i. _The Logic of Empiricism_
The path followed by English thought was a different one. Hobbes
developed the nominalism which had been the hallmark of revolt against
scholastic orthodoxy, and, when he brings this into relation with the
analysis and synthesis of scientific method, it is at the expense of
the latter.[102] Locke, when Cartesianism had raised the problem of the
contents of consciousness, and the spirit of Baconian positivism could
not accept of anything that bore the ill-omened name of innate ideas,
elaborated a theory of knowledge which is psychological in the sense
that its problem is how the simple data with which the individual is in
contact in sensation are worked up into a system. Though he makes his
bow to mathematical method, he, even more than Hobbes, misses its
constructive character. The clue of mathematical certainty is discarded
in substance in the English form of "the new way of ideas."
Hobbes.
With Hobbes logic is a calculus of marks and signs in the form of names.
Naming is what distinguishes man from the brutes. It enables him to fix
fleeting memories and to communicate with his fellows. He alone is
capable of truth in the due conjunction or disjunction of names in
propositions. Syllogism is simply summation of propositions, its
function being communication merely. Analysis is the sole way of
invention or discovery. There is more, however, in Hobbes, than the
paradox of nominalism. Spinoza could draw upon him for the notion of
genetic definition.[103] Leibnitz probably owes to him the thought of a
calculus of symbols, and the conception of demonstration as essentially
a chain of definitions.[104] His psychological account of syllogism[105]
is taken over by Locke. Hume derived from him the explanatory formula of
the association of ideas,[106] which is, however, still with Hobbes a
fact to be accounted for, not a theory to account for facts, being
grounded physically in "coherence of the matter moved." Finally Mill
took from him his definition of cause as sum of conditions,[107] which
played no small part in the applied logic of the 19th century.
Locke.
Locke is of more importance, if not for his logical doctrine, at least
for the theory of knowledge from which it flows. With Locke the mind is
comparable to white paper on which the world of things records itself in
ideas of sensation. Simple ideas of sensation are the only points of
contact we have with things. They are the atomic elements which "the
workmanship of the understanding" can thereafter do no more than
systematically compound and the like. It is Locke's initial attribution
of the primary rôle in mental process to the simple ideas of sensation
that precludes him from the development of the conception of another
sort of ideas, or mental contents that he notes, which are produced by
reflection on "the operations of our own mind within us." It is in the
latter group that we have the explanation of all that marks Locke as a
forerunner of the critical philosophy. It contains in germ a doctrine of
categories discovered but not generated in the psychological processes
of the individual. Locke, however, fails to "deduce" his categories. He
has read Plato's _Theaetetus_ in the light of Baconian and individualist
preconceptions. Reflection remains a sort of "internal sense," whose
ideas are of later origin than those of the external sense. His
successors emphasize the sensationist elements, not the workmanship of
the mind. When Berkeley has eliminated the literal materialism of
Locke's metaphors of sense-perception, Hume finds no difficulty in
accepting the sensations as present virtually in their own right, any
nonsensible ground being altogether unknown. From a point of view purely
subjectivist he is prepared to explain all that is to be left standing
of what Locke ascribes to the workmanship of the mind by the principle
of association or customary conjunction of ideas, which Locke had added
a chapter to a later edition of his _Essay_ explicitly to reject as an
explanatory formula. Condillac goes a step farther, and sees no
necessity for the superstructure at all, with its need of explanation
valid or invalid. Drawing upon Gassendi for his psychological atomism
and upon Hobbes for a thoroughgoing nominalism, he reproduces, as the
logical conclusion from Locke's premises, the position of Antisthenes.
The last word is that "une science bien traitée n'est qu'une langue
bien faite."[108]
Locke's logic comprises, amid much else, a theory of general terms[109]
and of definition, a view of syllogism[110] and a declaration as to the
possibility of inference from particular to particular,[111] a
distinction between propositions which are certain but trifling, and
those which add to our knowledge though uncertain, and a doctrine of
mathematical certainty.[112] As to the first, "words become general by
being made the signs of general ideas, and ideas become general by
separating from them" all "that may determine them to this or that
particular existence. By this way of abstraction they are made capable
of representing more individuals than one." This doctrine has found no
acceptance. Not from the point of view for which idea means image.
