although it has been disputed as to whether it must be considered so,
or rather as a connection of logical propositions or judgments, the
dispute is at once solved, so far as we are concerned, by observing
:hat precisely because the syllogism is a connection of concepts, and
concepts only exist in verbal forms, that is to say, in propositions
or judgments, the syllogism is also a connection of judgments. This
serves to reinforce the truth that if the effective presence of the
verbal form must always be recognized in the logical fact, it must, on
the other hand, be forgotten when Logic is being constructed and the
nature of Logic and of the concept is being sought. Now, the connection
of the concepts represents nothing new in relation to the thinking of
the concept. As has already been seen, to think the concept signifies
to think it in its distinctions, to place it in relation with the other
concepts and to unify it with them in the unique concept. A concept
thought outside its relations is indistinct, that is to say, not
thought at all.
Therefore, the connection of the concepts, or syllogizing, cannot be
conceived as a new and more complex logical act. To syllogize and
to think are synonymous; although, in the ordinary use of language,
the term "to syllogize" throws into special relief the verbal aspect
of thinking, and, more exactly, the _dynamic_ character of verbal
exposition, which is indeed the very character of this exposition,
for it is with difficulty, or only empirically, that it can be
distinguished into static and dynamic, definition and demonstration.
[Sidenote: _Identity of judgment and of syllogism._]
But if the syllogism be thus identified with the concept itself, it may
nevertheless seem that it must be distinguished from the judgment of
definition seeing that the syllogism is a form of logical thought, and
consequently of verbal expression, quite distinct from and incapable
of being confounded with any other: a connection of _three_ judgments,
two of which are called _premisses_ and the third _conclusion,_ closely
cemented by the syllogistic force, which is placed in the _middle_
term. This character of triplicity seems ineradicable and peculiar to
the syllogism in contrast with the judgment.
Some question, however, must be raised concerning this characteristic
because of another characteristic universally recognized in the
syllogism; namely, that the premisses are conclusions of other
syllogisms, just as the conclusion becomes, in its turn, a premiss.
This being so, it might be said with greater truth that the syllogism
is to syllogize or to think; and since this is infinite, so the
propositions of which it consists are also infinite. On the other hand,
there is no judgment which is not a syllogism, since it is clear that
he who affirms a judgment affirms it by some reasoning or syllogism,
present and active in his spirit, though more or less understood in
the words. And are not other propositions understood in the syllogisms
which are properly so-called, not only in the forms, which are called
abbreviated (immediate inferences, enthymemes, etc.), but also in all
the other forms; since it is admitted that every syllogism, as has
just been observed, presupposes other preceding syllogisms, indeed an
infinity of others? It will be replied that at the end of the chain
there must yet be found the difference between judgment and syllogism,
or two first judgments, which are not produced by syllogism, and form
the columns, upon which the structure of the first conclusion rests.
But such an answer (if it do not imply simply the strange fancy that
thought has a beginning and therefore also an end in time) will mean
that judgment and syllogism are distinct in intrinsic character, which
makes the one the necessary condition of the other. Now, this intrinsic
distinctive character is precisely what cannot be found, because it
does not exist; and if it be not in every link, it is vain to seek it
at the beginning of the chain.
[Sidenote: _The middle term and the nature of the concept._]
Certainly, that _venatio medii,_ that _ergo,_ that unification
of triplicity, are things of much importance. But whence comes
their importance if not from being the expression of the synthetic
force of thought, of thought which unifies and distinguishes, and
distinguishes because it unifies and unifies because it distinguishes?
And is triplicity truly triplicity, one, two, three, arithmetically
enumerable? But if this be so, how is it that we never succeed in
counting those three, resolving each one of them into a series of
similar terms, or of other propositions and concepts? Upon attentive
consideration we perceive that here, too, the number three is
symbolical, and that it does no more than designate the distinction,
which unifies or thinks the _singular_ concept in the _universal_
through the _particular,_ or determines the _universal_ through the
_particular,_ by making it a _singular_ concept, whence it remains
perfectly certain that the relation of these three determinations is
not numerical. Such a logical operation, not being anything special,
but simply logical reasoning itself, is of necessity found also in the
judgment.
