rises in the realm of physical speculation, passes over into the territory of ethics and theology, and makes its way through at least three well-defined stages. These are marked off by the names of Heraclitus of Ephesus, the Stoics and Philo.

It acquires its first importance in the theories of Heraclitus (6th century B.C.), who, trying to account for the aesthetic order of the visible universe, broke away to some extent from the purely physical conceptions of his predecessors and discerned at work in the cosmic process a [Greek: logos] analogous to the reasoning power in man. On the one hand the Logos is identified with [Greek: gnômê] and connected with [Greek: dikê], which latter seems to have the function of correcting deviations from the eternal law that rules in things. On the other hand it is not positively distinguished either from the ethereal fire, or from the [Greek: heimarmenê] and the [Greek: anankê] according to which all things occur. Heraclitus holds that nothing material can be thought of without this Logos, but he does not conceive the Logos itself to be immaterial. Whether it is regarded as in any sense possessed of intelligence and consciousness is a question variously answered. But there is most to say for the negative. This Logos is not one above the world or prior to it, but in the world and inseparable from it. Man's soul is a part of it. It is _relation_, therefore, as Schleiermacher expresses it, or reason, not speech or word. And it is objective, not subjective, reason. Like a law of nature, objective in the world, it gives order and regularity to the movement of things, and makes the system rational.[1]

The failure of Heraclitus to free himself entirely from the physical hypotheses of earlier times prevented his speculation from influencing his successors. With Anaxagoras a conception entered which gradually triumphed over that of Heraclitus, namely, the conception of a supreme, intellectual principle, not identified with the world but independent of it. This, however, was [Greek: nous], not Logos. In the Platonic and Aristotelian systems, too, the theory of ideas involved an absolute separation between the material world and the world of higher reality, and though the term Logos is found the conception is vague and undeveloped. With Plato the term selected for the expression of the principle to which the order visible in the universe is due is [Greek: nous] or [Greek: sophia], not [Greek: logos]. It is in the pseudo-Platonic _Epinomis_ that [Greek: logos] appears as a synonym for [Greek: nous]. In Aristotle, again, the principle which sets all nature under the rule of thought, and directs it towards a rational end, is [Greek: nous], or the divine spirit itself; while [Greek: logos] is a term with many senses, used as more or less identical with a number of phrases, [Greek: ou heneka], [Greek: energeia], [Greek: entelecheia], [Greek: ousia], [Greek: eidos], [Greek: morphê], &c.

In the reaction from Platonic dualism, however, the Logos doctrine reappears in great breadth. It is a capital element in the system of the Stoics. With their teleological views of the world they naturally predicated an active principle pervading it and determining it. This operative principle is called both Logos and God. It is conceived of as material, and is described in terms used equally of nature and of God. There is at the same time the special doctrine of the [Greek: logos spermatikos], the seminal Logos, or the law of generation in the world, the principle of the active reason working in dead matter. This parts into [Greek: logoi spermatikoi], which are akin, not to the Platonic ideas, but rather to the [Greek: logoi enuloi] of Aristotle. In man, too, there is a Logos which is his characteristic possession, and which is [Greek: endiathetos], as long as