Berkeley, though at length the _notions_ of spirits, acts and
relations[113] give him pause, prefers the formula which Hume expresses
in the phrase that "some ideas are particular in their nature but
general in their representation,"[114] and the after-history of
"abstraction" is a discussion of the conditions under which one idea
"stands for" a group. Not from those for whom general ideas mean
schematic concepts, not imageable. The critic from this side has little
difficulty in showing that abstraction of the kind alleged still leave
the residuum particular _this_ redness, e.g. not _redness_. It is,
however, of the sorts constituted by the representation which his
abstraction makes possible that definition is given, either by
enumeration of the simple ideas combined in the significance of the
sortal name, or "to save the labour of enumerating," and "for quickness
and despatch sake," by giving the next wider general name and the
proximate difference. We define essences of course in a sense, but the
essences of which men talk are abstractions, "creatures of the
understanding." Man determines the sorts or nominal essences, nature the
similitudes. The fundamentally enumerative character of the process is
clearly not cancelled by the recognition that it is possible to
abbreviate it by means of technique. So long as the relation of the
nominal to the real essence has no other background than Locke's
doctrine of perception, the conclusion that what Kant afterwards calls
analytical judgments a priori and synthetic judgments a posteriori
exhaust the field follows inevitably, with its corollary, which Locke
himself has the courage to draw, that the natural sciences are in
strictness impossible. Mathematical knowledge is not involved in the
same condemnation, solely because of the "archetypal" character, which,
not without indebtedness to Cumberland, Locke attributes to its ideas.
The reality of mathematics, equally with that of the ideals of morals
drawn from within, does not extend to the "ectypes" of the outer world.
The view of reasoning which Locke enunciates coheres with these views.
Reasoning from particular to particular, i.e. without the necessity of a
general premise, must be possible, and the possibility finds warranty in
a consideration of the psychological order of the terms in syllogism. As
to syllogism specifically, Locke in a passage,[115] which has an
obviously Cartesian ring, lays down four stages or degrees of reasoning,
and points out that syllogism serves us in but one of these, and that
not the all-important one of finding the intermediate ideas. He is
prepared readily to "own that all right reasoning may be reduced to
Aristotle's forms of syllogism," yet holds that "a man knows first, and
then he is able to prove syllogistically." The distance from Locke to
Stuart Mill along this line of thought is obviously but small.
Hume.
Apart from the adoption by Hume of the association of ideas as the
explanatory formula of the school--it had been allowed by Malebranche
within the framework of his mysticism and employed by Berkeley in his
theory of vision--there are few fresh notes struck in the logic of
sensationalism. The most notable of these are Berkeley's treatment of
"abstract" ideas and Hume's change of front as to mathematical
certainty. What, however, Hume describes as "all the _logic_ I think
proper to employ in my reasoning," viz. his "rules by which to judge
cause and effects,"[116] had, perhaps, farther-reaching historical
effects than either. In these the single method of Bacon is already
split up into separate modes. We have Mill's inductive methods in the
germ, though with an emphasis quite older than Mill's. Bacon's _form_
has already in transmission through Hobbes been transmuted into _cause_
as antecedent in the time series. It may, perhaps, be accounted to Hume
for righteousness that he declares--whether consistently or not is
another matter--that "the same effect never arises but from the same
cause," and that he still follows Bacon in the conception of _absentia
in proximo_. It is "when in any instance we find our expectation
disappointed" that the effect of one of "two resembling objects" will be
like that of the other that Hume proposes to apply his method of
difference.
No scientific discipline, however, with the doubtful exception of
descriptive psychology, stands to gain anything from a temper like that
of Hume. The whittling away of its formal or organizing rubrics, as
e.g., sameness into likeness, is disconcerting to science wherever the
significance of the process is realized. It was because the aftermath of
Newtonian science was so rich that the scientific faith of naturalism
was able to retain a place besides its epistemological creed that a
logician of the school could arise whose spirit was in some sort
Baconian, but who, unlike Bacon, had entered the modern world, and faced
the problems stated for it by Hume and by Newton.
