780 LOGIC 1 . T" OGIC, in the most general acceptation of the term, | J may be regarded as the systematic study of thought. So wide a definition is certainly sufficient to comprehend all that may have been at various times included within the scope of logical doctrine, but in other respects it is of small value. It does not serve to mark off logic from philosophy as a whole, which is unquestionably the systematic exposi tion of thought, nor from psychology, which includes within its wider range what may well be described as the study of thought. Without some more accurate discrimination of the province and method of logic, neither the extent of matter to be included within the study nor the pecu liarity of the method by which such matter is treated can be determined. Preliminary queries of a similar kind are naturally encountered in the case of all other branches of human knowledge, and are generally answered by two methods. We may refer either to the distinct characteristics of the matter to be treated, or to the essential features of the method of treatment. We may determine the province of a science either by external division, by classification of objects according to their prevailing resemblances and differences, or by internal definition, by exposition of the f u ndamental characters of the method employed. By neither process, unfortunately, can an unambiguous answer be sup plied, at least without much art, in the case of logic. 2. The reasons for the manifold difficulties encountered in the attempt to determine accurately the province of logic, whether by reference to a division of the sciences or by precise definition of the essential features of logical analysis, are not far to seek. The systematic classification of the sciences involves not only consideration of the con tents of the sciences as empirically presented, but also certain leading principles or fundamental views, which are in essence of a philosophical character. According to the general conception of knowledge which in various kinds is manifested in the special sciences, there will be radically divergent methods of classification, and the province assigned to each member of the ensemble will, for the most part, have its limits determined according to the character of the general view adopted. Moreover, if any of the more prominent specimens of classification of the .sciences be critically inspected, they will be found to presuppose a certain body of principles, of scope wider than any of the special disciplines, and to which no place in the ensemble can be assigned. In short, a systematic distribution of human knowledge into its distinctly marked varieties rests upon and presupposes a general philosophy, the character of which affects the place and function of each part of the distribution. Logic, as may readily be imagined, has therefore experienced a variety of treatment at the hands of systematizers of scientific knowledge. It has appeared as one of the abstract sciences, in opposition to those disciplines in which the character of the concrete material is the essential fact ; as a subordinate branch of a particular concrete science, the investigation of mental phenomena ; as a nondescript receptacle for the formulation in generalized fashion of the method and logical precepts exemplified in the special sciences. By such processes no more has been effected than to bring into light, more or^less clearly, some of the characteristics of the supposed science, without in any way supplying an exhaustive and comprehensive survey of its boundaries and relations to other branches of knowledge. Thus, when logic is marked off from ^ the concrete sciences and associated with mathematics in the most general sense, as the treatment of formal relations, 1 and further differentiated from mathematics as implying no reference to the quantitative character of the most general relations under which facts of experience present themselves, 2 there is certainly brought to the front what one would willingly allow to be a commonplace respecting all logical analysis, namely, that its principles are coextensive with human knowledge, and that all objects as matters of conscious experience have an aspect in which they are susceptible of logical treatment. But no more is effected. It is still left to a wider consider ation to determine what the specific aspect of things may be which shall be called the formal and be recognized as the peculiarly logical element in them. There may be selected for this purpose either the general relations of coincidence and succession in space and time, or the fundamental properties of identity and difference, or the existences of classes, but in any case such selection depends upon and refers to a theory of the nature of knowledge and of the constitution of things as known. In truth, the notions of form and formal relations are by no means so simple and free from ambiguity that by their aid one can at once solve a complicated problem of philosophic arraiagc- ment. To lay stress upon form as the special object of logical treatment still leaves undecided the nature and ground of the principles which are to be employed in evolving a science of form, and therefore leaves the logical problem untouched. Still less satisfactory are the results when logic is regarded as in some way a subordinate branch of the psychological analysis of mental phenomena. 3 Neither the grounds on which such a classification rests, nor the con clusions deduced from it, seem beyond criticism. The simple facts that certain mental processes are analysed in logic, and that psychology is generally the treatment of all mental processes, by no means necessitate the view that logic is therefore the outgrowth from and a subordinate part of psychology. For it is clear, on the one hand, that logic has a scope wider than psychology, since in any sense of the term it has to deal with all the processes (or with some aspect of all the processes) by which on any subject knowledge is formed out of disjointed or disconnected experiences. And, on the other hand, since the subordina tion of one science to another, as species to genus, is fallacious, unless the two agree in fundamental charac teristics, the position so assigned to logic would imply that in aim and method it shall be essentially one with psycho logy, a position equivalent to the negation of logic as a separate and independent discipline. It is not surprising therefore to find that so soon as logic has been distin guished as arising from psychology, and so dependent on it, the peculiarity of its position and functions compels the recognition of its more general scope and the reduction of its connexion with psychology to an amount small enough to be compatible with absolute independence. Strong 1 As, e.g., by H. Spencer, Classification of t/te Sciences, pp. 6, 12 ; H. Grassmann, Die Ausdehnunrjslehre von 1844 (1878), Einleitnng, xxii.-xxiii. 2 Logic and mathematics, under this view, may be regarded either as genetically distinct which is apparently the opinion of Spencer, H. Grassmann, and Jevons or as species of a more comprehensive genus, the theory of formal (symbolic) operations which is apparently the opinion of 11. Grassmann (see his Formenlehre, 1872) and Boole (see his Mathematical Analysis of Logic, 1847, p. 4, and Differential Equations, 1859, chap, xvi., specially pp. 388, 389). An admirable treatment of that which is implied in Boole s method is given in NT Venn s Symbolic Logic, 1881. 3 For this extremely common arrangement, see Hamilton, Lectures on Metaphysics, i. p. 121-3; Ueberweg, System der Loyik, 6.
