Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/817

 LOGIC 793 judgments, the criticism of syllogistic argument), but of more importance than these detached and direct portions is the general principle which underlies the whole view of human knowledge. This principle is briefly that of psychological genesis. All the com plex tacts of knowledge are regarded as mechanical compounds due to the coherence of simple data, the facts of inner and outer sense. The method of Locke is that which underlies and determines all the logical work of one very important school of logicians. It is not needful to enter into details of Locke s own contributions to the foundation of logic. But it may be pointed out that from his position there were two possible lines of development. In his view the primitive impressions, the facts of inner and outer sense, were in themselves primitive facts of cognition; they were cogni tions (it is the very essence of Locke s method to identify a simple impression of sense with the knowledge of a simple sense fact). The processes of abstraction, comparison, i.e., judging and reasoning, were exercised upon their data, and these products were, in conse quence, of a secondary and, so to speak, artificial character. It was natural that a thinker who identified impression of sense with knowledge of a sense fact should maintain that the secondary for mations of thought (general ideas, general propositions, syllogism) were not indispensable for cognition; that we could and did reason from particulars to particulars. At the same time Locke admitted the secondary processes as having actual existence, and in one important case (that of the judgment of coexistence, with which may be taken the idea of substance and of real relation) seemed to allow that in judgment something was added to the primitive data. It was possible, then, for development from Locke s position to proceed either by offering an explanation of the added elements, which should be in stricter harmony with the fundamental doctrine of psychological genesis, or by throwing them entirely out of account and concentrating attention on the primitive data as the only materials of cognition. The first is the line taken by Hume, which finds its .ogical completion in Mill; the second is the line taken by Condillac. Hume has an easy task so long as he merely subjects Locke s position to negative criticism; for the added elements, the ideas of substance, relation, cause, &c., are clearly inept and defenceless when the facts to be linked by them are already contemplated as so many completed, isolated cognitions. But where connectedness of cognition is in question, and where some explanation is demanded of the relations which seem to supply the universal rule in think ing, Hume s task is not so simple, and his final answer that these relations are psychological growths or products of association is neither satisfactory in itself nor quite in keeping with other portions of his doctrine. In Hume, however, we hnd the first thorough going attempt to construct a theory of knowledge on the basis of psychological empiricism or individualism, and the first contribu tions to a doctrine of inductive proof as portion of this more com prehensive theory. Briefly, so far as logic is concerned, Hume offers as explanation of the universal in thought association of ideas, but does not treat of logic specially or in detail. The complete statement of the theory of knowledge from the psychological point of view is that contained in Mill s System of Logic. The aim of that work is the exposition of the theory of knowledge. Now knowledge, the term being taken in a wide sense, is charac terized by one quality mainly, viz., evidentiary force. For every item entering into the sum of our beliefs at any moment, immediate perception being discounted, there may be reasons advanced, adequate or inadequate. The exposition of the relations between beliefs and their evidence or ground is logic, and logic is thus in one sense formal, inasmuch as the relations of evidence and belief are general, not dependent on the special nature of the facts believed, and in another sense real, in that knowledge is conceivable only in strictest ivLition to the tilings known. Now, the exposition of the general nature of grounds of belief is in fact identical with a theory of the universal element in thought or cognition, and this theory is the essential portion of Mill s logic. It being assumed that the facts with which knowledge is concerned are minds, bodies, states of consciousness, and the relations (coexistence, sequence, similarity) among these states, and that propositions express, therefore, existence, co existence, sequence, or resemblance, on what is based any inference going beyond a present perception? The propositions which make up cognition, strictly so called, are not mere expressions of momen tary states; they are expressions of belief regarding the more or less constant relations of facts. They are, in fact, conclusions. The theory of proposition and of reasoning is one. On what, then, do such conclusions rest? The warrant for any conclusion based upon experience, and referring to exjjerience itself, can be found only in experience or in some principle furnished by experience. It may be shown that evidence for a conclusion is adequate, if we can compare this evidence with the kind of evidence on which a wider conclusion, frequently or constantly verified, rests. This comparison of par ticular evidence with more general evidence is the preliminary answer furnished by Mill. But what is the general evidence referred to, and what is the