Part 20

Hegel's logic as a whole, however, stands and falls not with his thoughts on syllogism, but with the claim made for the dialectical method that it exhibits logic in its integral unity with metaphysic, the thought-process as the self-revelation of the Idea. The claim was disallowed. To the formalist proper it was self-condemned in its pretension to develop the content of thought and its rejection of the formula of bare-identity. To the epistemologist it seemed to confuse foundation and keystone, and to suppose itself to build upon the latter in a construction illegitimately appropriative of materials otherwise accumulated. At most it was thought to establish a schema of formal unity which might serve as a regulative ideal. To the methodologist of science in genesis it appeared altogether to fail to satisfy any practical interest. Finally, to the psychologist it spelt the failure of intellectualism, and encouraged, therefore, some form of rehabilitated experientialism.

In the Hegelian school in the narrower sense the logic of the master receives some exegesis and defence upon single points of doctrine rather than as a whole. Its effect upon logic is rather to be seen in the rethinking of the traditional body of logical doctrine in the light of an absolute presupposed as ideal, with the postulate that a regulative ideal must ultimately exhibit itself as constitutive, the justification of the postulate being held to lie in the coherence and all-inclusiveness of the result. In such a logic, if and so far as coherence should be attained, would be found something akin to the spirit of what Hegel achieves, though doubtless alien to the letter of what it is his pretension to have achieved. There is perhaps no serious misrepresentation involved in regarding a key-thought of this type, though not necessarily expressed in those verbal forms, as pervading such logic of the present as coheres with a philosophy of the absolute conceived from a point of view that is intellectualist throughout. All other contemporary movements may be said to be in revolt from Hegel.

v. _Logic from 1880-1910_

Logic in the present exhibits, though in characteristically modified shapes, all the main types that have been found in its past history. There is an intellectualist logic coalescent with an absolutist metaphysic as aforesaid. There is an epistemological logic with sometimes formalist, sometimes methodological leanings. There is a formal-symbolic logic engaged with the elaboration of a relational calculus. Finally, there is what may be termed psychological-voluntaryist logic. It is in the rapidity of development of logical investigations of the third and fourth types and the growing number of their exponents that the present shows most clearly the history of logic in the making. All these movements are logic of the present, and a very brief indication may be added of points of historical significance.

Of intellectualist logic Francis Herbert Bradley[142] (b. 1846) and Bernard Bosanquet[143] (1848) may be taken as typical exponents. The philosophy of the former concludes to an Absolute by the annulment of contradictions, though the ladder of Hegel is conspicuous by its absence. His metaphysical method, however, is like Herbart's, not identifiable with his logic, and the latter has for its central characteristic its thorough restatement of the logical forms traditional in language and the text-books, in such a way as to harmonize with the doctrine of a reality whose organic unity is all-inclusive. The thorough recasting that this involves, even of the thought of the masters when it occasionally echoes them, has resulted in a phrasing uncouth to the ear of the plain man with his world of persons and things in which the former simply think about the latter, but it is fundamentally necessary for Bradley's purpose. The negative judgment, for example, cannot be held in one and the same undivided act to presuppose the unity of the real, project an adjective as conceivably applicable to it and assert its rejection. We need, therefore, a restatement of it. With Bradley reality is the one subject of all judgment immediate or mediate. The act of judgment "which refers an ideal content (recognized as such) to a reality beyond the act" is the unit for logic. Grammatical subject and predicate necessarily both fall under the rubric of the adjectival, that is, within the logical idea or ideal content asserted. This is a meaning or universal, which can have no detached or abstract self-subsistence. As found in judgment it may exhibit differences within itself, but it is not two, but one, an articulation of unity, not a fusion, which could only be a confusion, of differences. With a brilliant subtlety Bradley analyses the various types of judgment in his own way, with results that must be taken into account by all subsequent logicians of this type. The view of inference with which he complements it is only less satisfactory because of a failure to distinguish the principle of nexus in syllogism from its traditional formulation and rules, and because he is hampered by the intractability which he finds in certain forms of relational construction.

Bosanquet had the advantage that his logic was a work of a slightly later date. He is, perhaps, more able than Bradley has shown himself, to use material from alien sources and to penetrate to what is of value in the thought of writers from whom, whether on the whole or on particular issues, he disagrees. He treats the book-tradition, however, a debt to which, nowadays inevitable, he is generous in acknowledging,[144] with a judicious exercise of freedom in adaptation, i.e. constructively as datum, never eclectically. In his fundamental theory of judgment his obligation is to Bradley. It is to Lotze, however, that he owes most in the characteristic feature of his logic, viz., the systematic development of the types of judgment, and inference from less adequate to more adequate forms. His fundamental continuity with Bradley may be illustrated by his definition of inference. "Inference is the indirect reference to reality of differences within a universal, by means of the exhibition of this universal in differences directly referred to reality."[145] Bosanquet's _Logic_ will long retain its place as an authoritative exposition of logic of this type.

