In 1787, in the preface to the second edition of the Kr. d. r. V., Kant wrote the following words: "That logic, from the earliest times, has followed that secure method" (namely, the secure method of a science witnessed by the unanimity of its workers and the stability of its results) "may be seen from the fact that since Aristotle it has not had to retrace a single step, unless we choose to consider as improvements the removal of some unnecessary subtleties, or the clearer definition of its matter, both of which refer to the elegance rather than to the solidity of the science. It is remarkable, also, that to the present day, it has not been able to make one step in advance, so that to all appearances it may be considered as completed and perfect. If some modern philosophers thought to enlarge it, by introducing psychological chapters on the different faculties of knowledge (faculty of imagination, wit, etc.), or metaphysical chapters on the origin of knowledge or different degrees of certainty according to the difference of objects (idealism, skepticism, etc.), or, lastly, anthropological chapters on prejudices, their causes and remedies, this could only arise from their ignorance of the peculiar nature of logical science. We do not enlarge, but we only disfigure the sciences, if we allow their respective limits to be confounded; and the limits of logic are definitely fixed by the fact that it is a science which has nothing to do but fully to exhibit and strictly to prove the formal rules of all thought (whether it be a priori or empirical, whatever be its origin or its object, and whatever be the impediments, accidental or natural, which it has to encounter in the human mind)."—[Translated by Max Müller.] Scarcely more than half a century after the publication of this statement of Kant's, John Stuart Mill (Introduction to System of Logic) wrote: "There is as great diversity among authors in the modes which they have adopted of defining logic, as in their treatment of the details of it. This is what might naturally be expected on any subject on which writers have availed themselves of the same language as a means of delivering different ideas.... This diversity is not so much an evil to be complained of, as an inevitable, and in some degree a proper result of the imperfect state of those sciences" (that is, of logic, jurisprudence, and ethics). "It is not to be expected that there should be agreement about the definition of anything, until there is agreement about the thing itself." This remarkable disparity of opinion is due partly to the changes in the treatment of logic from Kant to Mill, and partly to the fact that both statements are extreme. That the science of logic was "completed and perfect" in the time of Kant could only with any degree of accuracy be said of the treatment of syllogistic proof or the deductive logic of Aristotle. That the diversity was so great as pictured by Mill is not historically exact, but could be said only of the new epistemological and psychological treatment of logic and not of the traditional formal logic. The confusion in logic is no doubt largely due to disagreement in the delimitation of its proper territory and to the consequent variety of opinions as to its relations to other disciplines. The rise of inductive logic, coincident with the rise and growth of physical science and empiricism, forced the consideration of the question as to the relation of formal thought to reality, and the consequent entanglement of logic in a triple alliance of logic, psychology, and metaphysics. How logic can maintain friendly relations with both of these and yet avoid endangering its territorial integrity has not been made clear by logicians or psychologists or metaphysicians, and that, too, in spite of persistent attempts justly to settle the issue as to their respective spheres of influence. Until modern logic definitely settles the question of its aims and legitimate problems, it is difficult to see how any agreement can be reached as to its relation to the other disciplines. The situation as it confronts one in the discussion of the relations of logic to allied subjects may be analyzed as follows:

1. The relation of logic as science to logic as art.

2. The relation of logic to psychology.

3. The relation of logic to metaphysics.

The development of nineteenth century logic has made an answer to the last two of the foregoing problems exceedingly difficult. Indeed, one may say that the evolution of modern epistemology has had a centrifugal influence on logic, and instead of growth towards unity of conception we have a chaos of diverse and discordant theories. The apple of discord has been the theory of knowledge. A score of years ago when Adamson wrote his admirable article in the Encyclopædia Britannica (article "Logic," 1882), he found the conditions much the same as I now find them. "Looking to the chaotic state of logical text-books at the present time, one would be inclined to say that there does not exist anywhere a recognized currently received body of speculations to which the title logic can be unambiguously assigned, and that we must therefore resign the hope of attaining by any empirical consideration of the received doctrine a precise determination of the nature and limits of logical theory." I do not, however, take quite so despondent a view of the logical chaos as the late Professor Adamson; rather, I believe with Professor Stratton (Psy. Rev. vol. III) that something is to be gained for unity and consistency by more exact delimitation of the subject-matter of the philosophical disciplines and their interrelations, which precision, if secured, would assist in bringing into clear relief the real problems of the several departments of inquiry, and facilitate the proper classification of the disciplines themselves.

