Kant's transcendental teaching is summarily as follows: "Transcendental"
is his epithet for what is neither empirical--i.e. to be derived from
experience--nor yet transcendent--i.e. applicable beyond the limits of
experience, the mark of experience being the implication of sense or of
something which thought contra-distinguishes from its own spontaneous
activity as in some sense "the given." Those features in our organized
experience are to be regarded as transcendentally established which are
the presuppositions of our having that experience at all. Since they are
not empirical they must be structural and belong to "the mind"--i.e. the
normal human intelligence, and to like intelligence so far as like. If
we set aside such transcendental conditions as belong to sensibility or
to the receptive phase of mind and are the presuppositions of
juxtaposition of parts, the remainder are ascribable to spontaneity or
understanding, to thought with its unifying, organizing or focussing
function, and their elucidation is the problem of transcendental
analytic. It is still logic, indeed, when we are occupied with the
transcendent objects of the discursive faculty as it is employed beyond
the limits of experience where it cannot validate its ideas. Such a
logic, however, is a dialectic of illusion, perplexed by paralogisms and
helpless in the face of antinomies. In transcendental analytic on the
other hand we concern ourselves only with the transcendental "deduction"
or vindication of the conditions of experience, and we have a logic of
cognition in which we may establish our epistemological categories with
complete validity. Categories are the forms according to which the
combining unity of self-consciousness (synthetic unity of apperception)
pluralizes itself through the various functions involved in the
constitution of objectivity in different types of the one act of
thought, viz. judgment. The clue to the discovery of transcendental
conditions Kant finds in the existence of judgments, most manifest in
mathematics and in the pure science of nature, which are certain, yet
not trifling, necessary and yet not reducible to identities, synthetic
therefore and a priori, and so accounted for neither by Locke nor by
Leibnitz. "There lies a transcendental condition at the basis of every
necessity."
Form of Matter of Thought.
Kant's mode of conceiving the activity of thought in the constitution of
objects and of their connexion in experience was thought to lie open to
an interpretation in conformity with the spirit of his logic, in the
sense that the form and the content in knowledge are not merely
distinguishable functions within an organic whole, but either separable,
or at least indifferent one to the other in such a way as to be clearly
independent. Thought as form would thus be a factor or an element in a
composite unit. It would clearly have its own laws. It would be the
whole concern of logic, which, since in it thought has itself for
object, would have no reference to the other term of the antithesis, nor
properly and immediately to the knowledge which is compact of thought in
conjunction with something which, whatever it may be, is prima facie
other than thought. There is too much textual warrant for this
interpretation of Kant's meaning. Doubtless there are passages which
make against an extreme dualistic interpretation. Even in his "logic"
Kant speaks of abstraction from all particular objects of thought rather
than of a resolution of concrete thinking into thought and its "other"
as separable co-operating factors in a joint product. He spoke
throughout, however, as if form and content were mutually indifferent,
so that the abstraction of form from content implied nothing of
falsification or mutilation. The reserve, therefore, that it was
abstraction and not a decomposing that was in question remained to the
admirers of his logic quite nugatory. They failed to realize that
permissible abstraction from specific contents or methods of knowledge
does not obliterate reference to matter or content. They passed easily
from the acceptance of a priori forms of thinking to that of forms of a
priori thinking, and could plead the example of Kant's logic.
Kant's theory of knowledge, then, needed to be pressed to other
consequences for logic which were more consonant with the spirit of the
_Critique_. The forms of thought and what gives thought its particular
content in concrete acts of thinking could not be regarded as subsisting
in a purely external and indifferent relation one to the other. "Laws
according to which the subject thinks" and "laws according to which the
object is known" cannot be the concern of separate departments of
inquiry. As soon divorce the investigation of the shape and material of
a mirror from the laws of the incidence of the rays that form images in
it, and call it a science of reflection! An important group of writers
developed the conception of an adaptation between the two sides of
Kant's antithesis, and made the endeavour to establish some kind of
correlation between logical forms and the process of "the given." There
was a tendency to fall back upon the conception of some kind of
parallelism, whether it was taken to be interpretative or rather
corrective of Kant's meaning. This device was never remote from the
constructions of writers for whom the teaching of Spinoza and Leibnitz
was an integral part of their intellectual equipment. Other modes of
correlation, however, find favour also, and in some variety. Kant is
seldom the sole source of inspiration. His unresolved antithesis[131] is
interpreted either diversely or with a difference of emphasis. And the
light that later writers bring to bear on Kant's logic and epistemology
from other sides of his speculation varies in kind and in degree.
Another logical movement springs from those whom a correlation of fact
within the unity of a system altogether failed to satisfy. There must
also be development of the correlated terms from a single principle.
