and perfecting of syllogistic in the logical calculus, and some
followed him who did not, however, attain to true effectiveness in the
history of culture,[8] formalist Logic fell always more and more into
discredit, not only as Logica _utens,_ but also as _docens,_ that is to
say, as theory.
Hence the moderate tendency, to which Kant adhered, which consists of
preserving that Logic, while seeking to correct, and, in particular,
to simplify it. For example, Kant undertook to demonstrate the "false
subtlety of the four figures of the syllogism," and at the same time
rendered traditional Logic yet more formalist by withdrawing from it
all examination of the synthesis and the categories, which he referred
to his new transcendental Logic. Traditional Logic, which he respected
and held to be substantially perfect, constituted (he said) a canon
of the intellect and of reason, but only in the _formal_ aspect of
their employment, whatever be the content to which it is applied. Its
only criterion is the agreement or non-agreement of any knowledge
with the general and formal laws of the intellect and of reason; a
_conditio sine qua non_ of every truth, but a _conditio_ which is only
negative.[9]
[Sidenote: _Refutation of formalist Logic. Hegel; Schleiermacher._]
Hegel, on the contrary, opposed tradition. He understood the
character of formalist Logic marvellously well: this "_empirical_
Logic, a bizarre science, which is an _irrational_ knowledge of
the _rational,_ and sets the bad example of not following its own
doctrines. Indeed it assumes the licence of doing the opposite of
what its rules prescribe, when it neglects to deduce the concepts and
to demonstrate its affirmations."[10] In so far as it was empirical
it was intellectualist, and presented the determinations of reason
in an abstract and atomic manner in combining them mechanically. The
new concept of the concept, originated by Hegel, creates from itself
its own theories and allows the old formalist theories to disappear
as dead and dry remains. The forms of thought are henceforth the very
forms of the real; the Idea is the unity of concept and representation,
because it is the universal itself, big with the individual. Things
are realized judgments, and the syllogism is the Idea which identifies
itself with its own reality. This at bottom amounts to saying that
thought fully dominates reality, because it is not an extrinsic
addition or an interposed means, but Reality itself, which makes itself
thought, because it is thought. Other philosophers, too, contemporaries
and adversaries of Hegel, rejected formalist Logic, and among these
was Schleiermacher.[11] He made the logical forms of the _concept_ and
of the _judgment_ correspond to the two forms of reality, _being_ and
_doing,_ finding corresponding analogies in _space,_ a dividing of
being, and in _time,_ a dividing of doing. The concept and the judgment
mutually presuppose one another, and give rise to a circle, which is so
only when considered temporally; since at the point of indifference, of
fusion, of indistinction the two make one.[12] Schleiermacher differed
from Hegel (who attains in thought the unity of the real) in being
obliged to withdraw the syllogism from the number of the essential
forms of thought, because (he says), "if the syllogism were a true
form, a being of its own should correspond to it, and this is not found
to be the case."[13]
[Sidenote: _Its partial persistence owing to insufficient ideas as to
language._]
But if with the Hegelian criticism formalist Logic was surpassed by a
truly philosophical Logic, and thereupon lost all its importance, it
cannot be said that it was definitely dissolved. In Hegel himself there
remain traces of it in certain divisions of the forms of judgment and
of syllogism, which he either accepts and corrects or creates anew.
Definitive criticism demanded that in any case the error peculiar to
this empiricism should be recognized. This error consists in confusing
language and thought, taking thought as language, and therefore also
language as thought. Hegel could not effect this criticism, for he
was logistic as regards the theory of language, conceiving it to be a
complex of logical and universal elements.[14] Hence the coincidence
between the forms of language and those of thought did not seem to him
irrational, provided that both were taken in their true connection. The
revival of the Philosophy of language, begun by Vico and carried on
by Hamann and by Herder, and then again by Humboldt, remained unknown
to him or had no influence upon him. Nor, to tell the truth, has it
influenced even later Logic, for had it acquired this knowledge, it
would have been freed for ever from formalism or verbalism and have
possessed a method and a power of application to the nature of the
problems that belong to it. Just a trace of serious discussion (but
made rather in the interest of the Philosophy of language than in
that of Logic) appears in the polemic between Steinthal and Becker
concerning the relations between Logic and Grammar.[15]
[Sidenote: _Formalist Logic in Herbart, in Schopenhauer, in Hamilton._]
For this reason, formalist Logic has continued to exist (with
difficulty if you will, but yet to exist) in the nineteenth century.
