Chapter D: Modern Logic (2)

The brief logic of Herbart[135] is altogether formal too. Logical forms have for him neither psychological nor metaphysical reference, we are concerned in logic solely with the systematic clarification of concepts which are wholly abstract, so that they are not merely not ultimate realities, but also in no sense actual moments of our concrete thinking. The first task of logic is to distinguish and group such concepts according to their marks, and from their classification there naturally follows their connexion in judgment. It is in the logic of judgment that Herbart inaugurates a new era. He is not, of course, the first to note that even categorical judgments do not assert the realization of their subject. That is a thought which lies very near the surface for formal logic. He had been preceded too by Maimon in the attempt at a reduction of the traditional types of judgment. He was, however, the first whose analysis was sufficiently convincing to exorcise the tyranny of grammatical forms. The categorical and disjunctive judgment reduce to the hypothetical. By means of the doctrine of the quantification of the predicate, in which with his Leibnitzian conception of identity he anticipated Beneke and Hamilton alike, universal and particular judgments are made to pull together. Modal, impersonal, existential judgments are all accounted for. Only the distinction of affirmative and negative judgments remains unresolved, and the exception is a natural one from the point of view of a philosophy of pluralism. There was little left to be done here save in the way of an inevitable _mutatis mutandis_, even by Lotze and F. H. Bradley. From the judgment viewed as hypothetical we pass by affirmation of the antecedent or denial of the consequent to inference. This point of departure is noteworthy, as also is the treatment of the inductive syllogism as one in which the middle term is resoluble into a group or series (_Reihe_). In indicating specifically, too, the case of conclusion from a copulative major premise with a disjunctive minor, Herbart seems to have suggested the cue for Sigwart's exposition of Bacon's method of exclusions.

That it was the formal character of Herbart's logic which was ultimately fatal to its acceptance outside the school as an independent discipline is not to be doubted. It stands, however, on a different footing from that of the formal logic hitherto discussed, and is not to be condemned upon quite the same grounds. In the first place, Herbart is quite aware of the nature of abstraction. In the second, there is no claim that thought at one and the same time imposes form on "the given" and is susceptible of treatment in isolation by logic. With Herbart the forms of common experience, and indeed all that we can regard as his categories, are products of the psychological mechanism and destitute of logical import. And lastly, Herbart's logic conforms to the exigencies of his system as a whole and the principle of the bare or absolute self-identity of the ultimate "reals" in particular. It is for this reason that it finally lacks real affinity to the "pure logic" of Fries. For at the basis of Herbart's speculation there lies a conception of identity foreign to the thought of Kant with his stress on synthesis, in his thoroughgoing metaphysical use of which Herbart goes back not merely to Wolff but to Leibnitz. It is no mere coincidence that his treatment of all forms of continuance and even his positive metaphysic of "reals" show affinity to Leibnitz. It was in the pressing to its extreme consequences of the conception of uncompromising identity which is to be found in Leibnitz, that the contradictions took their rise which Herbart aimed at solving, by the method of relations and his doctrine of the ultimate plurality of "reals." The logic of relations between conceptual units, themselves unaltered by the relation, seems a kind of reflection of his metaphysical method. To those, of course, for whom the only real identity is identity in difference, while identity without difference, like difference without identity, is simply a limit or a vanishing point, Herbart's logic and metaphysic will alike lack plausibility.

The setting of Herbart's logic in his thought as a whole might of itself perhaps justify separate treatment. His far-reaching influence in the development of later logic must certainly do so. Directly he affected a school of thought which contained one logician of first-rate importance in Moritz Wilhelm Drobisch (1802-1896), professor at Leipzig. In less direct relation stands Lotze, who, although under other influences he developed a different view even in logic, certainly let no point in the doctrine of his great predecessor at Göttingen escape him. A Herbartian strain is to be met with also in the thought of writers much further afield, for example F. H. Bradley, far though his metaphysic is removed from Herbart's. Herbart's influence is surely to be found too in the evolution of what is called _Gegenstandstheorie_. Nor did he affect the logic of his successors through his logic alone. Reference has been made above to the effect upon the rise of the later psychological logic produced by Herbart's psychology of apperception, when disengaged from the background of his metaphysic taken in conjunction with his treatment in his practical philosophy of the judgment of value or what he calls the aesthetic judgment. Emerson's verdict upon a greater thinker--that his was "not a mind to nestle in"--may be true of Herbart, but there can be no doubt as to the stimulating force of this master.

Logic as the rationale of knowledge.

Schleiermacher.