[Sidenote: _Pretended non-definitive logical judgments._]
A possible objection at this point is that even if the unity of
judgment and syllogism can be held to be demonstrated as regards
definitions and syllogisms which are the basis of definitions, yet
it has not been demonstrated for the other forms of syllogisms and
logical judgments, which are not definitive. But if these judgments
and syllogisms be logical, they cannot fail to be definitive, or to
have for their content affirmations of concepts. "All men are mortal"
is a definition of the concept of man, whose mortality is verbally
emphasized or his immortality denied. It is without doubt an incomplete
definition, because it is torn from the web of thoughts and of speech
of which it formed part; and this web will also always be incomplete
or capable of infinite completion by means of new affirmations and
new negations. But in its incompleteness it is at the same time also
complete, because it affirms a concept of reality, of life and death,
of finite and infinite, of spirituality and of its forms, and so on;
these are all presupposed determinations, and therefore existing and
operating in the concepts of _man_ and _mortality._ "Caius is a man"
(which is the second premiss of the syllogism traditionally adduced as
an example) is certainly not a definition (though it presupposes and
contains many definitions) precisely for the reason that it is not a
pure logical judgment. Hence it happens that the conclusion itself:
"therefore Caius is mortal," is more than a pure logical conclusion,
since it also contains a historical element, the person of Caius. But
we shall speak further on of these individual or historical judgments;
and then we shall also see in what relation they stand to the universal
or pure logical judgments, and if it be truly possible to distinguish
between them, otherwise than for the sake of convenience. The
distinction is in any case convenient and does no harm at this point;
and therefore for didactic reasons we allow it to stand; indeed we make
use of it.
[Sidenote: _The syllogism as fixed verbal form. Its use and abuse._]
Just as in the case of definitions, so also in the case of the
syllogism, it is to be noted that the verbal expression does not
consist of an obligatory formula, but assumes the most varied forms,
apparently very remote from syllogizing as commonly understood. The
abuse of the syllogism as a formula continued for centuries, notably
in mediæval Scholasticism, and notwithstanding the rebellion of the
Renaissance, it has persisted among many philosophical schools,
its last conspicuous manifestation being the didactic elaboration
of the Leibnitzian philosophy, or Wolffianism. Certain of Wolff's
demonstrations have remained famous, such as that concerning the
construction of windows, contained in his _Manual of Architecture._ "A
window must be large enough for two persons to lean against it, side by
side," he developed it in this way: "_Demonstration._ It is customary
to lean against a window with another person in order to look out. But
the architect must serve the interests of his employer in everything.
Therefore he must make the window large enough for two persons to be
able to be there side by side.[1] _Q.E.D._"
No more such syllogistic pedantries have been seen in our times, but
(as has been already remarked in reference to pedantry of definition)
contempt for the formula has too often resulted in contempt even for
the correctness of the reasoning. So that it has sometimes been
necessary to advise a bracing bath of scholasticism, and it has been
observed and lamented of certain new civilizations (for example, of
Russian culture, or of the Japanese people, who are so little addicted
to mathematics), that they have not had a scholastic period, like that
of the West, so general with them is the habit of incorrect, loose, and
passionately impulsive and fantastic reasoning. Certainly the formula,
the exercise of disputation in _forma,_ the _logica scholastica
utens_ has its merits; and we must know how to have recourse to it
when it is advantageous to do so, and to express thought in the brief
and perspicuous formulæ of the syllogism, of the sorites, or of the
dilemma. From this point of view the new methods of mathematical Logic
or Logistic, upon which some are now working, and even the logical
machines which have been constructed, would help; they would help--if
they helped. For the point is just this: when formulæ, methods of
demonstration, machines and the like, are recommended, expedients
and instruments of practical or economic use are thereby proposed;
and these cannot make good their existence otherwise than by getting
themselves accepted for the utility--the saving of time and space, and
so of fatigue, which they effect. Like all technical inventions, those
products must be brought to the market; and the market alone decides
upon their value and assigns to them their price. At the present time,
it seems that logistic methods have no value and price, save for
certain narrow circles of people, who amuse themselves with them in
their own way and so pass the time.