The attempt to delimit the spheres of the disciplines, to state their interrelations and classify them, was made early in the history of philosophy, at the very beginning of the development of logic as a science by Aristotle. In Plato's philosophy, logic is not separated from epistemology and metaphysics. The key to his metaphysics is given essentially in his theory of the reality of the concept, which offers an interesting analogy to the position of logic in modern idealism. Before Plato there was no formulation of logical theory, and in his dialogues it is only contained in solution. The nearest approach to any formulation is to be found in an applied logic set forth in the precepts and rules of the rhetoricians and sophists. Properly speaking, Aristotle made the first attempt to define the subject of logic and to determine its relations to the other sciences. In a certain sense logic for Aristotle is not a science at all. For science is concerned with some ens, some branch of reality, while logic is concerned with the methodology of knowing, with the formal processes of thought whereby an ens or a reality is ascertained and appropriated to knowledge. In the sense of a method whereby all scientific knowledge is secured, logic is a propædeutic to the sciences. In the idealism of the Eleatics and Plato, thought and being are ultimately identical, and the laws of thought are the laws of being. In Aristotle's conception, while the processes of thought furnish a knowledge of reality or being, their formal operation constitutes the technique of investigation, and their systematic explanation and description constitute logic. Logic and metaphysics are distinguished as the science of being and the doctrine of the thought processes whereby being is known. Logic is the doctrine of the organon of science, and when applied is the organon of science. The logic of Aristotle is not a purely formal logic. He is not interested in the merely schematic character of the thought processes, but in their function as mediators of apodictic truth. He begins with the assumption that in the conjunction and disjunction of correctly formed judgments the conjunction or disjunction of reality is mirrored. Aristotle does not here examine into the powers of the mind as a whole; that is done, though fragmentarily, in the De Anima and Parva Naturalia, where the mental powers are regarded as phases of the processes of nature without reference to normation; but in his logic he inquires only into those forms and laws of thinking which mediate proof. Scientific proof, in his conception, is furnished in the form of the syllogism, whose component elements are terms and propositions. In the little tract On Interpretation (i. e. on the judgment as interpreter of thought), if it is genuine, the proposition is considered in its logical bearing. The treatise on the Categories, which discusses the nature of the most general terms, forms a connecting link between logic and metaphysics. The categories are the most general concepts or universal modes under which we have knowledge of the world. They are not simply logical relations; they are existential forms, being not only the modes under which thought regards being, but the modes under which being exists. Aristotle's theory of the methodology of science is intimately connected with his view of knowledge. Scientific knowledge in his opinion refers to the essence of things; for example, to those universal aspects of reality which are given in particulars, but which remain self-identical amidst the variation and passing of particulars. The universal, however, is known only through and after particulars. There is no such thing as innate knowledge or Platonic reminiscence. Knowledge, if not entirely empirical, has its basis in empirical reality. Causes are known only through effects. The universals have no existence apart from things, although they exist realiter in things. Empirical knowledge of particulars must, therefore, precede in time the conceptual or scientific knowledge of universals. In the evolution of scientific knowledge in the individual mind, the body of particulars or of sense-experience is to its conceptual transformation as potentiality is to actuality, matter to form, the completed end of the former being realized in the latter. Only in the sense of this power to transform and conceptualize, does the mind have knowledge within itself. The genetic content is experiential; the developed concept, judgment, or inference is in form noëtic. Knowledge is, therefore, not a mere "precipitate of experience," nor is Aristotle a complete empiricist. The conceptual form of knowledge is not immediately given in things experienced, but is a product of noëtic discrimination and combination. Of a sensible object as such there is no concept; the object of a concept is the generic essence of a thing; and the concept itself is the thought of this generic essence. The individual is generalized; every concept does or can embrace several individuals. It is an "aggregate of distinguishing marks," and is expressed in a definition. The concept as such is neither true nor false. Truth first arises in the form of a judgment or proposition, wherein a subject is coupled with a predicate, and something is said about something. A judgment is true when the thought (whose inward process is the judgment and the expression in vocal symbols is the proposition) regards as conjoined or divided that which is conjoined or divided in actuality; in other words, when the thought is congruous with the real. While Aristotle does not ignore induction as a scientific method, (how could he when he regards the self-subsistent individual as the only real?) yet he says that, as a method, it labors under the defect of being only proximate; a complete induction from all particulars is not possible, and therefore cannot furnish demonstration. Only the deductive process proceeding syllogistically from the universal (or essential truth) to the particular is scientifically cogent or apodictic. Consequently Aristotle developed the science of logic mainly as a syllogistic technique or instrument of demonstration. From this brief sketch of Aristotle's logical views it will be seen that the epistemological and metaphysical relations of logic which involve its greatest difficulty and cause the greatest diversity in its modern exponents, were present in undeveloped form to the mind of the first logician. It would require a mighty optimism to suppose that this difficulty and diversity, which has increased rather than diminished in the progress of historical philosophy, should suddenly be made to vanish by some magic of restatement of subject-matter, or theoretical delimitation of the discipline. As Fichte said of philosophy, "The sort of a philosophy that a man has, depends on the kind of man he is;" so one might almost say of logic, "The sort of logic that a man has, depends on the kind of philosopher he is." If the blight of discord is ever removed from epistemology, we may expect agreement as to the relations of logic to metaphysics. Meanwhile logic has the great body of scientific results deposited in the physical sciences on which to build and test, with some assurance, its doctrine of methodology; and as philosophy moves forward persistently to the final solution of its problems, logic may justly expect to be a beneficiary in its established theories.