Of epistemological logic in one sense of the phrase Lotze is still to be regarded as a typical exponent. Of another type Chr. Sigwart (q.v.) may be named as representative. Sigwart's aim was "to reconstruct logic from the point of view of methodology." His problem was the claim to arrive at propositions universally valid, and so true of the object, whosoever the individual thinker. His solution, within the Kantian circle of ideas, was that such principles as the Kantian principle of causality were justified as "postulates of the endeavour after complete knowledge." "What Kant has shown is not that irregular fleeting changes can never be the object of consciousness, but only that the ideal consciousness of complete science would be impossible without the knowledge of the necessity of all events."[146] "The universal presuppositions which form the outline of our ideal of knowledge are not so much laws which the understanding prescribes to nature ... as laws which the understanding lays down for its own regulation in its investigation and consideration of nature. They are a priori because no experience is sufficient to reveal or confirm them in unconditional universality; but they are a priori ... only in the sense of presuppositions without which we should work with no hope of success and merely at random and which therefore we must believe." Finally they are akin to our ethical principles. With this coheres his dictum, with its far-reaching consequences for the philosophy of induction, that "the logical justification of the inductive process rests upon the fact that it is an inevitable postulate of our effort after knowledge, that the given is necessary, and can be known as proceeding from its grounds according to universal laws."[147] It is characteristic of Sigwart's point of view that he acknowledges obligation to Mill as well as to Ueberweg. The transmutation of Mill's induction of inductions into a postulate is an advance of which the psychological school of logicians have not been slow to make use. The comparison of Sigwart with Lotze is instructive, in regard both to their agreement and their divergence as showing the range of the epistemological formula.

Of the formal-symbolic logic all that falls to be said here is, that from the point of view of logic as a whole, it is to be regarded as a legitimate praxis as long as it shows itself aware of the sense in which alone form is susceptible of abstraction, and is aware that in itself it offers no solution of the logical problem. "It is not an algebra," said Kant[148] of his technical logic, and the kind of support lent recently to symbolic logic by the _Gegenstandstheorie_ identified with the name of Alexius Meinong (b. 1853)[149] is qualified by the warning that the real activity of thought tends to fall outside the calculus of relations and to attach rather to the subsidiary function of denoting. The future of symbolic logic as coherent with the rest of logic, in the sense which the word has borne throughout its history seems to be bound up with the question of the nature of the analysis that lies behind the symbolism, and of the way in which this is justified in the setting of a doctrine of validity. The "theory of the object," itself, while affecting logic alike in the formal and in the psychological conception of it very deeply, does not claim to be regarded as logic or a logic, apart from a setting supplied from elsewhere.

Finally we have a logic of a type fundamentally psychological, if it be not more properly characterized as a psychology which claims to cover the whole field of philosophy, including the logical field. The central and organizing principle of this is that knowledge is in genesis, that the genesis takes place in the medium of individual minds, and that this fact implies that there is a necessary reference throughout to interests or purposes of the subject which thinks because it wills and acts. Historically this doctrine was formulated as the declaration of independence of the insurgents in revolt against the pretensions of absolutist logic. It drew for support upon the psychological movement that begins with Fries and Herbart. It has been chiefly indebted to writers, who were not, or were not primarily, logicians, to Avenarius, for example, for the law of the economy of thought, to Wundt, whose system, and therewith his logic,[150] is a pendant to his psychology, for the volitional character of judgment, to Herbert Spencer and others. A judgment is practical, and not to be divorced without improper abstraction from the purpose and will that informs it. A concept is instrumental to an end beyond itself, without any validity other than its value for action. A situation involving a need of adaptation to environment arises and the problem it sets must be solved that the will may control environment and be justified by success. Truth is the improvised machinery that is interjected, so far as this works. It is clear that we are in the presence of what is at least an important half-truth, which intellectuallism with its statics of the rational order viewed as a completely articulate system has tended to ignore. It throws light on many phases of the search for truth, upon the plain man's claim to start with a subject which he knows whose predicate which he does not know is still to be developed, or again upon his use of the negative form of judgment, when the further determination of his purposive system is served by a positive judgment from without, the positive content of which is yet to be dropped as irrelevant to the matter in hand. The movement has, however, scarcely developed its logic[151] except as polemic. What seems clear is that it cannot be the whole solution. While man must confront nature from the human and largely the practical standpoint, yet his control is achieved only by the increasing recognition of objective controls. He conquers by obedience. So truth works and is economical because it is truth. Working is proportioned to inner coherence. It is well that the view should be developed into all its consequences. The result will be to limit it, though perhaps also to justify it, save in its claim to reign alone.