The second way of interpreting the antithesis of thought to what is thought of, was taken by a group of thinkers among whom a central and inspiring figure was Schleiermacher. They in no sense constitute a school and manifest radical differences among themselves. They are agreed, however, in the rejection, on the one hand, of the subjectivist logic with its intrinsic implication that knowledge veils rather than reveals the real world, and, on the other hand, of the logic of the speculative construction with its pretension to "deduce," to determine, and finally at once to cancel and conserve any antithesis in its all-embracing dialectic. They agree, then, in a maintenance of the critical point of view, while all alike recognize the necessity of bringing the thought-function in knowledge into more intimate relation with its "other" than Kant had done, by means of some formula of correlation or parallelism. Such an advance might have taken its cue directly from Kant himself. As an historical fact it tended rather to formulate itself as a reaction towards Kant in view of the course taken by the speculative movement. Thus Schleiermacher's posthumously published _Dialektik_ (1839) may be characterized as an appeal from the absolutist element in Schelling's philosophy to the conception of that correlation or parallelism which Schelling had exhibited as flowing from and subsisting within his absolute, and therein as a return upon Kant's doctrine of limits. Schleiermacher's conception of dialectic is to the effect that it is concerned with the principles of the art of philosophizing, as these are susceptible of a relatively independent treatment by a permissible abstraction. Pure thinking or philosophizing is with a view to philosophy or knowledge as an interconnected system of all sciences or departmental forms of knowledge, the mark of knowledge being its identity for all thinking minds. Dialectic then investigates the nexus which must be held to obtain between all thoughts, but also that agreement with the nexus in being which is the condition of the validity of the thought-nexus. In knowing there are two functions involved, the "organic" or animal function of sensuous experience in virtue of which we are in touch with being, directly in inner perception, mediately in outer experience, and the "intellectual" function of construction. Either is indispensable, though in different departments of knowledge the predominant rôle falls to one or other, e.g. we are more dependent in physics, less so in ethics. The idea of a perfect harmony of thinking and being is a presupposition that underlies all knowing but cannot itself be realized in knowledge. In terms of the agreement of thought and being, the logical forms of the part of dialectic correspondent to knowledge statically considered have parallels and analogies in being, the concept being correlated to substance, the judgment to causal nexus. Inference, curiously enough, falls under the technical side of dialectic concerned with knowledge in process or becoming, a line of cleavage which Ueberweg has rightly characterized as constituting a rift within Schleiermacher's parallelism.

Schleiermacher's formula obviously ascribes a function in knowledge to thought as such, and describes in a suggestive manner a duality of the intellectual and organic functions, resting on a parallelism of thought and being whose collapse into identity it is beyond human capacity to grasp. It is rather, however, a statement of a way in which the relations of the terms of the problem may be conceived than a system of necessity. It may indeed be permitted to doubt whether its influence upon subsequent theory would have been a great one apart from the spiritual force of Schleiermacher's personality. Some sort of correlationist conception, however, was an inevitable development, and the list[136] of those who accepted it in something of the spirit of Schleiermacher is a long one and contains many distinguished names, notably those of Trendelenburg and Ueberweg. The group is loosely constituted however. There was scope for diversity of view and there was diversity of view, according as the vital issue of the formula was held to lie in the relation of intellectual function to organic function or in the not quite equivalent relation of thinking to being. Moreover, few of the writers who, whatsoever it was that they baptized with the name of logic, were at least earnestly engaged in an endeavour to solve the problem of knowledge within a circle of ideas which was on the whole Kantian, were under the dominance of a single inspiration. Beneke's philosophy is a striking instance of this, with application to Fries and affinity to Herbart conjoined with obligations to Schelling both directly and through Schleiermacher. Lotze again wove together many threads of earlier thought, though the web was assuredly his own. Finally it must not be forgotten that the host of writers who were in reaction against Hegelianism tended to take refuge in some formula of correlation, as a half-way house between that and formalism or psychologism or both, without reference to, and often perhaps without consciousness of, the way in which historically it had taken shape to meet the problem held to have been left unresolved by Kant.

Lotze.

Lotze on the one hand held the Hegelian "deduction" to be untenable, and classed himself with those who in his own phrase "passed to the order of the day," while on the other hand he definitely raised the question, how an "object" could be brought into forms to which it was not in some sense adapted. Accordingly, though he regards logic as formal, its forms come into relation to objectivity in some sort even within the logical field itself, while when taken in the setting of his system as a whole, its formal character is not of a kind that ultimately excludes psychological and metaphysical reference, at least speculatively. As a logician Lotze stands among the masters. His _flair_ for the essentials in his problem, his subtlety of analysis, his patient willingness to return upon a difficulty from a fresh and still a fresh point of view, and finally his fineness of judgment, make his logic[137] so essentially logic of the present, and of its kind not soon to be superseded, that nothing more than an indication of the historical significance of some of its characteristic features need be attempted here.