After Aristotle's death logic lapsed into a formalism more and more removed from any vital connection with reality and oblivious to the profound epistemological and methodological questions that Aristotle had at least raised. In the Middle Ages it became a highly developed exercise in inference applied to the traditional dogmas of theology and science as premises, with mainly apologetic or polemical functions. Its chief importance is found in its application to the problem of realism and nominalism, the question as to the nature of universals. At the height of scholasticism realism gained its victory by syllogistically showing the congruity of its premises with certain fundamental dogmas of the Church, especially with the dogma of the unity and reality of the Godhead. The heretical conclusion involved in nominalism is equivalent (the accepted dogma of the Church being axiomatic) to reductio ad absurdum. A use of logic such as this, tending to conserve rather than to increase the body of knowledge, was bound to meet with attack on the awakening of post-renaissance interest in the physical world, and the acquirement of a body of truth to which the scholastic formal logic had no relation. The anti-scholastic movement in logic was inaugurated by Francis Bacon, who sought in his Novum Organum to give science a real content through the application of induction to experience and the discovery of universal truths from particular instances. The syllogism is rejected as a scientific instrument, because it does not lead to principles, but proceeds only from principles, and is therefore not useful for discovery. It permits at most only refinements on knowledge already possessed, but cannot be regarded as creative or productive. The Baconian theory of induction regarded the accumulation of facts and the derivation of general principles and laws from them as the true and fruitful method of science. In England this empirical view of logic has been altogether dominant, and the most illustrious English exponents of logical theory, Herschel, Whewell, and Mill, have stood on that ground. Since the introduction of German idealism in the last half century a new logic has grown up whose chief business is with the theory of knowledge.

Kant's departure in logic is based on an epistemological examination of the nature of judgment, and on the answer to his own question, "How are synthetic judgments a priori possible?" The a priori elements in knowledge make knowledge of the real nature of things impossible. Human knowledge extends to the phenomenal world, which is seen under the a priori forms of the understanding. Logic for Kant is the science of the formal and necessary laws of thought, apart from any reference to objects. Pure or universal logic aims to understand the forms of thought without regard to metaphysical or psychological relations, and this position of Kant is the historical beginning of the subjective formal logic.

In the metaphysical logic of Hegel, which rests on a panlogistic basis, being and thought, form and content, are identical. Logical necessity is the measure and criterion of objective reality. The body of reality is developed through the dialectic self-movement of the idea. In such an idealistic monism, formal and real logic are by the metaphysical postulate coincident.

Schleiermacher in his dialectic regards logic from the standpoint of epistemological realism, in which the real deliverances of the senses are conceptually transformed by the spontaneous activity of reason. This spirit of realism is similar to that of Aristotle, in which the one-sided a priori view of knowledge is controverted. Space and time are forms of the existence of things, and not merely a priori forms of knowing. Logic he divides into dialectic and technical logic. The former regards the idea of knowledge as such; the formal or technical regards knowledge in the process of becoming or the idea of knowledge in motion. The forms of this process are induction and deduction. The Hegelian theory of the generation of knowledge out of the processes of pure thought is emphatically rejected.

Lotze, who is undoubtedly one of the most influential and fruitful writers on logic in the last century, attempts to bring logic into closer relations with contemporary science, and is an antagonist of one-sided formal logics. For him logic falls into the three parts of (1) pure logic or the logic of thought; (2) applied logic or the logic of investigation; (3) the logic of knowledge or methodology; and this classification of the matter and problems of logic has had an important influence on subsequent treatises on the discipline. His logic is formal, as he describes it himself, in the sense of setting forth the modes of the operation of thought and its logical structure; it is real in the sense that these forms are dependent on the nature of things and not something independently given in the mind. While he aims to maintain the distinct separation of logic and metaphysics, he says (in the discussion of the relations between formal and real logical meaning) the question of meaning naturally raises a metaphysical problem: "Ich thue besser der Metaphysik die weitere Erörterung dieses wichtigen Punktes zu überlassen." (Log. 2d ed. p. 571.) How could it be otherwise when his whole view of the relations and validity of knowledge is inseparable from his realism or teleological idealism, as he himself characterizes his own standpoint?