There is, perhaps, an increasing tendency to recognize that the organism of knowledge is a thing which from any single viewpoint must be seen in perspective. It is of course a postulate that all truths harmonize, but to give the harmonious whole in a projection in one plane is an undertaking whose adequacy in one sense involves an inadequacy in another. No human architect can hope to take up in succession all essential points of view in regard to the form of knowledge or to logic. "The great campanile is still to finish."

BIBLIOGRAPHY.--Historical: No complete history of logic in the sense in which it is to be distinguished from theoretical philosophy in general has as yet been written. The history of logic is indeed so little intelligible apart from constant reference to tendencies in philosophical development as a whole, that the historian, when he has made the requisite preparatory studies, inclines to essay the more ambitious task. Yet there are, of course, works devoted to the history of logic proper.

Of these Prantl's _Geschichte der Logik im Abendlande_ (4 vols., 1855-1870), which traces the rise, development and fortunes of the Aristotelian logic to the close of the middle ages, is monumental. Next in importance are the works of L. Rabus, _Logik und Metaphysik_, i. (1868) (pp. 123-242 historical, pp. 453-518 bibliographical, pp. 514 sqq. a section on apparatus for the study of the history of logic), _Die neuesten Bestrebungen auf dem Gebiete der Logik bei den Deutschen_ (1880), _Logik_ (1895), especially for later writers § 17. Ueberweg's _System der Logik und Geschichte der logischen Lehren_ (4th ed. and last revised by the author, 1874, though it has been reissued later, Eng. trans., 1871) is alone to be named with these. Harms' posthumously published _Geschichte der Logik_ (1881) (_Die Philosophie in ihrer Geschichte_, ii.) was completed by the author only so far as Leibnitz. Blakey's _Historical Sketch of Logic_ (1851), though, like all this writer's works, closing with a bibliography of some pretensions, is now negligible. Franck, _Esquisse d'une histoire de la logique_ (1838) is the chief French contribution to the subject as a whole.

Of contributions towards the history of special periods or schools of logical thought the list, from the opening chapters of Ramus's _Scholae Dialecticae_ (1569) downwards (v. Rabus _loc. cit._) would be endless. What is of value in the earlier works has now been absorbed. The _System der Logik_ (1828) of Bachmann (a Kantian logician of distinction) contains a historical survey (pp. 569-644), as does the _Denklehre_ (1822) of van Calker (allied in thought to Fries) pp. 12 sqq.; Eberstein's _Geschichte der Logik und Metaphysik bei den Deutschen von Leibniz bis auf gegenwärtige Zeit_ (latest edition, 1799) is still of importance in regard to logicians of the school of Wolff and the origines of Kant's logical thought. Hoffmann, the editor and disciple of von Baader, published _Grundzüge einer Geschichte der Begriffe der Logik in Deutschland von Kant bis Baader_ (1851). Wallace's prolegomena and notes to his _Logic of Hegel_ (1874, revised and augmented 1892-1894) are of use for the history and terminology, as well as the theory. Riehl's article entitled _Logik in Die Kultur der Gegenwart_, vi. 1. _Systematische Philosophie_ (1907), is excellent, and touches on quite modern developments. Liard, _Les Logiciens Anglais Contemporains_ (5th ed., 1907), deals only with the 19th-century inductive and formal-symbolic logicians down to Jevons, to whom the book was originally dedicated. Venn's _Symbolic Logic_ (1881) gave a careful history and bibliography of that development. The history of the more recent changes is as yet to be found only in the form of unshaped material in the pages of review and _Jahresbericht_. (H. W. B.*)

FOOTNOTES:

[1] Cf. Heidel, "The Logic of the Pre-Socratic Philosophy," in Dewey's _Studies in Logical Theory_ (Chicago, 1903).

[2] Heraclitus, _Fragmm._ 107 (Diels, _Fragmente der Vorsokratiker_) and 2, on which see Burnet, _Early Greek Philosophy_, p. 153 note (ed. 2).

[3] e.g. Diog. Laërt. ix. 25, from the lost _Sophistes_ of Aristotle.

[4] _Plato and Platonism_, p. 24.