In Lotze's pure logic it is the Herbartian element that tends to be disconcerting. Logic is formal. Its unit, the logical concept, is a manipulated product and the process of manipulation may be called abstraction. Processes of the psychological mechanism lie below it. The paradox of the theory of judgment is due to the ideal of identity, and the way in which this is evaded by supplementation to produce a non-judgmental identity, followed by translation of the introduced accessories with conditions in the hypothetical judgment, is thoroughly in Herbart's manner. The reduction of judgments is on lines already familiar. Syllogism is no instrumental method by which we compose our knowledge, but an ideal to the form of which it should be brought. It is, as it were, a schedule to be filled in, and is connected with the disjunctive judgment as a schematic setting forth of alternatives, not with the hypothetical, and ultimately the apodictic judgment with their suggestion that it is the real movement of thought that is subjected to analysis. Yet the resultant impression left by the whole treatment is not Herbartian. The concept is accounted for in Kantian terms. There is no discontinuity between the pre-logical or sub-logical conversion of impressions into "first universals" and the formation of the logical concept. Abstraction proves to be synthesis with compensatory universal marks in the place of the particular marks abstracted from. Synthesis as the work of thought always supplies, beside the mere conjunction or disjunction of ideas, a ground of their coherence or non-coherence. It is evident that thought, even as dealt with in pure logic, has an objectifying function. Its universals have objective validity, though this does not involve direct real reference. The formal conception of pure logic, then, is modified by Lotze in such a way as not only to be compatible with a view of the structural and functional adequacy of thought to that which at every point at which we take thinking is still distinguishable from thought, but even inevitably to suggest it. That the unit for logic is the concept and not the judgment has proved a stumbling-block to those of Lotze's critics who are accustomed to think in terms of the act of thought as unit. Lotze's procedure is, indeed, analogous to the way in which, in his philosophy of nature, he starts from a plurality of real beings, but by means of a reductive movement, an application of Kant's transcendental method, arrives at the postulate or fact of a law of their reciprocal action which calls for a monistic and idealist interpretation. He starts, that is in logic, with conceptual units apparently self-contained and admitting of nothing but external relation, but proceeds to justify the intrinsic relation between the matter of his units by an appeal to the fact of the coherence of all contents of thought. Indeed, if thought admits irreducible units, what can unite? Yet he is left committed to his puzzle as to a reduction of judgment to identity, which partially vitiates his treatment of the theory of judgment. The outstanding feature of this is, nevertheless, not affected, viz. the attempt that he makes, inspired clearly by Hegel, "to develop the various forms of judgment systematically as members of a series of operations, each of which leaves a part of its problem unmastered and thereby gives rise to the next."[138] As to inference, finally, the ideal of the articulation of the universe of discourse, as it is for complete knowledge, when its disjunctions have been thoroughly followed out and it is exhaustively determined, carried the day with him against the view that the organon for gaining knowledge is syllogism. The Aristotelian formula is "merely the expression, formally expanded and complete, of the truth already embodied in disjunctive judgment, namely, that every S which is a specific form of M possesses as its predicate a particular modification of each of the universal predicates of M to the exclusion of the rest." Schleiermacher's separation of inference from judgment and his attribution of the power to knowledge in process cannot find acceptance with Lotze. The psychologist and the formal logician do indeed join hands in the denial of a real movement of thought in syllogism. Lotze's logic then, is formal in a sense in which a logic which does not find the conception of synthetic truth embarrassing is not so. It is canon and not organon. In the one case, however, where it recognizes what is truly synthesis, i.e. in its account of the concept, it brings the statics of knowledge, so to speak, into integral relation with the dynamics. And throughout, wherever the survival from 1843, the identity bug-bear, is for the moment got rid of in what is really a more liberal conception, the statical doctrine is developed in a brilliant and informing manner. Yet it is in the detail of his logical investigations, something too volatile to fix in summary, that Lotze's greatness as a logician more especially lies.

With Lotze the ideal that at last the forms of thought shall be realized to be adequate to that which at any stage of actual knowledge always proves relatively intractable is an illuminating projection of faith. He takes courage from the reflection that to accept scepticism is to presume the competence of the thought that accepts. He will, however, take no easy way of parallelism. Our human thought pursues devious and circuitous methods. Its forms are not unseldom scaffolding for the house of knowledge rather than the framework of the house itself. Our task is not to realise correspondence with something other than thought, but to make explicit those justificatory notions which condition the form of our apprehension. "However much we may presuppose an original reference of the forms of thought to that nature of things which is the goal of knowledge, we must be prepared to find in them many elements which do not directly reproduce the actual reality to the knowledge of which they are to lead us."[139] The impulse of thought to reduce coincidence to coherence reaches immediately only to objectivity or validity. The sense in which the presupposition of a further reference is to be interpreted and in which justificatory notions for it can be adduced is only determinable in a philosophic system as a whole, where feeling has a place as well as thought, value equally with validity.

Lotze's logic then represents the statical aspect of the function of thought in knowledge, while, so far as we go in knowledge thought is always engaged in the unification of a manifold, which remains contradistinguished from it, though not, of course, completely alien to and unadapted to it. The further step to the determination of the ground of harmony is not to be taken in logic, where limits are present and untranscended.

Logic as Metaphysic.