Drobisch, a follower of Herbart, is one of the most thoroughgoing formalists in modern logical theory. He attempts to maintain strictly the distinction between thought and knowledge. Logic is the science of thought. He holds that there may be formal truth, for example, logically valid truth, which is materially false. Logic, in other words, is purely formal; material truth is matter for metaphysics or science. Drobisch holds, therefore, that the falsity of the judgment expressed in the premise from which a formally correct syllogism may be deduced, is not subject-matter for logic. The sphere of logic is limited to the region of inference and forms of procedure, his view of the nature and function of logic being determined largely by the bias of his mathematical standpoint. The congruity of thought with itself, judgments, conclusions, analyses, etc., is the sole logical truth, as against Trendelenburg, who took the Aristotelian position that logical truth is the "agreement of thought with the object of thought."

Sigwart looks at logic mainly from the standpoint of the technology of science, in which, however, he discovers the implications of a teleological metaphysic. Between the processes of consciousness and external changes he finds a causal relation and not parallelism. Inasmuch as thought sometimes misses its aim, as is shown by the fact that error and dispute exist, there is need of a discipline whose purpose is to show us how to attain and establish truth and avoid error. This is the practical aim of logic, as distinguished from the psychological treatment of thought, where the distinction between true and false has no more place than the distinction between good and bad. Logic presupposes the impulse to discover truth, and it therefore sets forth the criteria of true thinking, and endeavors to describe those normative operations whose aim is validity of judgment. Consequently logic falls into the two parts of (1) critical, (2) technical, the former having meaning only in reference to the latter; the main value of logic is to be sought in its function as art. "Methodology, therefore, which is generally made to take a subordinate place, should be regarded as the special, final, and chief aim of our science." (Logic, vol. i, p. 21, Eng. Tr.) As an art, logic undertakes to determine under what conditions and prescriptions judgments are valid, but does not undertake to pass upon the validity of the content of given judgments. Its prescriptions have regard only to formal correctness and not to the material truth of results. Logic is, therefore, a formal discipline. Its business is with the due procedure of thought, and it attempts to show no more than how we may advance in the reasoning process in such way that each step is valid and necessary. If logic were to tell us what to think or give us the content of thought, it would be commensurate with the whole of science. Sigwart, however, does not mean by formal thought independence of content, for it is not possible to disregard the particular manner in which the materials and content of thought are delivered through sensation and formed into ideas. Further, logic having for its chief business the methodology of science, the development of knowledge from empirical data, it ought to include a theory of knowledge, but it should not so far depart from its subjective limits as to include within its province the discussion of metaphysical implications or a theory of being. For this reason, Sigwart relegates to a postscript his discussion of teleology, but he gives an elaborate treatment of epistemology extending through vol. i and develops his account of methodology in vol. ii. The question regarding the relation between necessity, the element in which logical thought moves, and freedom, the postulate of the will, carries one beyond the confines of logic and is, in his opinion, the profoundest problem of metaphysics, whose function is to deal with the ultimate relation between "subject and object, the world and the individual, and this is not only basal for logic and all science, but is the crown and end of them all."