[5] Nothing is. If anything is, it cannot be known. If anything is known it cannot be communicated.

[6] _Metaphys. [mu]. 1078b_ 28 sqq.

[7] Cf. Arist. _Top. [theta]_. i. 1 _ad fin_.

[8] For whom see Dümmler, _Antisthenica_ (1882, reprinted in his _Kleine Schriften_, 1901).

[9] Aristotle, _Metaphys._ 1024b 32 sqq.

[10] Plato, _Theaetetus_, 201 E. sqq., where, however, Antisthenes is not named, and the reference to him is sometimes doubted. But cf. Aristotle, _Met._ H 3. 1043b 24-28.

[11] Diog. Laërt. ii. 107.

[12] Aristotle, _An. Pr._ i. 31, 46a 32 sqq.; cf. 91b 12 sqq.

[13] Athenaeus ii. 59c. See Usener, _Organisation der wissenschaftl. Arbeit_ (1884; reprinted in his _Vorträge und Aufsätze_, 1907).

[14] Socrates' reference of a discussion to its presuppositions (Xenophon, _Mem._ iv. 6, 13) is not relevant for the history of the terminology of induction.

[15] _Theaetetus_, 186c.

[16] Timaeus, 37a, b (quoted in H. F. Carlill's translation of the _Theaetetus_, p. 60).

[17] _Theaetetus_, 186d.

[18] Sophistes, 253d.

[19] _Ib. id._; cf. _Theaetetus_, 197d.

[20] Aristotle, _de An._ 430b 5, and generally iii. 2, iii. 5.

[21] For Plato's Logic, the controversies as to the genuineness of the dialogues may be treated summarily. The _Theaetetus_ labours under no suspicion. The _Sophistes_ is apparently matter for animadversion by Aristotle in the _Metaphysics_ and elsewhere, but derives stronger support from the testimonies to the _Politicus_ which presumes it. The _Politicus_ and _Philebus_ are guaranteed by the use made of them in Aristotle's Ethics. The rejection of the _Parmenides_ would involve the paradox of a nameless contemporary of Plato and Aristotle who was inferior as a metaphysician to neither. No other dialogue adds anything to the _logical_ content of these.

Granted their genuineness, the relative dating of three of them is given, viz. _Theaetetus_, _Sophistes_ and _Politicus_ in the order named. The _Philebus_ seems to presuppose _Politicus_, 283-284, but if this be an error, it will affect the logical theory not at all. There remains the _Parmenides_. It can scarcely be later than the _Sophistes_. The antinomies with which it concludes are more naturally taken as a prelude to the discussion of the _Sophistes_ than as an unnecessary retreatment of the doctrine of the one and the many in a more negative form. It may well be earlier than the _Theaetetus_ in its present form. The stylistic argument shows the _Theaetetus_ relatively early. The maturity of its philosophic outlook tends to give it a place relatively advanced in the Platonic canon. To meet the problem here raised, the theory has been devised of an earlier and a later version. The first may have linked on to the series of Plato's dialogues of search, and to put the _Parmenides_ before it is impossible. The second, though it might still have preceded the _Parmenides_ might equally well have followed the negative criticism of that dialogue, as the beginning of reconstruction. For Plato's logic this question only has interest on account of the introduction of an [Greek: Aristotelês] in a non-speaking part in the _Parmenides_. If this be pressed as suggesting that the philosopher Aristotle was already in full activity at the date of writing, it is of importance to know what Platonic dialogues were later than the début of his critical pupil.

On the stylistic argument as applied to Platonic controversies Janell's _Quaestiones Platonicae_ (1901) is important. On the whole question of genuineness and dates of the dialogues, H. Raeder, _Platons philosophische Entwickelung_ (1905), gives an excellent conspectus of the views held and the grounds alleged. See also PLATO.

[22] E.g. that of essence and accident. Republic, 454.

[23] E.g. the discussion of correlation, ib. 437 sqq.

[24] _Politicus_, 285d.

[25] _Sophistes_, 261c sqq.

[26] E.g. in _Nic. Eth._ i. 6.

[27] _Philebus_, 16d.

[28] Principal edition still that of Waitz, with Latin commentary, (2 vols., 1844-1846). Among the innumerable writers who have thrown light upon Aristotle's logical doctrine, St Hilaire, Trendelenburg, Ueberweg, Hamilton, Mansel, G. Grote may be named. There are, however, others of equal distinction. Reference to Prantl, op. cit., is indispensable. Zeller, _Die philosophie der Griechen_, ii. 2, "Aristoteles" (3rd ed., 1879), pp. 185-257 (there is an Eng. trans.), and Maier, _Die Syllogistik des Aristoteles_ (2 vols., 1896, 1900) (some 900 pp.), are also of first-rate importance.