From Kant it had received with the name _formal_ a new baptism and
a new legitimization. Among post-Kantians Herbart clung closely
to it, though he somewhat simplified it, and hostile as he was to
all transcendental Logic, he continued to conceive it as the sole
instrument of thought. Schopenhauer held logical forms to be a good
parallel to rhetorical forms, and limited himself to proposing some
slight remodelling of the former: for example, to consider judgments
as always universal (both those called by that name and particular
and singular judgments as well), and to explain hypothetical and
disjunctive judgments as pronounced upon the comparison of two or
more categorical judgments. From the syllogism, which he defined as
"a judgment drawn from two other judgments, without the intervention
of new conditions," he dropped the fourth figure, but he proclaimed
the first three to be "ectypes" of three real and essentially
different operations of thought.[16] Kant's teaching was followed in
England by Hamilton. Hamilton insisted upon the purely hypothetical
character of logical reasonings; he excluded from Logic discussions
of possibility and impossibility and of the modalities, and declared
that the intrusion into that science of the concepts of perfect or
imperfect induction, which refer to material differences and are
therefore extralogical,[17] was a fundamental error. In this way he
reacted against inductive Logic, which, in his country especially, had
prevailed against formalist Logic or had strangely accompanied it. He
persuaded himself that he could perfect the latter, by simplifying
the doctrine of the judgment, by means of what is called the
_quantification of the predicate._[18]
[Sidenote: _More recent theories._]
Later logicians continued to employ these partial and superficial
modifications. Trendelenburg, as has been mentioned, believed that
he could make progress by referring the thing to its beginning,
that is, by turning from Aristotelianism to Aristotle, and owing to
the curious influence of a thought of Hegel, he assigned to logic
and reality a common foundation which, for him, was not the Idea,
but Movement. Lotze reduced the forms of judgments to three only,
according to the variations of the copula: categorical, hypothetical
and disjunctive judgments; and he made impersonal judgments precede
categorical. By this last class he vainly sought to satisfy the
desire for a theoretic form which is presupposed in properly
logical thought, and it is yet to seek. Lotze always had at bottom
an intellectualistic concept of language: poetry and art seemed to
him to be directed, not to contemplation and expression, but to
emotion and to feelings of pleasure and pain. He could not therefore
recognize the primitive theoretic form in art, in intuition, in pure
expressiveness. Drobisch, the Herbartian, revealed formalism in all
its crudity, beginning with the affirmation that "there are certainly
necessary judgments and syllogisms, but no necessary concepts."
Sigwart reformed the classification of judgments (of denomination, of
property and activity, impersonal, of relation, abstract, narrative and
explicative), and retouched that of syllogisms. Wundt, accepting the
old tripartition of logical forms, also attempts new sub-divisions,
distinguishing judgments for example, according to their subject, into
indeterminate, singular and plural; according to their predicate,
into narrative, descriptive and explicative; according to their
relation, into judgments of identity, superordination, subordination,
co-ordination and dependence; and into negative predications and
negative oppositions. Brentano's reform does not in general abandon the
formalist circle; hence, having assigned the quantity of judgments to
their matter, he limits himself to dividing them into affirmative and
negative; among immediate inferences he accepts only the inference _ad
contradictoriam_; among the laws of the syllogism he denies the law
_ex mere negativis,_ maintaining indeed that _ex mere affirmativis nil
sequitur;_ he defends, as the law of all syllogisms, that of _quaternio
terminorum,_ which used to pass for the sign of the sophism; and he
further abolishes the vain distinctions of figures and moods.
[Sidenote: _Mathematical Logic._]
Opposed as radical innovators to these logicians, who work more or less
with traditional formulas, are the mathematical logicians, who follow,
not philosophy, but certain fictions of the Leibnitzian philosophy.
George Bentham, De Morgan, Boole, Jevons, Grassman and now several in
England, in France, in Germany and in Italy (Peano), have been and are
representative of this tendency. They are innovators only in a manner
of speaking, for they are ultra-reactionaries, far more formalist than
the formalist Aristotle. They are dissatisfied with the divisions made
by him, not because they are toe numerous and arbitrary, but because
they are toe few and still bear some traces of rationality They strive
to the uttermost to provide a theory of thought, from which all thought
is absent This kind of Logic has been well defined by Windelband as
"Logic of the green cloth."[19]
[Sidenote: _Inexact idea of language among mathematical logicians and
intuitionists._]
These logicians have naturally inherited the other fiction of
Leibnitz, namely that of the possibility of a constant and universal
language,[20] thus revealing another reason for their aberration,
and the usual support of the whole formalist error--ignorance of the
alogical nature of language. The nature of language remains obscure
from another point of view, even to the modern intuitionists (Bergson).
They continue to regard as language, not language in its simplicity,
but the intellectualist procedure (classificatory and abstractive)
which falsifies the continuous in the discontinuous, breaks up
duration, and builds a fictitious world upon the real world. They are
therefore ultimately led to attribute the value of a pure expression
of reality to music, as though music were not language, and true
language (not the intellectualist discourse which they accept in place
of it) were not essentially music, that is to say, poetry. For the
intellectualists also, a Logic (were they to resolve upon constructing
one) would be nothing but formalist.