J. S. Mill.
Stuart Mill's _System of Logic_ marked a fresh stage in the history of
empiricism, for the reason that it made the effort to hold an even
balance between the two moments in the thought of the school. Agreement
in the use of a common watchword had masked as it seems a real
divergence of meaning and purpose. The apostles of inductive method had
preached recourse to experience, but had meant thereby nature as a
constituted order. They had devised canons for the investigation of the
concrete problems of this, but had either ignored altogether the need to
give an account of the mirroring mind, or, in the alternative had been,
with some naïveté, content to assume that their nominalist friends,
consistently their allies in the long struggle with traditionalism, had
adequately supplied or could adequately supply the need. The exponents
of psychological atomism, on the other hand, with the association of
ideas for their one principle of agglutination had come to mean by
experience the mental phantasmagoria of the individual. They had
undermined the foundations of scientific certainty, and so far as the
fecundity of contemporary science did not give them pause, were ready,
notwithstanding the difference of their starting-point, to acquiesce in
the formula as well as the temper of Pyrrhonism. They could concede the
triumphant achievement of science only with the proviso that it must be
assumed to fall within the framework of their nominalism. Mill aspired
after a doctrine of method such as should satisfy the needs of the
natural sciences, notably experimental physics and chemistry as
understood in the first half of the 19th century and, _mutatis
mutandis_, of the moral sciences naturalistically construed. In uniting
with this the Associationism which he inherited, through his father,
from Hume, he revealed at once the strength and weakness of the dual
conception of naturalism. His rare thoroughness and rarer candour made
it at once unnecessary and impossible that the work should be done
again.
If judged by what he denies, viz. the formal logic of Hamilton and
Mansel, whose Aristotelian and scholastic learning did but accentuate
their traditionalism, and whose acquiescence in consistency constituted
in Mill's view a discouragement of research, such as men now incline to
attribute at the least equally to Hume's idealism, Mill is only
negatively justified. If judged by his positive contribution to the
theory of method he may claim to find a more than negative justification
for his teaching in its success. In the field covered by scholastic
logic Mill is frankly associationist. He aims at describing what he
finds given, without reference to insensible implications of doubtful
validity and value. The upshot is a psychological account of what from
one aspect is evidence, from the other, belief. So he explains "concepts
or general notions"[117] by an abstraction which he represents as a sort
of alt-relief operated by attention and fixed by naming, association
with the name giving to a set of attributes a unity they otherwise lack.
This is manifestly, when all is said, a particular psychological event,
a collective fact of the associative consciousness. It can exercise no
organizing or controlling function in knowledge. So again in determining
the "import" of propositions, it is no accident that in all save
existential propositions it is to the familiar rubrics of
associationism--co-existence, sequence, causation and resemblance--that
he refers for classification, while his general formula as to the
conjunctions of connotations is associationist through and through. It
follows consistently enough that inference is from particular to
particular. Mill holds even the ideas of mathematics to be hypothetical,
and in theory knows nothing of a non-enumerative or non-associative
universal. A premise that has the utmost universality consistent with
this view can clearly be of no service for the establishment of a
proposition that has gone to the making of it. Nor again of one that has
not. Its use, then, can only be as a memorandum. It is a shorthand
formula of registration. Mill's view of ratiocinative process clearly
stands and falls with the presumed impossibility of establishing the
necessity for universals of another type than his, for what may be
called principles of construction. His critics incline to press the
point that association itself is only intelligible so far as it is seen
to depend on universals of the kind that he denies.