Wundt's psychological and methodological treatment of logic stands midway between the purely formal treatises on the one hand, and the metaphysical treatises on the other hand. The general standpoint of Wundt is similar to that of Sigwart, in that he discovers the function of logic in the exposition of the formation and methods of scientific knowledge; for example, in epistemology and methodology. Logic must conform to the conditions under which scientific inquiry is actually carried on; the forms of thought, therefore, cannot be separate from or indifferent to the content of knowledge; for it is a fundamental principle of science that its particular methods are determined by the nature of its particular subject-matter. Scientific logic must reject the theory that identifies thought and being (Hegel) and the theory of parallelism between thought and reality (Schleiermacher, Trendelenburg, and Ueberweg), in which the ultimate identity of the two is only concealed. Both of these theories base logic on a metaphysics, which makes it necessary to construe the real in terms of thought, and logic, so divorced from empirical reality, is powerless to explain the methods of scientific procedure. One cannot, however, avoid the acceptance of thought as a competent organ for the interpretation of reality, unless one abandons all question of validity and accepts agnosticism or skepticism. This interpretative power of thought or congruity with reality is translated by metaphysical logic into identity. Metaphysical logic concerns itself fundamentally with the content of knowledge, not with its evidential or formal logical aspects, but with being and the laws of being. It is the business of metaphysics to construct its notions and theories of reality out of the deliverances of the special sciences and inferences derived therefrom. The aim of metaphysics is the development of a world-view free from internal contradictions, a view that shall unite all particular and plural knowledges into a whole. Logic stands in more intimate relation to the special sciences, for here the relations are reciprocal and immediate; for example, from actual scientific procedure logic abstracts its general laws and results, and these in turn it delivers to the sciences as their formulated methodology. In the history of science the winning of knowledge precedes the formulation of the rules employed, that is, precedes any scientific methodology. Logic, as methodology, is not an a priori construction, but has its genesis in the growth of science itself and in the discovery of those tests and criteria of truth which are found to possess an actual heuristic or evidential value. It is not practicable to separate epistemology and logic, for such concepts as causality, analogy, validity, etc., are fundamental in logical method, and yet they belong to the territory of epistemology, are epistemological in nature, as one may indeed say of all the general laws of thought. A formal logic that is merely propædeutic, a logic that aims to free itself from the quarrels of epistemology, is scientifically useless. Its norms are valueless, in so far as they can only teach the arrangement of knowledge already possessed, and teach nothing as to how to secure it or test its real validity. While formal logic aims to put itself outside of philosophy, metaphysical logic would usurp the place of philosophy. Formal logic is inadequate, because it neither shows how the laws of thought originate, why they are valid, nor in what sense they are applicable to concrete investigation. Wundt, therefore, develops a logic which one may call epistemological methodological, and which stands between the extremes of formal logic and metaphysical logic. The laws of logic must be derived from the processes of psychic experience and the procedure of the sciences. "Logic therefore needs," as he says, "epistemology for its foundation and the doctrine of methods for its completion."

Lipps takes the view outright that logic is a branch of psychology; Husserl in his latest book goes to the other extreme of a purely formal and technical logic, and devotes almost his entire first volume to the complete sundering of psychology and logic.

Bradley bases his logic on the theory of the judgment. The logical judgment is entirely different from the psychological. The logical judgment is a qualification of reality by means of an idea. The predicate is an adjective or attribute which in the judgment is ascribed to reality. The aim of truth is to qualify reality by general notions. But inasmuch as reality is individual and self-existent, whereas truth is universal, truth and reality are not coincident. Bradley's metaphysical solution of the disparity between thought and reality is put forward in his theory of the unitary Absolute, whose concrete content is the totality of experience. But as thought is not the whole of experience, judgments cannot compass the whole of reality. Bosanquet objects to this, and maintains that reality must not be regarded as an ideal construction. The real world is the world to which our concepts and judgments refer. In the former we have a world of isolated individuals of definite content; in the latter, we have a world of definitely systematized and organized content. Under the title of the Morphology of Knowledge Bosanquet considers the evolution of judgment and inference in their varied forms. "Logic starts from the individual mind, as that within which we have the actual facts of intelligence, which we are attempting to interpret into a system" (Logic, vol. i, p. 247). The real world for every individual is his world. "The work of intellectually constituting that totality which we call the real world is the work of knowledge. The work of analyzing the process of this constitution or determination is the work of logic, which might be described ... as the reflection of knowledge upon itself" (Logic, vol. i, p. 3). "The relation of logic to truth consists in examining the characteristics by which the various phases of the one intellectual function are fitted for their place in the intellectual totality which constitutes knowledge" (ibid.). The real world is the intelligible world; reality is something to which we attain by a constructive process. We have here a type of logic which is essentially a metaphysic. Indeed, Bosanquet says in the course of his first volume: "I entertain no doubt that in content logic is one with metaphysics, and differs, if at all, simply in mode of treatment—in tracing the evolution of knowledge in the light of its value and import, instead of attempting to summarize its value and import apart from the details of its evolution" (Logic, vol. i, 247).