The position of the search for truth, for which knowledge is a growing organism in which thought needs, so to speak, to feed on something other than itself, is conditioned in the post-Kantian period by antagonism to the speculative movement which culminated in the dialectic of Hegel. The radical thought of this movement was voiced in the demand of Reinhold[140] that philosophy should "deduce" it all from a single principle and by a single method. Kant's limits that must needs be thought and yet cannot be thought must be thought away. An earnest attempt to satisfy this demand was made by Fichte whose single principle was the activity of the pure Ego, while his single method was the assertion of a truth revealed by reflection on the content of conscious experience, the characterization of this as a half truth and the supplementation of it by its other, and finally the harmonization of both. The pure ego is inferred from the fact that the non-ego is realized only in the act of the ego in positing it. The ego posits itself, but reflection on the given shows that we must add that it posits also the non-ego. The two positions are to be conciliated in the thought of reciprocal limitation of the posited ego and non-ego. And so forth. Fichte cannot be said to have developed a logic, but this rhythm of thesis, antithesis and synthesis, foreshadowed in part for Fichte in Spinoza's formula, "omnis determinatio est negatio" and significantly in Kant's triadic grouping of his categories, gave a cue to the thought of Hegel. Schelling, too, called for a single principle and claimed to have found it in his Absolute, "the night" said Hegel, "in which all cows are black," but his historical influence lay, as we have seen, in the direction of a parallelism within the unity, and he also developed no logic. It is altogether otherwise with Hegel.

Hegel.

Hegel's logic,[141] though it involves inquiries which custom regards as metaphysical, is not to be characterized as a metaphysic with a method. It is logic or a rationale of thought by thought, with a full development among other matters of all that the most separatist of logicians regards as thought forms. It offers a solution of what has throughout appeared as the logical problem. That solution lies doubtless in the evolution of the Idea, i.e. an all-inclusive in which mere or pure thought is cancelled in its separateness by a transfiguration, while logic is nothing but the science of the Idea viewed in the medium of pure thought. But, whatever else it be, this _Panlogismus_, to use the word of J. E. Erdmann, is at least a logic. Thought in its progressive unfolding, of which the history of philosophy taken in its broad outline offers a pageant, necessarily cannot find anything external to or alien from itself, though that there is something external for it is another matter. As Fichte's Ego finds that its _non-ego_ springs from and has its home within its very self, so with Hegel thought finds itself in its "other," both subsisting in the Idea which is both and neither. Either of the two is the all, as, for example, the law of the convexity of the curve is the law of the curve and the law of its concavity. The process of the development of the Idea or Absolute is in one regard the immanent process of the all. Logically regarded, i.e. "in the medium of mere thought," it is dialectical method. Any abstract and limited point of view carries necessarily to its contradictory. This can only be atoned with the original determination by fresh negation in which a new thought-determination is born, which is yet in a sense the old, though enriched, and valid on a higher plane. The limitations of this in turn cause a contradiction to emerge, and the process needs repetition. At last, however, no swing into the opposite, with its primarily conflicting, if ultimately complementary function, is any longer possible. That in which no further contradiction is possible is the absolute Idea. Bare or indeterminate being, for instance, the first of the determinations of Hegel's logic, as the being of that which is not anything determinate, of Kant's thing-in-itself, for example, positively understood, implicated at once the notion of not-being, which negates it, and is one with it, yet with a difference, so that we have the transition to determinate being, the transition being baptized as becoming. And so forth. It is easy to raise difficulties not only in regard to the detail in Hegel's development of his categories, especially the higher ones, but also in regard to the essential rhythm of his method. The consideration that mere double negation leaves us precisely where we were and not upon a higher plane where the dominant concept is richer, is, of course, fatal only to certain verbal expressions of Hegel's intent. There is a differentiation in type between the two negations. But if we grant this it is no longer obviously the simple logical operation indicated. It is inferred then that Hegel complements from the stuff of experience, and fails to make good the pretension of his method to be by itself and of itself the means of advance to higher and still higher concepts till it can rest in the Absolute. He discards, as it were, and takes in from the stock while professing to play from what he has originally in his hand. He postulates his unity in senses and at stages in which it is inadmissible, and so supplies only a schema of relations otherwise won, a view supported by the way in which he injects certain determinations in the process, e.g. the category of chemism. Has he not cooked the process in the light of the result? In truth the Hegelian logic suffers from the fact that the good to be reached is presupposed in the beginning. Nature, e.g., is not deduced as real because rational, but being real its rationality is presumed and, very imperfectly, exhibited in a way to make it possible to conceive it as in its essence the reflex of Reason. It is a vision rather than a construction. It is a "theosophical logic." Consider the rational-real in the unity that must be, and this is the way of it, or an approximation to the way of it! It was inevitable that the epistemologists of the search for truth would have none of it. The ideal in whatsoever sense real still needs to be realized. It is from the human standpoint regulative and only hypothetically or formally constitutive. We must not confuse [Greek: ousia] with [Greek: einai], nor [Greek: einai] with [Greek: gignesthai].

Yet in a less ambitious form the fundamental contentions of Hegel's method tend to find a qualified acceptance. In any piece of presumed knowledge its partial or abstract character involves the presence of loose edges which force the conviction of inadequacy and the development of contradictions. Contradictions must be annulled by complementation, with resultant increasing coherence in ascending stages. At each successive stage in our progress fresh contradictions break out, but the ideal of a station at which the thought-process and its other, if not one, are at one, is permissible as a limiting conception. Yet if Hegel meant only this he has indeed succeeded in concealing his meaning.