[Footnote 1: See the recent exposition of the secular Indian Logic, in
its most complete form, as found in a treatise of the twelfth century,
in II. Jacobi, "Die indische Logik," in the _Nachrichten v. d. Königl.
Gesellsch. d. Wissenschaft zu Göttingen,_ Philol.-hist. Klasse, 1901,
fasc. iv. pp. 460-484.]
[Footnote 2: _Gesch. d. Logik,_ i. p. 362.]
[Footnote 3: Hamilton, _Fragments philosophiques,_ French tr. pp.
238-242.]
[Footnote 4: Frantl, "Über Petrus Ramus," in the _Sitzungsberichte d.
k. bayer. Akad. d. Wissensch.,_ Philol.-hist. Klasse, 1878, ii. pp.
157-169.]
[Footnote 5: _De dign. et augm._ iv. ch. 2-5.]
[Footnote 6: _Ib._ ch. 2.]
[Footnote 7: _Nov. Org._ i., aphorism 14.]
[Footnote 8: It is pertinent to translate here a passage of Hegel, in
relation to this Leibnitzian tendency, which is now again becoming
fashionable. "The extreme form of this (syllogistic) disconceptualized
manner of dealing with the conceptual determinations of the syllogism,
is found in Leibnitz, who (_Opp._ t. ii. p. i) places the syllogism
under the calculus of combination. By this means he has calculated
how many positions of the syllogism are possible, and thus, by taking
count of the differences of positive and negative judgments, then of
universal, particular, indeterminate and singular judgments, he has
arrived at the result that the possible combinations are 2048, of
which, after excluding the invalid, there remain 24 valid. Leibnitz
boasts much of the utility possessed by the analysis of combination in
finding, not only the forms of the syllogism, but also the connections
of other concepts. This operation is the same as that of calculating
the number of possible combinations of letters that can be made from
an alphabet, or of moves in a game of draughts, or of different hands
in a game of _hombre,_ and so on. From which it is clear that the
determinations of a syllogism are placed on a level with moves in
draughts, or hands in _hombre._ The rational is taken as something
dead, altogether deprived of the concept, and the peculiar character
of the concept and its determinations is left out; that is to say,
the character that in so far as they are spiritual facts, they are
_relation,_ and that, in virtue of this relation, they suppress their
_immediate_ determination. This Leibnitzian application of the calculus
of combination to the syllogism and to the connection of other concepts
is not to be distinguished in any way from the discredited _art of
Lully,_ save for the greater methodicalness in calculation of which
it gives proof; it resembles that absurdity in every other respect.
Another thought, dear to Leibnitz, was included in the calculus
of combination. He had nourished this thought in his youth, and
notwithstanding its immaturity and superficiality, he never afterwards
abandoned it. This was the thought of a _universal characteristic_ of
concepts, of a writing, in which every concept should be represented as
proceeding from others or as referring to another; almost as though, in
a rational connection, which is essentially dialectic, a content should
preserve the same determinations that it has when standing alone.
"The calculus of Ploucquet is doubtless supported by the most cogent
mode of submitting the relation of the syllogism to calculation. He
abstracts in the judgment from the difference of relation; that is to
say, from its singularity, particularity and universality, and fixes
the _abstract identity_ of subject and predicate, placing them in a
_mathematical relation._ This relation reduces reason to an empty,
tautological formation of propositions. In the proposition, 'the rose
is red,' the predicate must signify, not red in general, but only the
determinate 'red of the rose.' In the proposition, 'all Christians are
men,' the predicate must signify only 'those men who are Christians.'
From this and from the other proposition, 'Hebrews are not Christians,'
follows the conclusion (which did not constitute a good recommendation
for this calculus with Mendelssohn): 'hence, Hebrews are not men' (that
is to say, they are not those men, who are Christians).
"Ploucquet gives as a consequence of his invention _posse etiant rudes
mechanice tot am logicam doceri, uti pueri arithmeticam docentur. ita
quidem, ut nulla formidine in ratiociniis suis errandi lorqueri, vel
fallaciis circumveniri possint, si in calculo non errant._ This eulogy
of the calculus, to the effect that by its means it is possible to
supply uneducated people with the whole of Logic, is certainly the
worst that can be said of an invention which concerns logical Science'"
(_Wiss. d. Logik,_ iii. pp. 142-43).]
[Footnote 9: _Kr. d. rein. Vern.,_ ed. quoted, pp. 101-2.]
[Footnote 10: _Wiss. d. Logik,_ iii. p. 51.]
[Footnote 11: _Dialektik,_ ed. quoted, pp. 74-5.]
[Footnote 12: Work cited, pp. 145, 147-9.]
[Footnote 13: Work cited, pp. 146, 291-2.]