Form and content must not only correspond one to the other. They must be
exhibited as distinguishable moments within a unity which can at one and
the same time be seen to be the ground from which the distinction
springs and the ground in virtue of which it is over-ruled. Along this
line of speculation we have a logic which claims that whatsoever is in
one plane or at one stage in the development of thought a residuum that
apparently defies analysis must at another stage and on a higher plane
be shown so to be absorbed as to fall altogether within thought. This is
the view of Hegel upon which logic comes to coincide with the
progressive self-unfolding of thought in that type of metaphysic which
is known as absolute, i.e. all-inclusive idealism. The exponent of logic
as metaphysic, for whom the rational is the real is necessarily in
revolt against all that is characteristically Kantian in the theory of
knowledge, against the transcendental method itself and against the
doctrine of limits which constitutes the nerve of "criticism." Stress
was to be laid upon the constructive character of the act of thought
which Kant had recognized, and without Kant's qualifications of it. In
all else the claim is made to have left the Kantian teaching behind as a
cancelled level of speculation.
Limitation of Transcendental Method.
Transcendental method is indeed not invulnerable. A principle is
transcendentally "deduced" when it and only it can explain the validity
of some phase of experience, some order of truths. The order of truths,
the phase of experience and its certainty had to be taken for granted.
The sense, for example, in which the irreversibility of sequence which
is the more known _in ordine ad hominem_ in the case of the causal
principle differs from merely psychological conviction is not made fully
clear. Even so the inference to the a priori ground of its necessity is,
it has been often pointed out, subject to the limitation inherent in any
process of reduction, in any regress, that is, from conditionate to
condition, viz. that in theory an alternative is still possible. The
inferred principle may hold the field as explanation without obvious
competitor potential or actual. Nevertheless its claim to be the sole
possible explanation can in nowise be validated. It has been established
after all by dialectic in the Aristotelian sense of the word. But if
transcendental method has no special pride of place, Kant's conclusion
as to the limits of the competence of intellectual faculty falls with
it. Cognition manifestly needs the help of Reason even in its
theoretical use. Its speculation can no longer be stigmatized as
vaticination _in vacuo_, nor its results as illusory.
Logic and Psychology.
Finally, to logic as metaphysic the polar antithesis is psychology as
logic. The turn of this also was to come again. If logic were treated as
merely formal, the stress of the problem of knowledge fell upon the
determination of the processes of the psychological mechanism. If
alleged a priori constituents of knowledge--such rubrics as substance,
property, relation--come to be explained psychologically, the formal
logic that has perforce to ignore all that belongs to psychology is
confined within too narrow a range to be able to maintain its place as
an independent discipline, and tends to be merged in psychology. This
tendency is to be seen in the activity of Fries and Herbart and Beneke,
and was actualized as the aftermath of their speculation. It is no
accident that it was the psychology of apperception and the voluntaryist
theory or practice of Herbart, whose logical theory was so closely
allied to that of the formal logicians proper, that contributed most to
the development of the post-Kantian psychological logic. Another
movement helped also; the exponents of naturalistic evolution were
prepared with Spencer to explain the so-called _a priori_ in knowledge
as in truth _a posteriori_, if not to the individual at any rate to the
race. It is of course a newer type of psychological logic that is in
question, one that is aware of Kant's "answer to Hume." Stuart Mill,
despite of his relation of antagonism to Hamilton and Mansel, who held
themselves to be Kantian in spirit, is still wholly pre-Kantian in his
outlook.
Summary.
Kant's influence, then, upon subsequent logic is least of all to be
measured by his achievement in his professed contribution to technical
logic. It may be attributed in some slight degree, perhaps, to
incidental flashes of logical insight where his thought is least of what
he himself calls logic, e.g. his exposition of the significance of
synthetic judgments _a priori_, or his explanation of the function of
imagery in relation to thought, whereby he offers a solution of the
problem of the conditions under which one member of a group unified
through a concept can be taken to stand for the rest, or again the way
in which he puts his finger on the vital issue in regard to the alleged
proof from essence to existence, and illustrations could be multiplied.
But much more it belongs to his transformation of the epistemological
problem, and to the suggestiveness of his philosophy as a whole for an
advance in the direction of a speculative construction which should be
able to cancel all Kant's surds, and in particular vindicate a "ground
of the unity of the supersensible which lies back of nature with that
which the concept of freedom implies in the sphere of practice,"[132]
which is what Kant finally asserts.
iv. _After Kant._
Starting from the obvious antithesis of thought and that of which it is
the thought, it is possible to view the ultimate relation of its term as
that of mutual indifference or, secondly, as that of a correspondence
such that while they retain their distinct character modification of the
one implies modification of the other, or thirdly and lastly, as that of
a mergence of one in the other of such a nature that the merged term,
whichever it be, is fully accounted for in a complete theory of that in
which it is merged.