Hegel's treatment of the categories or thought determinations which arise in the development of the immanent dialectic is rich in flashes of insight, but most of them are in the ordinary view of logic wholly metaphysical. In the stage, however, of his process in which he is concerned with the notion are to be found concept, judgment, syllogism. Of the last he declares that it "is the reasonable and everything reasonable" (_Encyk._ § 181), and has the phantasy to speak of the definition of the Absolute as being "at this stage" simply the syllogism. It is, of course, the rhythm of the syllogism that attracts him. The concept goes out from or utters itself in judgment to return to an enhanced unity in syllogism. Ueberweg (_System_ § 101) is, on the whole, justified in exclaiming that Hegel's rehabilitation of syllogism "did but slight service to the Aristotelian theory of syllogism," yet his treatment of syllogism must be regarded as an acute contribution to logical criticism in the technical sense. He insists on its objectivity. The transition from judgment is not brought about by our subjective action. The syllogism of "all-ness" is convicted of a _petitio principii_ (_Encyk._ § 190), with consequent lapse into the inductive syllogism, and, finally, since inductive syllogism is involved in the infinite process, into analogy. "The syllogism of necessity," on the contrary, does not presuppose its conclusion in its premises. The detail, too, of the whole discussion is rich in suggestion, and subsequent logicians--Ueberweg himself perhaps, Lotze certainly in his genetic scale of types of judgment and inference, Professor Bosanquet notably in his systematic development of "the morphology of knowledge," and others--have with reason exploited it.

Hegel's logic as a whole, however, stands and falls not with his thoughts on syllogism, but with the claim made for the dialectical method that it exhibits logic in its integral unity with metaphysic, the thought-process as the self-revelation of the Idea. The claim was disallowed. To the formalist proper it was self-condemned in its pretension to develop the content of thought and its rejection of the formula of bare-identity. To the epistemologist it seemed to confuse foundation and keystone, and to suppose itself to build upon the latter in a construction illegitimately appropriative of materials otherwise accumulated. At most it was thought to establish a schema of formal unity which might serve as a regulative ideal. To the methodologist of science in genesis it appeared altogether to fail to satisfy any practical interest. Finally, to the psychologist it spelt the failure of intellectualism, and encouraged, therefore, some form of rehabilitated experientialism.

In the Hegelian school in the narrower sense the logic of the master receives some exegesis and defence upon single points of doctrine rather than as a whole. Its effect upon logic is rather to be seen in the rethinking of the traditional body of logical doctrine in the light of an absolute presupposed as ideal, with the postulate that a regulative ideal must ultimately exhibit itself as constitutive, the justification of the postulate being held to lie in the coherence and all-inclusiveness of the result. In such a logic, if and so far as coherence should be attained, would be found something akin to the spirit of what Hegel achieves, though doubtless alien to the letter of what it is his pretension to have achieved. There is perhaps no serious misrepresentation involved in regarding a key-thought of this type, though not necessarily expressed in those verbal forms, as pervading such logic of the present as coheres with a philosophy of the absolute conceived from a point of view that is intellectualist throughout. All other contemporary movements may be said to be in revolt from Hegel.

v. _Logic from 1880-1910_

Logic in the present exhibits, though in characteristically modified shapes, all the main types that have been found in its past history. There is an intellectualist logic coalescent with an absolutist metaphysic as aforesaid. There is an epistemological logic with sometimes formalist, sometimes methodological leanings. There is a formal-symbolic logic engaged with the elaboration of a relational calculus. Finally, there is what may be termed psychological-voluntaryist logic. It is in the rapidity of development of logical investigations of the third and fourth types and the growing number of their exponents that the present shows most clearly the history of logic in the making. All these movements are logic of the present, and a very brief indication may be added of points of historical significance.

Of intellectualist logic Francis Herbert Bradley[142] (b. 1846) and Bernard Bosanquet[143] (1848) may be taken as typical exponents. The philosophy of the former concludes to an Absolute by the annulment of contradictions, though the ladder of Hegel is conspicuous by its absence. His metaphysical method, however, is like Herbart's, not identifiable with his logic, and the latter has for its central characteristic its thorough restatement of the logical forms traditional in language and the text-books, in such a way as to harmonize with the doctrine of a reality whose organic unity is all-inclusive. The thorough recasting that this involves, even of the thought of the masters when it occasionally echoes them, has resulted in a phrasing uncouth to the ear of the plain man with his world of persons and things in which the former simply think about the latter, but it is fundamentally necessary for Bradley's purpose. The negative judgment, for example, cannot be held in one and the same undivided act to presuppose the unity of the real, project an adjective as conceivably applicable to it and assert its rejection. We need, therefore, a restatement of it. With Bradley reality is the one subject of all judgment immediate or mediate. The act of judgment "which refers an ideal content (recognized as such) to a reality beyond the act" is the unit for logic. Grammatical subject and predicate necessarily both fall under the rubric of the adjectival, that is, within the logical idea or ideal content asserted. This is a meaning or universal, which can have no detached or abstract self-subsistence. As found in judgment it may exhibit differences within itself, but it is not two, but one, an articulation of unity, not a fusion, which could only be a confusion, of differences. With a brilliant subtlety Bradley analyses the various types of judgment in his own way, with results that must be taken into account by all subsequent logicians of this type. The view of inference with which he complements it is only less satisfactory because of a failure to distinguish the principle of nexus in syllogism from its traditional formulation and rules, and because he is hampered by the intractability which he finds in certain forms of relational construction.