[Footnote 14: _Wiss. d. Logik,_ i. pp. 10-11 and _passim; Encykl._ §
205 and elsewhere.]
[Footnote 15: _Estetica_², p. II, ch. xii.]
[Footnote 16: _Werke,_ ed. cited, ii. pp. 120-135.]
[Footnote 17: Work cited, pp. 159, 165.]
[Footnote 18: See above, pp. 297, dealing with Ploucquet.]
[Footnote 19: In his remarks upon the present state of Logic, contained
in his work _Die Philosophie im Beginn des zwanzigsten Jahrhunderts_
(Heidelberg 1904), i. pp. 163-186.]
[Footnote 20: See my remarks in the _Critica,_ iii. pp. 428-433
(concerning the work of Messrs. Couturat and Léau); and cf. same, iv.
pp. 379-381.]
V
CONCERNING THIS LOGIC
[Sidenote: _Traditional character of this Logic and its connection with
the Logic of the philosophic concept._]
The Logic which we have expounded in this treatise is also in a certain
sense traditional Logic. But it should be connected, not with the
tradition of formalism, but rather with that of the Hegelian Logic,
of Kantian transcendental Logic, and so of the loftiest Hellenic
speculative thought. In other words, its affinity should be sought in
the logical sections of the _Critique of Pure Reason_ of Kant, or in
the _Metaphysic_ of Aristotle, and not in the _Lessons in Logic_ or in
the _Analytics_ of the same authors. This traditional character endows
it with confidence, because man has always thought the true, and it
is to be doubted if he who fails to discover the truth in the past,
possesses the truth of the present and of the future, of which in his
proud isolation he thinks himself secure.
[Sidenote: _Its innovations._]
But to be truly attached to tradition means to carry it on and to
collaborate with it. Contact with thought is always dynamic and
propulsive and urges us to go forward, since it is impossible to stop
or to turn back. For this reason, this Logic presents some novelties,
of which the fundamental and principal can be thus enumerated:
[Sidenote: _I. Exclusion of empirical and abstract concepts._]
I. Accepting the doctrine, which culminates in the last great modern
philosophy of the _pure Concept,_ as the only doctrine of logical
truth, this Logic excludes empirical and abstract concepts, declaring
them to be irreducible to the pure concept.
[Sidenote: _II. Non-theoretic character of the second and autonomy of
the empirical and mathematical sciences._]
II. Accepting for these last the _economic theory_ of the empirical and
abstract sciences and considering them as having a practical character
and therefore as non-concepts (pseudoconcepts), this Logic denies that
they exhaust logical thought, indeed it altogether denies that they
belong to it and demonstrates that their very existence presupposes
the reality of the pure concept. Hence, it connects the two doctrines
with one another and asserts the _autonomy_ of philosophy, at the same
time respecting the relative autonomy of the empirical and mathematical
sciences thus rendered atheoretical.
[Sidenote: _III. The concept as unity of distinctions._]
III. In the doctrine concerning the organism of the pure concept, it
accepts the _dialectic_ view or the unity of opposites, but denies
its immediate validity for the distinctions of the concept; the unity
of which is organized as a unity of distinctions in the theory of
_degrees_ of reality. In this way, the autonomy of the forms of reality
or of the spirit is also respected and the _practical_ nature of error
established.
[Sidenote: _IV. Identity of the concept with the individual judgment
and of philosophy with history._]
IV. The richness of reality, of facts, of experience, which seemed
to be withdrawn from the pure concept and so from philosophy by the
separation of it from the empirical sciences, is on the contrary
restored to and recognized in philosophy, not in the diminished and
improper form which is that of empirical science, but in a total and
integral manner. This is effected by means of the connection, which
is a _unity,_ between _Philosophy_ and _History_--a unity obtained by
making clear and profoundly studying the nature of the concept and the
logical _a priori_ synthesis.
[Sidenote: _V. Impossibility of defining thought by means of verbal
forms, and refutation of formalists Logic._]
V. Finally, the doctrines and the presuppositions of formalist Logic
are refuted in a precise manner. The autonomy of the _logical form_ is
asserted and consequently the effort to contain its determinations in
words or expressive forms is declared to be vain. These are certainly
necessary, but obey, not the law of logic, but that of the æsthetic
spirit.
[Sidenote: _Conclusion._]
Such, summarily indicated, is the progress upon previous thought, which
this Logic would wish to represent. To gain this end, it has availed
itself, not only of the help afforded by ancient and modern Logic,
concentrated in the Hegelian Logic, but also of those others that have
come into being since Hegel, and especially of æsthetic, of the theory
of historical writing and of the gnoseology of the sciences. It has
striven to avail itself of all scattered truths, but of none in an
eclectic manner, that is to say, by making arbitrary collections or
merely aggregations, for it has been conscious that scattered truths
become truly truths when they are no longer scattered but fused, not
many, but one.
THE END