The Formal Logicians.
The first way is that of the purely formal logicians, of whom
Twesten[133] and in England H. L. Mansel may be regarded as typical.
They take thought and "the given" as self-contained units which, if not
in fact separable, are at any rate susceptible of an abstraction the one
from the other so decisive as to constitute an ideal separation. The
laws of the pure activity of thought must be independently determined,
and since the contribution of thought to knowledge is form they must be
formal only. They cannot go beyond the limits of formal consistency or
analytic correctness. They are confined to the determination of what the
truth of any matter of thought, taken for granted upon grounds
psychological or other, which are extraneous to logic, includes or
excludes. The unit for logic is the concept taken for granted. The
function of logic is to exhibit its formal implications and repulsions.
It is questionable whether even this modest task could be really
achieved without other reference to the content abstracted from than
Mansel, for example, allows. The analogy of the resolution of a chemical
compound with its elements which is often on the lips of those who would
justify the independence of thought and the real world, with an agnostic
conclusion as to non-phenomenal or trans-subjective reality, is not
really applicable. The oxygen and hydrogen, for example, into which
water may be resolved are not in strictness indifferent one to the
other, since both are members of an order regulated according to laws of
combination in definite ratios. Or, if applicable, it is double-edged.
Suppose oxygen to be found only in water. Were it to become conscious,
would it therefore follow that it could infer the laws of a separate or
independent activity of its own? Similarly forms of thinking, the law of
contradiction not excepted, have their meaning only in reference to
determinate content, even though distributively all determinate contents
are dispensable. The extreme formalist is guilty of a fallacy of
composition in regard to abstraction.
It does not follow, however, that the laws asserted by the formal
logicians are invalid or unimportant. There is a permissible
abstraction, and in general they practise this, and although they narrow
its range unduly, it is legitimately to be applied to certain characters
of thinking. As the living organism includes something of mechanism--the
skeleton, for example--so an organic logic doubtless includes
determinations of formal consistency. The skeleton is meaningless apart
from reference to its function in the life of an organism, yet there are
laws of skeleton structure which can be studied with most advantage if
other characters of the organism are relegated to the background. To
allow, however, that abstraction admits of degrees, and that it never
obliterates all reference to that from which it is abstracted, is to
take a step forward in the direction of the correlation of logical forms
with the concrete processes of actual thinking. What was true in formal
logic tended to be absorbed in the correlationist theories.
Those formal logicians of the Kantian school, then, may be summarily
dismissed, though their undertaking was a necessary one, who failed to
raise the epistemological issue at all, or who, raising it, acquiesced
in a naïve dualism agnostic of the real world as Kant's essential
lesson. They failed to develop any view which could serve either in fact
or in theory as a corrective to the effect of their formalism. What they
said with justice was said as well or better elsewhere.
Among them it is on the whole impossible not to include the names of
Hamilton and Mansel. The former, while his erudition in respect to the
history of philosophical opinion has rarely been equalled, was not a
clear thinker. His general theory of knowledge deriving from Kant and
Reid, and including among other things a _contaminatio_ of their
theories of perception,[134] in no way sustains or mitigates his narrow
view of logic. He makes no effective use of his general formula that to
think is to condition. He appeals to the direct testimony of
consciousness in the sense in which the appeal involves a fallacy. He
accepts an ultimate antinomy as to the finiteness or infinity of "the
unconditioned," yet applies the law of the excluded middle to insist
that one of the two alternatives must be true, wherefore we must make
the choice. And what is to be said of the judgment of a writer who
considers the relativity of thought demonstrated by the fact that every
judgment unites two members? Hamilton's significance for the history of
logic lies in the stimulus that he gave to the development of symbolic
logic in England by his new analytic based upon his discovery or
adoption of the principle of the quantification of the predicate.
Mansel, too, was learned, specially in matters of Aristotelian exegesis,
and much that is of value lies buried in his commentation of the dry
bones of the _Artis Logicae Rudimenta_ of Locke's contemporary Aldrich.
And he was a clearer thinker than Hamilton. Formal logic of the
extremest rigour is nowhere to be found more adequately expressed in all
its strength, and it must be added in all its weakness, than in the
writings of Mansel. But if the view maintained above that formal logic
must compromise or mitigate its rigour and so fail to maintain its
independence, be correct, the logical consistency of Mansel's logic of
consistency does but emphasize its barrenness. It contains no germ for
further development. It is the end of a movement.
Herbart.
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.*)