Bosanquet had the advantage that his logic was a work of a slightly later date. He is, perhaps, more able than Bradley has shown himself, to use material from alien sources and to penetrate to what is of value in the thought of writers from whom, whether on the whole or on particular issues, he disagrees. He treats the book-tradition, however, a debt to which, nowadays inevitable, he is generous in acknowledging,[144] with a judicious exercise of freedom in adaptation, i.e. constructively as datum, never eclectically. In his fundamental theory of judgment his obligation is to Bradley. It is to Lotze, however, that he owes most in the characteristic feature of his logic, viz., the systematic development of the types of judgment, and inference from less adequate to more adequate forms. His fundamental continuity with Bradley may be illustrated by his definition of inference. "Inference is the indirect reference to reality of differences within a universal, by means of the exhibition of this universal in differences directly referred to reality."[145] Bosanquet's _Logic_ will long retain its place as an authoritative exposition of logic of this type.

Of epistemological logic in one sense of the phrase Lotze is still to be regarded as a typical exponent. Of another type Chr. Sigwart (q.v.) may be named as representative. Sigwart's aim was "to reconstruct logic from the point of view of methodology." His problem was the claim to arrive at propositions universally valid, and so true of the object, whosoever the individual thinker. His solution, within the Kantian circle of ideas, was that such principles as the Kantian principle of causality were justified as "postulates of the endeavour after complete knowledge." "What Kant has shown is not that irregular fleeting changes can never be the object of consciousness, but only that the ideal consciousness of complete science would be impossible without the knowledge of the necessity of all events."[146] "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."[147] 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[148] 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)[149] 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,[150] 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[151] 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."

BIBLIOGRAPHY.--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_. (H. W. B.*)

FOOTNOTES:

[1] Cf. Heidel, "The Logic of the Pre-Socratic Philosophy," in
Dewey's _Studies in Logical Theory_ (Chicago, 1903).

[2] Heraclitus, _Fragmm._ 107 (Diels, _Fragmente der Vorsokratiker_)
and 2, on which see Burnet, _Early Greek Philosophy_, p. 153 note
(ed. 2).

[3] e.g. Diog. Laërt. ix. 25, from the lost _Sophistes_ of Aristotle.

[4] _Plato and Platonism_, p. 24.

[5] Nothing is. If anything is, it cannot be known. If anything is
known it cannot be communicated.

[6] _Metaphys. [mu]. 1078b_ 28 sqq.

[7] Cf. Arist. _Top. [theta]_. i. 1 _ad fin_.

[8] For whom see Dümmler, _Antisthenica_ (1882, reprinted in his
_Kleine Schriften_, 1901).

[9] Aristotle, _Metaphys._ 1024b 32 sqq.

[10] Plato, _Theaetetus_, 201 E. sqq., where, however, Antisthenes is
not named, and the reference to him is sometimes doubted. But cf.
Aristotle, _Met._ H 3. 1043b 24-28.

[11] Diog. Laërt. ii. 107.

[12] Aristotle, _An. Pr._ i. 31, 46a 32 sqq.; cf. 91b 12 sqq.

[13] Athenaeus ii. 59c. See Usener, _Organisation der wissenschaftl.
Arbeit_ (1884; reprinted in his _Vorträge und Aufsätze_, 1907).

[14] Socrates' reference of a discussion to its presuppositions
(Xenophon, _Mem._ iv. 6, 13) is not relevant for the history of the
terminology of induction.

[15] _Theaetetus_, 186c.

[16] Timaeus, 37a, b (quoted in H. F. Carlill's translation of the
_Theaetetus_, p. 60).

[17] _Theaetetus_, 186d.

[18] Sophistes, 253d.

[19] _Ib. id._; cf. _Theaetetus_, 197d.

[20] Aristotle, _de An._ 430b 5, and generally iii. 2, iii. 5.

[21] For Plato's Logic, the controversies as to the genuineness of
the dialogues may be treated summarily. The _Theaetetus_ labours
under no suspicion. The _Sophistes_ is apparently matter for
animadversion by Aristotle in the _Metaphysics_ and elsewhere, but
derives stronger support from the testimonies to the _Politicus_
which presumes it. The _Politicus_ and _Philebus_ are guaranteed by
the use made of them in Aristotle's Ethics. The rejection of the
_Parmenides_ would involve the paradox of a nameless contemporary of
Plato and Aristotle who was inferior as a metaphysician to neither.
No other dialogue adds anything to the _logical_ content of these.