In Mill's inductive logic, the nominalistic convention has, through his
tendency to think in relatively watertight compartments,[118] faded
somewhat into the background. Normally he thinks of what he calls
phenomena no longer as psychological groupings of sensations, as "states
of mind," but as things and events in a physical world howsoever
constituted and apprehended. His free use of relating concepts, that of
sameness, for instance, bears no impress of his theory of the general
notion, and it is possible to put out of sight the fact that, taken in
conjunction with his nominalism, it raises the whole issue of the
possibility of the equivocal generation of formative principles from the
given contents of the individual consciousness, in any manipulation of
which they are already implied. Equally, too, the deductive character,
apparently in intention as well as in actual fact, of Mill's
experimental methods fails to recall the point of theory that the
process is essentially one from particular to particular. The nerve of
proof in the processes by which he establishes causal conjunctions of
unlimited application is naturally thought to lie in the special canons
of the several processes and the axioms of universal and uniform
causation which form their background. The conclusions seem not merely
to fall within, but to depend on these organic and controlling formulae.
They follow not merely according to them but from them. The reference to
the rule is not one which may be made and normally is made as a
safeguard, but one which must be made, if thought is engaged in a
forward and constructive movement at all. Yet Mill's view of the
function of "universal" propositions had been historically suggested by
a theory--Dugald Stewart's--of the use of axioms![119] Once more, it
would be possible to forget that Mill's ultimate laws or axioms are not
in his view intuitions, nor forms constitutive of the rational order,
nor postulates of all rational construction, were it not that he has
made the endeavour to establish them on associationist lines. It is
because of the failure of this endeavour to bring the technique of
induction within the setting of his Humian psychology of belief that the
separation of his contribution to the applied logic of science from his
sensationism became necessary, as it happily was easy. Mill's device
rested special inductions of causation upon the laws that every event
has a cause, and every cause has always the same effect. It rested these
in turn upon a general induction enumerative in character of enormous
and practically infinite range and always uncontradicted. Though
obviously not exhaustive, the unique extent of this induction was held
to render it competent to give practical certainty or psychological
necessity. A vicious circle is obviously involved. It is true, of
course, that ultimate laws need discovery, that they are discovered in
some sense in the medium of the psychological mechanism, and that they
are nevertheless the grounds of all specific inferences. But that truth
is not what Mill expounds, nor is it capable of development within the
limits imposed by the associationist formula.
It is deservedly, nevertheless, that Mill's applied logic has retained
its pride of place amid what has been handed on, if in modified shape,
by writers, e.g., Sigwart, and Professor Bosanquet, whose theory of
knowledge is quite alien from his. He prescribed regulative or limiting
formulae for research as it was actually conducted in his world. His
grasp of the procedure by which the man of science manipulated his
particular concrete problems was admirable. In especial he showed clear
understanding of the functions of hypothesis and verification in the
investigations of the solitary worker, with his facts still in course of
accumulation and needing to be lighted up by the scientific imagination.
He was therefore enabled to formulate the method of what Bacon had
tended to despise as merely the "first vintage." Bacon spent his
strength upon a dream of organization for all future discovery. Mill was
content to codify. The difference between Bacon and Mill lies chiefly in
this, and it is because of this difference that Mill's contribution,
spite of its debt to the Baconian tradition, remains both characteristic
and valuable. It is of course possible to criticise even the
experimental canons with some severity. The caveats, however, which are
relevant within the circle of ideas within which Mill's lesson can be
learned and improved on,[120] seem to admit of being satisfied by
relatively slight modifications in detail, or by explanations often
supplied or easily to be supplied from points brought out amid the
wealth of illustration with which Mill accompanied his formal or
systematic exposition of method. The critic has the right of it when he
points out, for example, that the practical difficulty in the Method of
Agreement is not due to plurality of causes, as Mill states, but rather
to intermixture of effects, while, if the canon could be satisfied
exactly, the result would not be rendered uncertain in the manner or to
the extent which he supposes. Again the formula of the Joint-Method,
which contemplates the enumeration of cases "which have nothing in
common but the absence of one circumstance," is ridiculously unsound as
it stands. Or, on rather a different line of criticism, the use of
corresponding letters in the two series of antecedents and consequents
raises, it is said, a false presumption of correlation. Nay, even the
use of letters at all suggests that the sort of analysis that actually
breaks up its subject-matter is universally or all but universally
applicable in nature, and this is not the case. Finally, the conditions
of the methods are either realized or not. If they are realized, the
work of the scientist falls entirely within the field of the processes
preliminary to the satisfaction of the canon. The latter becomes a mere
memorandum or formula of registration. So is it possible "to have the
enginer hoist with his own petar." But the conditions are not realized,
and in an experiential subject-matter are not realizable. Not one
circumstance only in common but "apparently one relevant circumstance
only in common" is what we are able to assert. If we add the
qualification of relevance we destroy the cogency of the method. If we
fail to add it, we destroy the applicability.