Dewey (Studies in Logical Theory, p. 5) describes the essential function of logic as the inquiry into the relations of thought as such to reality as such. Although such an inquiry may involve the investigation of psychological processes and of the concrete methods of science and verification, a description and analysis of the forms of thought, conception, judgment, and inference, yet its concern with these is subordinate to its main concern, namely, the relation of "thought at large to reality at large." Logic is not reflection on thought, either on its nature as such or on its forms, but on its relations to the real. In Dewey's philosophy, logical theory is a description of thought as a mode of adaptation to its own conditions, and validity is judged in terms of the efficiency of thought in the solution of its own problems and difficulties. The problem of logic is more than epistemological. Wherever there is striving there are obstacles; and wherever there is thinking there is a "material-in-question." Dewey's logic is a theory of reflective experience regarded functionally, or a pragmatic view of the discipline. This logic of experience aims to evaluate the significance of social research, psychology, fine and industrial art, and religious aspiration in the form of scientific statement, and to accomplish for social values in general what the physical sciences have done for the physical world. In Dewey's teleological pragmatic logic the judgment is essentially instrumental, the whole of thinking is functional, and the meaning of things is identical with valid meaning (Studies in Logical Theory, cf. pp. 48, 82, 128). The real world is not a self-existent world outside of knowledge, but simply the totality of experience; and experience is a complex of strains, tensions, checks, and attitudes. The function of logic is the redintegration of this experience. "Thinking is adaptation to an end through the adjustment of particular objective contents" (ibid. p. 81). Logic here becomes a large part, if not the whole, of a metaphysics of experience; its nature and function are entirely determined by the theory of reality.

In this brief and fragmentary résumé are exhibited certain characteristic movements in the development of logical theory, the construction put upon its subject-matter and its relation to other disciplines. The résumé has had in view only the making of the diversity of opinion on these questions historically salient. There are three distinct types of logic noticed here: (1) formal, whose concern is merely with the structural aspect of inferential thought, and its validity in terms of internal congruity; (2) metaphysical logic whose concern is with the functional aspect of thought, its validity in terms of objective reference, and its relation to reality; (3) epistemological and methodological logic, whose concern is with the genesis, nature, and laws of logical thinking as forms of scientific knowledge, and with their technological application to the sciences as methodology. I am not at present concerned with a criticism of these various viewpoints, excepting in so far as they affect the problem of the interrelationship of logic and the allied disciplines.

For my present purpose I reject the extreme metaphysical and formal positions, and assume that logic is a discipline whose business is to describe and systematize the formal processes of inferential thought and to apply them as practical principles to the body of real knowledge.

I wish now to take up seriatim the several questions touching the various relations of logic enumerated above, and first of all the question of the relation of logic as science to logic as art.

I. Logic as science and logic as art.

It seems true that the founder of logic, Aristotle, regarded logic not as a science, but rather as propædeutic to science, and not as an end in itself, but rather technically and heuristically as an instrument. In other words, logic was conceived by him rather in its application or as an art, than as a science, and so it continued to be regarded until the close of the Middle Ages, being characterized indeed as the ars artium; for even the logica docens of the Scholastics was merely the formulation of that body of precepts which are of practical service in the syllogistic arrangement of premises, and the Port Royal Logic aims to furnish l'art de penser. This technical aspect of the science has clung to it down to the present day, and is no doubt a legitimate description of a part of its function. But no one would now say that logic is an art; rather it is a body of theory which may be technically applied. Mill, in his examination of Sir William Hamilton's Philosophy (p. 391), says of logic that it "is the art of thinking, which means of correct thinking, and the science of the conditions of correct thinking," and indeed, he goes so far as to say (System of Logic, Introd. § 7): "The extension of logic as a science is determined by its necessities as an art." Strictly speaking, logic as a science is purely theoretical, for the function of science as such is merely to know. It is an organized system of knowledge, namely, an organized system of the principles and conditions of correct thinking. But because correct thinking is an art, it does not follow that a knowledge of the methods and conditions of correct thinking is art, which would be a glaring case of μετάβασις εἰς ἄλλο γένος. The art-bearings of the science are given in the normative character of its subject-matter. As a science logic is descriptive and explanatory, that is, it describes and formulates the norms of valid thought, although as science it is not normative, save in the sense that the principles formulated in it may be normatively or regulatively applied, in which case they become precepts. What is principle in science becomes precept in application, and it is only when technically applied that principles assume a mandatory character. Validity is not created by logic. Logic merely investigates and states the conditions and criteria of validity, being in this reference a science of evidence. In the very fact, however, that logic is normative in the sense of describing and explaining the norms of correct thinking, its practical or applied character is given. Its principles as known are science; its principles as applied are art. There is, therefore, no reason to sunder these two things or to call logic an art merely or a science merely; for it is both when regarded from different viewpoints, although one must insist on the fact that the rules for practical guidance are, so far as the science is concerned, quite ab extra. Logic, ethics, and æsthetics are all commonly (and rightly) called normative disciplines: they are all concerned with values and standards; logic with validity and evidence, or values for cognition; ethics with motives and moral quality in conduct, or values for volition; æsthetics with the standards of beauty, or values for appreciation and feeling. Yet none of them is or can be merely normative, or indeed as science normative at all; if that were so, they would not be bodies of organized knowledge, but bodies of rules. They might be well-arranged codes of legislation on conduct, fine art, and evidence, but not sciences. Strictly regarded, it is the descriptive and explanatory aspect of logic that constitutes its scientific character, while it is the specific normative aspect that constitutes its logical character. Values, whether ethical or logical, without an examination and formulation of their ground, relations, origin, and interconnection, would be merely rules of thumb, popular phrases, or pastoral precepts. The actual methodology of the sciences or applied logic is logic as art.