[29] _Sophist. Elench._ 184, espec. b 1-3, but see Maier, _loc. cit._ i. 1.

[30] References such as 18b 12 are the result of subsequent editing and prove nothing. See, however, ARISTOTLE.

[31] Adrastus is said to have called them [Greek: pro tôn topikôn].

[32] _Metaphys._ E. 1.

[33] _De Part. Animal._ A. 1, 639a 1 sqq.; cf. _Metaphys._ 1005b 2 sqq.

[34] _De Interpretatione_ 16a sqq.

[35] _De Interpretatione_ 16a 24-25.

[36] _Ib._ 18a 28 sqq.

[37] _Ib._ 19a 28-29.

[38] As shown e.g. by the way in which the relativity of sense and the object of sense is conceived, 7b 35-37.

[39] _Topics_ 101a 27 and 36-b 4.

[40] _Topics_ 100.

[41] _Politics_ 1282a 1 sqq.

[42] 103b 21.

[43] _Topics_ 160a 37-b 5.

[44] This is the explanation of the formal definition of induction, _Prior Analytics_, ii. 23, 68b 15 sqq.

[45] 25b 36.

[46] _Prior Analytics_, i. 1. 24a 18-20, [Greek: Syllogismos de esti logos en ô tethentôn tinôn eteron ti tôn keimenôn ex anankês snmbainei tô tauta einai]. The equivalent previously in _Topics_ 100a 25 sqq.

[47] _Prior Analytics_, ii. 21; _Posterior Analytics_, i. 1.

[48] 67a 33-37, [Greek: mê syntheôrôn to kath' ekateron].

[49] 67a 39-63.

[50] 79a 4-5.

[51] 24b 10-11.

[52] _Posterior Analytics_, i. 4 [Greek: kath auto] means (1) contained in the definition of the subject; (2) having the subject contained in its definition, as being an alternative determination of the subject, crooked, e.g. is _per se_ of line; (3) self-subsistent; (4) connected with the subject as consequent to ground. Its needs stricter determination therefore.

[53] 73b 26 sqq., 74a 37 sqq.

[54] 90b 16.

[55] _Metaphys. Z._ 12, H. 6 ground this formula metaphysically.

[56] 94a 12, 75b 32.

[57] 90a 6. Cf. Ueberweg, _System der Logik_, § 101.

[58] 78a 30 sqq.

[59] _Topics_, 101b 18, 19.

[60] _Posterior Analytics_, ii. 13.

[61] _Posterior Analytics_, ii. 16.

[62] _Posterior Analytics_, i. 13 ad. fin., and i. 27. The form which a mathematical science treats as relatively self-subsistent is certainly not the constitutive idea.

[63] _Posterior Analytics_, i. 3.

[64] _Posterior Analytics_, ii. 19.

[65] _De Anima_, 428b 18, 19.

[66] _Prior Analytics_, i. 30, 46a 18.

[67] _Topics_, 100b 20, 21.

[68] _Topics_, 101a 25, 36-37, b1-4, &c.

[69] Zeller (_loc. cit._ p. 194), who puts this formula in order to reject it.

[70] _Metaphys._ [Delta] 1, 1013a 14.

[71] _Posterior Analytics_, 72a 16 seq.

[72] _Posterior Analytics_, 77a 26, 76a 37 sqq.

[73] _Metaphys._ [Gamma].

[74] _Posterior Analytics_, ii. 19.

[75] _de Anima_, iii. 4-6.

[76] _Metaphys._ M. 1087a 10-12; Zeller loc. cit. 304 sqq.; McLeod Innes, _The Universal and Particular in Aristotle's Theory of Knowledge_ (1886).

[77] _Topics_, 105a 13.

[78] _Metaphys._ 995a 8.

[79] E.g., _Topics_, 108b 10, "to induce" the universal.

[80] _Posterior Analytics_, ii. 19, 100b 3, 4.

[81] _Topics_, i. 18, 108b 10.

[82] _Prior Analytics_, ii. 23.

[83] [Greek: Paradeigma], Prior Analytics, ii. 24.

[84] Sigwart, _Logik_, Eng. trans. vol. ii. p. 292 and elsewhere.

[85] Ueberweg, _System_, § 127, with a ref. to _de Partibus Animalium_, 667a.

[86] See 67a 17 [Greek: ex hapantôn tôn atomôn].