The objections turn on two main issues. One is the exaggeration of the
possibilities of resolution into separate elements that is due to the
acceptance of the postulate of an alphabet of nature. This so soon as
noted can be allowed for. It is to the combination of this doctrine
with a tendency to think chiefly of experiment, of the controlled
addition or subtraction of these elements one at a time, that we owe the
theoretically premature linking of a as effect to _A_ as cause. This too
can be met by a modification of form. The other issue is perhaps of more
significance. It is the oscillation which Mill manifests between the
conception of his formula as it is actually applicable to concrete
problems in practice, and the conception of it as an expression of a
theoretical limit to practical procedure. Mill seems most often to think
of the former, while tending to formulate in terms of the latter. At any
rate, if relevance _in proximo_ is interpolated in the peccant clause of
the canon of the Joint-Method, the practical utility of the method is
rehabilitated. So too, if the canon of the Method of Agreement is never
more than approximately satisfied, intermixture of effects will in
practice mean that we at least often do not know the cause or antecedent
equivalent of a given effect, without the possibility of an alternative.
Finally, it is on the whole in keeping with Mill's presuppositions to
admit even in the case of the method of difference that in practice it
is approximative and instructive, while the theoretical formula, to
which it aims at approaching asymptotically as limit, if exact, is in
some sense sterile. Mill may well have himself conceived his methods as
practically fruitful and normally convincing with the limiting formula
in each case more cogent in form but therewith merely the skeleton of
the process that but now pulsed with life.
Enough has been said to show why the advance beyond the letter of Mill
was inevitable while much in the spirit of Mill must necessarily affect
deeply all later experientialism. After Mill experientialism takes
essentially new forms. In part because of what Mill had done. In part
also because of what he had left undone. After Mill means after Kant and
Hegel and Herbart, and it means after the emergence of evolutionary
naturalism. Mill, then, marks the final stage in the achievement of a
great school of thought.
ii. _The Logic of Rationalism._
Spinoza.
A fundamental contrast to the school of Bacon and of Locke is afforded
by the great systems of reason, owning Cartesian inspiration, which are
identified with the names of Spinoza and Leibnitz. In the history of
logic the latter thinker is of the more importance. Spinoza's philosophy
is expounded _ordine geometrico_ and with Euclidean cogency from a
relatively small number of definitions, axioms and postulates. But how
we reach our assurance of the necessity of these principles is not made
specifically clear. The invaluable tractate _De Intellectus
emendatione_, in which the agreement with and divergence from Descartes
on the question of method could have been fully elucidated, is unhappily
not finished. We know that we need to pass from what Spinoza terms
_experientia vaga_,[121] where imagination with its fragmentary
apprehension is liable to error and neither necessity nor impossibility
can be predicated, right up to that which _fictionem terminat_--namely,
_intellectio_. And what Spinoza has to say of the requisites of
definition and the marks of intellection makes it clear that insight
comes with coherence, and that the work of method on the "inductive"
side is by means of the unravelling of all that makes for artificial
limitation to lay bare what can then be seen to exhibit nexus in the one
great system. When all is said, however, the geometric method as
universalized in philosophy is rather used by Spinoza than expounded.
Leibnitz.