II. Relation of logic to psychology.

The differentiation of logic and psychology in such way as to be of practical value in the discussion of the disciplines has always been a difficult matter. John Stuart Mill was disposed to merge logic in psychology, and Hobhouse, his latest notable apologete, draws no fixed distinction between psychology and logic, merely saying that they have different centres of interest, and that their provinces overlap. Lipps, in his Grundzüge der Logik (p. 2), goes the length of saying that "Logic is a psychological discipline, as certainly as knowledge occurs only in the Psyche, and thought, which is developed in knowledge, is a psychical event." Now, if we were to take such extreme ground as this, their ethics, æsthetics, and pure mathematics would become at once branches of psychology and not coördinate disciplines with it, for volitions, the feelings of appreciation, and the reasoning of pure mathematics are psychical events. Such a theory plainly carries us too far and would involve us in confusion. That the demarcation between the two disciplines is not a chasmic cleavage, but a line, and that, too, an historically shifting line, is apparent from the foregoing historical résumé.

The four main phases of logical theory include: (1) the concept (although some logicians begin with the judgment as temporally prior in the evolution of language), (2) judgment, (3) inference, (4) the methodology of the sciences. The entire concern of logic is, indeed, with psychical processes, but with psychical processes regarded from a specific standpoint, a standpoint different from that of psychology. In the first place psychology in a certain sense is much wider than logic, being concerned with the whole of psychosis as such, including the feelings and will and the entire structure of cognition, whereas logic is concerned with the particular cognitive processes enumerated above (concept, judgment, inference), and that, too, merely from the point of view of validity and the grounds of validity. In another sense psychology is narrower than logic, being concerned purely with the description and explanation of a particular field of phenomena, whereas logic is concerned with the procedure of all the sciences and is practically related to them as their formulated method. The compass and aims of the two disciplines are different; for while psychology is in different references both wider and narrower than logic, it is also different in the problems it sets itself, its aim being to describe and explain the phenomena of mind in the spirit of empirical science, whereas the aim of logic is only to explain and establish the laws of evidence and standards of validity. Logic is, therefore, selective and particular in the treatment of mental phenomena, whereas psychology is universal, that is, it covers the entire range of mental processes as a phenomenalistic science; logic dealing with definite elements as a normative science. By this it is not meant that the territory of judgment and inference should be delivered from the psychologist into the care of the logician; through such a division of labor both disciplines would suffer. The two disciplines handle to some extent the same subjects, so far as names are concerned; but the essence of the logical problem is not touched by psychology, and should not be mixed up with it, to the confusion and detriment of both disciplines. The field of psychology, as we have said, is the whole of psychical phenomena; the aim of individual psychology in the investigation of its field is: (1) to give a genetic account of cognition, feeling, and will, or whatever be the elements into which consciousness is analyzed; (2) to explain their interconnections causally; (3) as a chemistry of mental life to analyze its complexes into their simplest elements; (4) to explain the totality structurally (or functionally) out of the elements; (5) to carry on its investigation and set forth its results as a purely empirical science; (6) psychology makes no attempt to evaluate the processes of mind either in terms of false and true, or good and bad. From this description of the field and function of psychology, based on the expressions of its modern exponents, it will be found impossible to shelter logic under it as a subordinate discipline. If one were to enlarge the scope of psychology to mean rational psychology, in the sense which Professor Howison advocates (Psychological Review, vol. iii, p. 652), such a subordination might be possible, but it would entail the loss of all that the new psychology has gained by the sharper delimitation of its sphere and problems, and would carry us back to the position of Mill, who appears to identify psychology with philosophy at large and with metaphysics.

