The most ambitious of recent works on Logic is that of W. E. Johnson (3 vols. 1921-4, vol. 4 to follow). John son attempts to combine the epistemological with the empirical view of Logic. Logic, he holds, is concerned with the analysis and criticism of thought, and it is impossible to draw a rigid distinc tion between Logic and Philosophy, or between Logic and Science. Thought has two aspects, an epistemic and a constitutive aspect. The constitutive consists of the content of knowledge ; the epis temic is that which depends on the variable conditions and capacities for the acquisition of knowledge. The unit of logic is the proposition, of which truth or falsity can be significantly predicated, and of which the intensive aspect is the most im portant. "Implication" is potential inference, and assumes dif ferent relations in different cases. There are two principles of deduction:—The applicative principle states that All S is P war rants the inference of The given S is P; (2) the implicative prin ciple states that a compound proposition of the form "x" and "x implies y" warrants the inference of "y." The syllogism involves both principles. These principles require universal premises and these are obtained by induction, a term which he applies to every process of reaching a generalization from instantial premises. He enumerates four types of induction, namely (I) intuitive, (2) summary, (3) demonstrative and (4) probable. Of these the last corresponds to ordinary empirical induction ; and the second is the old "perfect" induction. Intuitive induction is the process by which we obtain the principles of Logic, of Mathematics, etc. These are obtained by reflection on particular instances in one of two ways:—(i) the counter-applicative way, when we see that what is true of a given instance is true of any other instance; ( 2 ) the counter-implicative way, when, having made an inference which is valid we see that its validity is due to a certain form of relation between the premises and the conclusion. Demonstrative induction includes certain types of hypothetical syllogism in which an instantial premise leads to a universal conclusion, and the familiar canons of induction, reformulated by him as four "fig ures" of agreement, difference, composition and resolution. Under probable inductions he distinguishes pure generalization from class-fractional inductions, which are usually known as statistical generalizations. From all these forms of induction he distinguishes eduction, the argument from "certain instances of S which are M are P" to "the next S that is M will also be P." The discussion of many psychological and philosophical problems is a feature of Johnson's Logic.
The above accounts of Bradley, Bosan quet and Johnson contain references to new formulations or re formulations of various logical principles and types of inference. In this connection reference may also be made to E. E. C. Jones's New Law of Thought (1918) which reformulates the old Law of Identity in the form of a "Law of Significant Association" (ac cording to which every Subject of Predication is an identity of denotation in diversity of intension) and to A. Wolf's Essentials of Logic, and Essentials of Scientific Method (1925, 1926) in which there are formulated the "Principle of Uniformity of Rea sons" (namely, whatever is regarded as a sufficient reason in any one case must be regarded as a sufficient reason in all cases of the same type), and a number of types of inference which had not been formulated before.
Of symbolic logic all that needs 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 form alone 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 Gegen standstheorie 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 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" it self, while affecting logic alike in the formal and in the psycho logical 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 funda mentally psychological, if it be not more properly characterized as a psychology which claims to cover the whole field of philos ophy, including the logical field. The central and organizing prin ciple of this is that knowledge is in genesis, that the genesis takes place in the medium of individual minds, and that this fact im plies 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 Her bert 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 en vironment 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 intellectualism with its statics of the rational order viewed as a completely articulate system has tended to ig nore. 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 posi tive judgment from without, the positive content of which is yet to be dropped as irrelevant to the matter in hand. The move ment has, however, scarcely developed its logic except as a polemic. What seems clear is that it cannot be the whole solu tion. 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 obe dience. 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.
BIBLIOGRAPHY.—Prantl's Geschichte der Logik (4 vols. 1885-7o, re-issued 1926) gives a full account of the history of logic to the close of the Middle Ages; Harms's Geschichte der Logik 0880 brings the history up to Leibniz ; Ueberweg's System der Logik (4th ed. 1874, Eng. Transl. 1871) and T. Ziehen's Lehrbuch der Logik (1920) contain historical sketches. See also the bibliographies under LOGIC, LOGISTIC, SCIENTIFIC METHOD and KNOWLEDGE, THEORY OF.