With Leibnitz, on the other hand, the logical problem holds the foremost
place in philosophical inquiry.[122] From the purely logical thesis,
developed at quite an early stage of his thinking,[123] that in any true
proposition the predicate is contained in the subject, the main
principles of his doctrine of Monads are derivable with the minimum of
help from his philosophy of dynamics. _Praedicatum inest subjecto._ All
valid propositions express in the last resort the relation of predicate
or predicates to a subject, and this Leibnitz holds after considering
the case of relational propositions where either term may hold the
position of grammatical subject, A = B and the like. There is a subject
then, or there are subjects which must be recognized as not possible to
be predicated, but as absolute. For reasons not purely logical Leibnitz
declares for the plurality of such subjects. Each contains all its
predicates: and this is true not only in the case of truths of reason,
which are necessary, and ultimately to be exhibited as coming under the
law of contradiction, "or, what comes to the same thing, that of
identity," but also in the case of truths of fact which are contingent,
though a sufficient reason can be given for them which "inclines"
without importing necessity. The extreme case of course is the human
subject. "The individual notion of each person includes once for all
what is to befall it, world without end," and "it would not have been
our Adam but another, if he had had other events." Existent subjects,
containing eternally all their successive predicates in the time-series,
are substances, which when the problems connected with their activity,
or dynamically speaking their force, have been resolved, demand--and
supply--the metaphysic of the Monadology.
Complex truths of reason or essence raise the problem of definition,
which consists in their analysis into simpler truths and ultimately into
simple--i.e. indefinable ideas, with primary principles of another
kind--axioms, and postulates that neither need nor admit of proof. These
are identical in the sense that the opposite contains an express
contradiction.[124] In the case of non-identical truths, too, there is a
priori proof drawn from the notion of the terms, "though it is not
always in our power to arrive at this analysis,"[125] so that the
question arises, specially in connexion with the possibility of a
calculus, whether the contingent is reducible to the necessary or
identical at the ideal limit. With much that suggests an affirmative
answer, Leibnitz gives the negative. Even in the case of the Divine
will, though it be always for the best possible, the sufficient reason
will "incline without necessitating." The propositions which deal with
actual existence are still of a unique type, with whatever limitation to
the calculus.
Leibnitz's treatment of the primary principles among truths of reason as
identities, and his examples drawn _inter alia_ from the "first
principles" of mathematics, influenced Kant by antagonism. Identities
some of them manifestly were not. The formula of identity passed in
another form to Herbart and therefore to Lotze. In recognizing, further,
that the relation of an actual individual fact to its sufficient ground
was not reducible to identity, he set a problem diversely treated by
Kant and Herbart. He brought existential propositions, indeed, within a
rational system through the principle that it must be feasible to assign
a sufficient reason for them, but he refused to bring them under the
conception of identity or necessity, i.e. to treat their opposites as
formally self-contradictory. This bore interest in the Kantian age in
the treatment alike of cause and effect, and of the ontological proof of
existence from essence. Not that the Law of Sufficient Reason is quite
free from equivoque. Propositions concerning the _possible_ existence of
individuals put Leibnitz to some shifts, and the difficulty accounts for
the close connexion established in regard to our actual world between
the law of sufficient reason and the doctrine of the final cause. This
connexion is something of an afterthought to distinguish from the
potential contingency of the objectively possible the real contingency
of the actual, for which the "cause or reason" of Spinoza[126] could not
account. The law, however, is not invalidated by these considerations,
and with the degree of emphasis and the special setting that Leibnitz
gives the law, it is definitely his own.
If we may pass by the doctrine of the Identity of Indiscernibles, which
played a part of some importance in subsequent philosophy, and the Law
of Continuity, which as Leibnitz represents it is, if not sheer dogma,
reached by something very like a fallacy, we have as Leibnitz's
remaining legacy to later logicians the conception of _Characteristica
Universalis_ and _Ars Combinatoria_, a universal denoting by symbols and
a calculus working by substitutions and the like. The two positions that
a subject contains all its predicates and that all non-contingent
propositions--i.e. all propositions not concerned with the existence of
individual facts ultimately analyse out into identities--obviously lend
themselves to the design of this algebra of thought, though the
mathematician in Leibnitz should have been aware that a significant
equation is never an identity. Leibnitz, fresh from the battle of the
calculus in the mathematical field, and with his conception of logic, at
least in some of its aspects, as a generalized mathematic,[127] found a
fruitful inspiration, harmonizing well with his own metaphysic, in
Bacon's alphabet of nature. He, too, was prepared to offer a new
instrument. That the most important section, the list of forms of
combination, was never achieved--this too was after the Baconian example
while the mode of symbolization was crude with a = _ab_ and the
like--matters little. A new technique of manipulation--it is, of course,
no more--had been evolved.
