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Rh be impossible without the knowledge of the necessity of all events.” “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.” 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 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) 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, 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 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.”

—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.