Granted their genuineness, the relative dating of three of them is
given, viz. _Theaetetus_, _Sophistes_ and _Politicus_ in the order
named. The _Philebus_ seems to presuppose _Politicus_, 283-284, but
if this be an error, it will affect the logical theory not at all.
There remains the _Parmenides_. It can scarcely be later than the
_Sophistes_. The antinomies with which it concludes are more
naturally taken as a prelude to the discussion of the _Sophistes_
than as an unnecessary retreatment of the doctrine of the one and the
many in a more negative form. It may well be earlier than the
_Theaetetus_ in its present form. The stylistic argument shows the
_Theaetetus_ relatively early. The maturity of its philosophic
outlook tends to give it a place relatively advanced in the Platonic
canon. To meet the problem here raised, the theory has been devised
of an earlier and a later version. The first may have linked on to
the series of Plato's dialogues of search, and to put the
_Parmenides_ before it is impossible. The second, though it might
still have preceded the _Parmenides_ might equally well have followed
the negative criticism of that dialogue, as the beginning of
reconstruction. For Plato's logic this question only has interest on
account of the introduction of an [Greek: Aristotelês] in a
non-speaking part in the _Parmenides_. If this be pressed as
suggesting that the philosopher Aristotle was already in full
activity at the date of writing, it is of importance to know what
Platonic dialogues were later than the début of his critical pupil.

On the stylistic argument as applied to Platonic controversies
Janell's _Quaestiones Platonicae_ (1901) is important. On the whole
question of genuineness and dates of the dialogues, H. Raeder,
_Platons philosophische Entwickelung_ (1905), gives an excellent
conspectus of the views held and the grounds alleged. See also PLATO.

[22] E.g. that of essence and accident. Republic, 454.

[23] E.g. the discussion of correlation, ib. 437 sqq.

[24] _Politicus_, 285d.

[25] _Sophistes_, 261c sqq.

[26] E.g. in _Nic. Eth._ i. 6.

[27] _Philebus_, 16d.

[28] Principal edition still that of Waitz, with Latin commentary, (2
vols., 1844-1846). Among the innumerable writers who have thrown
light upon Aristotle's logical doctrine, St Hilaire, Trendelenburg,
Ueberweg, Hamilton, Mansel, G. Grote may be named. There are,
however, others of equal distinction. Reference to Prantl, op. cit.,
is indispensable. Zeller, _Die philosophie der Griechen_, ii. 2,
"Aristoteles" (3rd ed., 1879), pp. 185-257 (there is an Eng. trans.),
and Maier, _Die Syllogistik des Aristoteles_ (2 vols., 1896, 1900)
(some 900 pp.), are also of first-rate importance.

[29] _Sophist. Elench._ 184, espec. b 1-3, but see Maier, _loc. cit._
i. 1.

[30] References such as 18b 12 are the result of subsequent editing
and prove nothing. See, however, ARISTOTLE.

[31] Adrastus is said to have called them [Greek: pro tôn topikôn].

[32] _Metaphys._ E. 1.

[33] _De Part. Animal._ A. 1, 639a 1 sqq.; cf. _Metaphys._ 1005b 2
sqq.

[34] _De Interpretatione_ 16a sqq.

[35] _De Interpretatione_ 16a 24-25.

[36] _Ib._ 18a 28 sqq.

[37] _Ib._ 19a 28-29.

[38] As shown e.g. by the way in which the relativity of sense and
the object of sense is conceived, 7b 35-37.

[39] _Topics_ 101a 27 and 36-b 4.

[40] _Topics_ 100.

[41] _Politics_ 1282a 1 sqq.

[42] 103b 21.

[43] _Topics_ 160a 37-b 5.

[44] This is the explanation of the formal definition of induction,
_Prior Analytics_, ii. 23, 68b 15 sqq.

[45] 25b 36.

[46] _Prior Analytics_, i. 1. 24a 18-20, [Greek: Syllogismos de esti
logos en ô tethentôn tinôn eteron ti tôn keimenôn ex anankês
snmbainei tô tauta einai]. The equivalent previously in _Topics_ 100a
25 sqq.

[47] _Prior Analytics_, ii. 21; _Posterior Analytics_, i. 1.

[48] 67a 33-37, [Greek: mê syntheôrôn to kath' ekateron].

[49] 67a 39-63.

[50] 79a 4-5.

[51] 24b 10-11.

[52] _Posterior Analytics_, i. 4 [Greek: kath auto] means (1)
contained in the definition of the subject; (2) having the subject
contained in its definition, as being an alternative determination of
the subject, crooked, e.g. is _per se_ of line; (3) self-subsistent;
(4) connected with the subject as consequent to ground. Its needs
stricter determination therefore.

[53] 73b 26 sqq., 74a 37 sqq.

[54] 90b 16.

[55] _Metaphys. Z._ 12, H. 6 ground this formula metaphysically.

[56] 94a 12, 75b 32.

[57] 90a 6. Cf. Ueberweg, _System der Logik_, § 101.

[58] 78a 30 sqq.

[59] _Topics_, 101b 18, 19.

[60] _Posterior Analytics_, ii. 13.

[61] _Posterior Analytics_, ii. 16.

[62] _Posterior Analytics_, i. 13 ad. fin., and i. 27. The form which
a mathematical science treats as relatively self-subsistent is
certainly not the constitutive idea.