It may be said that among Leibnitz's successors there is no Leibnitzian.
The system as a whole is something too artificial to secure
whole-hearted allegiance. Wolff's formalism is the bastard outcome of
the speculation of Leibnitz, and is related to it as remotely as
Scholasticism is to Aristotle. Wolff found a sufficient reason for
everything and embodied the results of his inquiries in systematic
treatises, sometimes in the vernacular. He also, by a transparent
_petitio principii_, brought the law of the sufficient reason under that
of non-contradiction. Wolff and his numerous followers account for the
charge of dogmatism against "the Leibnitzio-Wolffian school." They are
of importance in the history of logic for two reasons only: they
affected strongly the German vocabulary of philosophy and they
constituted the intellectual environment in which Kant grew to manhood.
A truer continuator of Leibnitz in the spirit was Herbart.
iii. _Kant's Logic._
Herbart's admitted allegiance, however, was Kantian with the
qualification, at a relatively advanced stage of his thinking, that it
was "of the year 1828"--that is, after controversy had brought out
implications of Kant's teaching not wholly contemplated by Kant himself.
The critical philosophy had indeed made it impossible to hark back to
Leibnitz or any other master otherwise than with a difference.
Yet it is not a single and unambiguous logical movement that derives
from Kant. Kant's lesson was variously understood. Different moments in
it were emphasized, with a large diversity of result. As interpreted it
was acquiesced in or revolted from and revolt ranged from a desire for
some modifications of detail or expression to the call for a radical
transformation. Grounds for a variety of developments are to be found in
the imperfect harmonization of the rationalistic heritage from the
Wolffian tradition which still dominates Kant's pure general logic with
the manifest epistemological intention of his transcendental theory. Or
again, within the latter in his admission of a duality of thought and
"the given" in knowledge, which within knowledge was apparently
irreducible, concurrently with hints as to the possibility, upon a wider
view, of the sublation of their disparateness at least hypothetically
and speculatively. The sense in which there must be a ground of the
unity of the supersensible[128] while yet the transcendent use of
Reason--i.e. its use beyond the limits of experience was denied
theoretical validity--was not unnaturally regarded as obscure.
Formal Logic.
Kant's treatment of technical logic was wholly traditional, and in
itself is almost negligible. It is comprised[129] in an early essay on
the mistaken subtlety of the syllogistic figures, and a late compilation
by a pupil from the introductory matter and running annotations with
which the master had enriched his interleaved lecture-room copy of
Meyer's _Compendium_ of 1752. Wolff's general logic, "the best," said
Kant, "that we possess," had been abridged by Baumgarten and the
abridgment then subjected to commentation by Meyer. With this
traditional body of doctrine Kant was, save for matters of minor detail,
quite content. Logic was of necessity formal, dealing as it must with
those rules without which no exercise of the understanding would be
possible at all. Upon abstraction from all particular methods of thought
these rules were to be discerned a priori or without dependence on
experience by reflection solely upon the use of the understanding in
general. The science of the form of thought abstracted in this way from
its matter or content was regarded as of value both as propaedeutic and
as canon. It was manifestly one of the disciplines in which a position
of finality was attainable. Aristotle might be allowed, indeed, to have
omitted no essential point of the understanding, what the moderns had
achieved consisted in an advance in accuracy and methodical
completeness. "Indeed, we do not require any new discoverers in
logic,"[130] said the discoverer of a priori synthesis, "since it
contains merely the form of thought." Applied logic is merely
psychology, and not properly to be called logic at all. The technical
logic of Kant, then, justifies literally a movement among his successors
in favour of a formal conception of logic with the law of contradiction
and the doctrine of formal implication for its equipment. Unless the
doctrine of Kant's "transcendental logic" must be held to supply a point
of view from which a logical development of quite another kind is
inevitable, Kant's mantle, so far as logic is concerned, must be
regarded as having fallen upon the formal logicians.