principle founded on it? The general evidence is the repeated experience of constancy of connexion among groups of phenomena, and the principle founded on it is that of the existence of uniformity or rather of uniformities in nature. The evidence and the principle are purely psychological in character; that is to say, repeated experience, beginning with familiar cases and extending itself as time goes on, produces, by the natural laws of association, an assured belief that phenomena as a whole, or at least in the main, are connected together in constant, uniform, invariable modes. Such a belief, once established, serves as an ultimate criterion of proof, and as an index for research. We pro ceed in our investigations in the light of this principle, and the tests by which we estimate the validity of evidence for any parti cular inference as to uniformity are generalized statements deducible from it. So soon as our evidence is of such a character that, in the case before us, either the inference of uniformity is warranted or the general principle must be held not to apply to this particular case, we have proof as cogent as experience can afford. The universal in knowledge, then, is this naturally formed assumption regarding the course of nature. The logic of know ledge is the exposition of the modes in which evidence is obtained, of the tests by which its validity is estimated, and of the forms in which evidence and conclusion are connected. The characteristic features of the subordinate processes of proof are at once deducible from this fundamental view. For if the simplest form of inference be, psychologically, the transition effected by association from one particular case to another resembling it, and if the essence of proof consist in comparison of the evidence for any one conclusion with the type of evidence for the general assumption regarding nature (or at least a wider portion of nature), it is evident that syllogism, in the ordinary acceptation of the term (in which it implies a concrete general proposition, a particular subsumed there under, and a conclusion), is neither a primitive form of inference nor a valid mode of proof. Doubtless we do in reasoning employ general propositions in order to express the determination of some particulars Belonging to the same class, but the general proposition is itself a conclusion, resting on evidence of the kind above described, and the essence of syllogistic reasoning is not the sub- sumption of a particular under a general in which it is included, but the expression of belief that the evidence for the general pro position is adequate to cover all the particular cases, including those which have not been taken into account in formulating it. The major premiss of a syllogism is the record of a previous induction, and the syllogistic process, bringing forward a new case, is a valu able method for testing the adequacy of the previous generalization. As to generalization itself, the basis is evidently to be sought in experience, apprehended by observation and experiment. Did experience present to us isolated phenomena, i.e., phenomena so arranged that enumeration of the elementary constituents, whether antecedents or consequents, were possible, then our inductive pro cedure must be regulated by those canons or axioms which express the kind of evidence already referred to as establishing uniformity. These canons or axioms, however, are, like the Baconian method of exclusion, tests for an ideally perfect experience, and they, there fore, only lie in the background of actual scientific procedure, which has to employ other processes, both of inference and of proof. For, if we can in no way obtain more than a knowledge of the coexistence of facts, we are unable to bring our evidence into conformity with the inductive canons, save in the ideal instance in which absolutely exhaustive experience both of positive and negative cases is possible. Inferences as to law or uniformity of coexistence must here be based on numerical calculation of probability, and the conclusions present themselves in the peculiar numerical form appropriate to proposi tions of probability. Further, if the phenomena under investigation be complex, so that the canons of neither observation nor experiment are immediately applicable, the process of investigation must of necessity be the combined method of analysis and synthesis : analysis, aided by hypothetical conjecture, formulating such general laws of elementary factors as are known or presumed to exist in the case in question; synthesis, combining these laws and calculating with greater or less numerical exactness, according to the nature of the matter, the probable combined effect, the whole tested by critical comparison of the calculated result with the actual pheno mena. Here, as one can see, syllogistic procedure appears in its true scientific aspect as the form of thought by which we pass from the simple to the more complex, from the elementary essence or cause to the complex accident or effect. The elementary causes, no doubt, have no more cogent evidence than that which can be afforded by experience viewed in the light of our psychological assumption of uniformities; nevertheless the whole procedure of scientific investigation is recognized as being essentially of the type sketched in somewhat imperfect outline by Aristotle. So far, then, as the logic of Mill is concerned, and apart from the undeniable richness and completeness of knowledge with which the various processes are treated, we note but one fundamentally new feature, namely, the explanation offered of the universal element XIV. ioo