In contradistinction to the aims of psychology as described in the foregoing, the sphere and problems of logic may be summarily characterized as follows: (1) All concepts and judgments are psychological complexes and processes and may be genetically and structurally described; that is the business of psychology. They also have a meaning value, or objective reference, that is, they may be correct or incorrect, congruous or incongruous with reality. The meaning, aspect of thought, or its content as truth is the business of logic. This subject-matter is got by regarding a single aspect in the total psychological complex. (2) Its aim is not to describe factual thought or the whole of thought, or the natural processes of thought, but only certain ideals of thinking, namely, the norms of correct thinking. Its object is not a datum, but an ideal. (3) While psychology is concerned with the natural history of reasoning, logic is concerned with the warrants of inferential reasoning. In the terminology of Hamilton it is the nomology of discursive thought. To use an often employed analogy, psychology is the physics of thought, logic an ethics of thought. (4) Logic implies an epistemology or theory of cognition in so far as epistemology discusses the concept and judgment and their relations to the real world, and here is to be found its closest connection with psychology. A purely formal logic, which is concerned merely with the internal order of knowledge and does not undertake to show how the laws of thought originate, why they hold good as the measures of evidence, or in what way they are applicable to concrete reality, would be as barren as scholasticism. (5) While logic thus goes back to epistemology for its bases and for the theoretical determination of the interrelation of knowledge and truth, it goes forward in its application to the practical service of the sciences as their methodology. Apart of its subject-matter is therefore the actual procedure of the sciences, which it attempts to organize into systematic statements as principles and formulæ. This body of rules given implicitly or explicitly in the workings and structure of the special sciences, consisting in classification, analysis, experiment, induction, deduction, nomenclature, etc., logic regards as a concrete deposit of inferential experience. It abstracts these principles from the content and method of the sciences, describes and explains them, erects them into a systematic methodology, and so creates the practical branch of real logic. Formal logic, therefore, according to the foregoing account, would embrace the questions of the internal congruity and self-consistency of thought and the schematic arrangement of judgments to insure formally valid conclusions; real logic would embrace the epistemological questions of how knowledge is related to reality, and how it is built up out of experience, on the one hand, and the methodological procedure of science, on the other. The importance of mathematical logic seems to be mainly in the facilitation of logical expression through symbols. It is rather with the machinery of the science than with its content and real problem that the logical algorithm or calculus is concerned. In these condensed paragraphs sufficient has been said, I think, to show that logic and psychology should be regarded as coördinate disciplines; for their aims and subject-matter differ too widely to subordinate the former under the latter without confusion to both.

I wish now to add a brief note on the relation of logic to another discipline.

III. Relation of logic to metaphysics.

As currently expounded, logic either abuts immediately on the territory of metaphysics at certain points or is entirely absorbed in it as an integral part of the metaphysical subject-matter. I regard the former view as not only the more tenable theoretically, but as practically advantageous for working purposes, and necessary for an intelligible classification of the philosophical disciplines. The business of metaphysics, as I understand it, is with the nature of reality; logic is concerned with the nature of validity, or with the relations of the elements of thought within themselves (self-consistency) and with the relations of thought to its object (real truth), but not with the nature of the objective world or reality as such. Further, metaphysics is concerned with the unification of the totality of knowledge in the form of a scientific cosmology; logic is concerned merely with the inferential and methodological processes whereby this result is reached. The former is a science of content; the latter is a science of procedure and relations. Now, inasmuch as procedure and relations apply to some reality and differ with different forms of reality, logic necessitates in its implications a theory of being, but such implications are in no wise to be identified with its subject-matter or with its own proper problems. Their consideration falls within the sphere of metaphysics or a broadly conceived epistemology, whose business it is to solve the ultimate questions of subject and object, thought and thing, mind and matter, that are implied and pointed to rather than formulated by logic. Inasmuch as the logical judgment says something about something, the scientific impulse drives us to investigate what the latter something ultimately is; but this is not necessary for logic, nor is it one of logic's legitimate problems, any more than it is the proper business of the physicist to investigate the mental implications of his scientific judgments and hypotheses or the ultimate nature of the theorizing and perceiving mind, or of causality to his world of matter and motion, although a general scientific interest may drive him to seek a solution of these ultimate metaphysical problems. Scientifically the end of logic and of every discipline is in itself; it is a territorial unity, and its government is administered with a unitary aim. Logic is purely a science of evidential values, not a science of content (in the meaning of particular reality, as in the special sciences, or of ultimate reality, as in metaphysics); its sole aim and purpose, as I conceive it, is to formulate the laws and grounds of evidence, the principles of method, and the conditions and forms of inferential thinking. When it has done this, it has, as a single science, done its whole work. When one looks at the present tendencies of logical theory, one is inclined to believe that the discipline is in danger of becoming an "Allerleiwissenschaft," whose vast undefined territory is the land of "Weissnichtwo." The strict delimitation of the field and problems of science is demanded in the interest of a serviceable division of scientific labor and in the interest of an intelligible classification of the accumulated products of research.

THE FIELD OF LOGIC