[63] _Posterior Analytics_, i. 3.

[64] _Posterior Analytics_, ii. 19.

[65] _De Anima_, 428b 18, 19.

[66] _Prior Analytics_, i. 30, 46a 18.

[67] _Topics_, 100b 20, 21.

[68] _Topics_, 101a 25, 36-37, b1-4, &c.

[69] Zeller (_loc. cit._ p. 194), who puts this formula in order to
reject it.

[70] _Metaphys._ [Delta] 1, 1013a 14.

[71] _Posterior Analytics_, 72a 16 seq.

[72] _Posterior Analytics_, 77a 26, 76a 37 sqq.

[73] _Metaphys._ [Gamma].

[74] _Posterior Analytics_, ii. 19.

[75] _de Anima_, iii. 4-6.

[76] _Metaphys._ M. 1087a 10-12; Zeller loc. cit. 304 sqq.; McLeod
Innes, _The Universal and Particular in Aristotle's Theory of
Knowledge_ (1886).

[77] _Topics_, 105a 13.

[78] _Metaphys._ 995a 8.

[79] E.g., _Topics_, 108b 10, "to induce" the universal.

[80] _Posterior Analytics_, ii. 19, 100b 3, 4.

[81] _Topics_, i. 18, 108b 10.

[82] _Prior Analytics_, ii. 23.

[83] [Greek: Paradeigma], Prior Analytics, ii. 24.

[84] Sigwart, _Logik_, Eng. trans. vol. ii. p. 292 and elsewhere.

[85] Ueberweg, _System_, § 127, with a ref. to _de Partibus
Animalium_, 667a.

[86] See 67a 17 [Greek: ex hapantôn tôn atomôn].

[87] [Greek: Epiphora]. [Greek: Epi] = "in" as in [Greek: epagôgê],
inductio, and [Greek: -phora] = -ferentia, as in [Greek: diaphora],
dif_ferentia_.

[88] Diog. Laërt. x. 33 seq.; Sext. Emp. Adv. Math. vii. 211.

[89] Diog. Laërt. x. 87; cf. Lucretius, vi. 703 sq., v. 526 sqq. (ed.
Munro).

[90] Sextus Empiricus, _Pyrrhon. Hypotyp._ ii. 195, 196.

[91] Sextus, _op. cit._ ii. 204.

[92] _Op. cit._ iii. 17 sqq., and especially 28.

[93] The point is raised by Aristotle, 95A.

[94] See Jourdain, _Recherches critiques sur l'âge et l'origine des
traductions latines d'Aristote_ (1843).

[95] See E. Cassirer, _Das Erkenntnisproblem_, i. 134 seq., and the
justificatory excerpts, pp. 539 sqq.

[96] See Riehl in _Vierteljahrschr. f. wiss. Philos._ (1893).

[97] Bacon, _Novum Organum_, ii. 22, 23; cf. also Aristotle, _Topics_
i. 12. 13, ii. 10. 11 (Stewart, ad _Nic. Eth._ 1139b 27) and Sextus
Empiricus, _Pyrr. Hypot._ iii. 15.

[98] Bacon's _Works_, ed. Ellis and Spedding, iii. 164-165.

[99] A notable formula of Bacon's _Novum Organum_ ii. 4 § 3 turns
out, _Valerius Terminus_, cap. 11, to come from Aristotle, _Post.
An._ i. 4 _via_ Ramus. See Ellis in Bacon's _Works_, iii. 203 sqq.

[100] _De Civitate Dei_, xi. 26. "Certum est me esse, si fallor."

[101] Cf. Plato, _Republic_, 381E seq.

[102] _Elementa Philosophiæ_, i. 3. 20, i. 6. 17 seq.

[103] Hobbes, _Elementa Philosophiæ_, i. 1. 5.

[104] _Id. ib._ i. 6. 16.

[105] _Id. ib._ i. 4. 8; cf. Locke's _Essay of Human Understanding_,
iv. 17.

[106] _Id. Leviathan_, i. 3.

[107] _Id. Elem. Philos._ i. 6. 10.

[108] Condillac, _Langue des Calculs_, p. 7.

[109] Locke, _Essay_, iii. 3.

[110] _Id. ib._ iv. 17.

[111] _Loc. cit._ § 8.

[112] _Id. ib._ iv. 4, §§ 6 sqq.

[113] Berkeley, _Of the Principles of Human Knowledge_, § 142.

[114] Hume, _Treatise of Human Nature_, i. 1. 7 (from Berkeley, _op.
cit._, introd., §§ 15-16).

[115] _Essay_, iv. 17, § 3.

[116] Hume, _Treatise of Human Nature_, i. 3. 15.

[117] Mill, _Examination of Sir William Hamilton's Philosophy_, cap.
17.

[118] Cf. Mill, _Autobiography_, p. 159. "I grappled at once with the
problem of Induction, postponing that of Reasoning." _Ib._ p. 182
(when he is preoccupied with syllogism), "I could make nothing
satisfactory of Induction at this time."

[119] _Autobiography_, p. 181.