[Sidenote: _Erroneous separation of truth and reason of truth in the
pure concepts._]
Certain erroneous doctrines take their origin from the undue separation
of demonstration and definition, conspicuously that particular error
which places a difference of degree between _truth_ and _reason_ of
truth, and consequently admits that a truth can be known without its
reason being known. But a truth, of which the reason is not known, is
not even truth; or it is truth only in preparation and in hypothesis.
We hear much about the _intuition_ with which men of genius are
equipped, and which enables them to go straight to the truth, even when
they are not capable of demonstrating it. But this intuition, when it
is not that truth in preparation, or that orientation towards a truth
still quite hypothetical, must of necessity be thought and thus also
be demonstration of truth; it must be truth and also reason of truth;
thought and reasoning performed no doubt with lightning rapidity,
which is expressed in brief propositions and needs going over again
and rethinking, in order that it may afford a more ample and, from the
didactic point of view, a more persuasive, exposition; but it is always
thought and reasoning.
Things are still worse, when not only is a diversity of degree
admitted, but the complete _indifference_ of demonstration to truth is
proclaimed, so that many or infinite possible demonstrations of one
identical truth would be possible. If by this it were meant merely that
one identical truth, or one identical concept, can assume infinite
verbal or expressive forms, and if demonstration were understood as
"exposition" or "expression," there would be nothing to object. But
if by demonstration be meant something truly logical, that which is
properly called by that name in Logic, this thesis leads directly to
the negation of truth, making the demonstration of truth, or truth
itself, an illusion, a sophistical appearance created simply to
persuade. Those acquainted with courts of law know that very often when
a magistrate has made his decision and pronounced sentence he deputes
to a younger colleague the task of "reasoning" it, or of providing an
appearance of reasoning to what is indeed not a logical product, but
simply the _voluntas_ of a certain provision. But though this procedure
be intelligible and useful when it occurs in the field of practice and
of law, it cannot be admitted in the theoretical field, where it would
be the ruin of thought and indirectly of the will itself.
[Sidenote: _Difference between truth and reason of truth in the
pseudoconcepts._]
Naturally, all that has been said as to the definition and the
syllogism has reference to the true and proper concept, or the pure
concept. In the case of pseudoconcepts, where practical motives enter,
definition is a simple _command_ (a nominalist definition), and
demonstration has no place, save for those of its elements that are
derived from the pure concept: _given_ the definitions, the reasoning
must logically proceed in a determinate manner. In pseudoconcepts,
then, definitions are separate from demonstrations: the first do not
spring from the second and are not all one with them; the second
presuppose the first and do not produce them. Of these definitions
infinite demonstrations are possible, precisely because in reality
none is possible, for the definitions themselves are infinite; and
when a demonstration is given, this is done only _pro forma_; it is
a deception, to conceal a practical convenience, or rather a logical
reasoning employed to make it clear. It is for this reason also that
the definitions employed in those demonstrations seem to be obtained
by means of an act of _faith_ in the irrational; and here faith
signifies, not the confidence of thought in itself, but the making a
virtue of necessity, accepting as true what is not known as such.--For
the rest, pseudoconcepts and concepts have the same relation with the
verbal form; that is to say, all are expressed in the most various
ways, and there is no obligatory form of language, which can be called
the literary form of logical character. The style of the _Civil Code,_
which aroused the admiration of Stendhal, is not the eternal style
of laws, for laws were once even put into verse; as in like barbaric
times the sciences used to be put into verse. In the life of the word,
concepts and pseudoconcepts rush forward in such a way that it is vain
to seek there for distinction among them.
[Footnote 1: Mentioned in Hegel, _Wiss. d. Logik 2,_ iii. 370 _n._]
III
CRITIQUE OF FORMALIST LOGIC
[Sidenote: _Intrinsic impossibility of formal Logic._]
From the fact that in the verbal form all distinctions (pure
concepts, and empirical and abstract concepts, distinct concepts and
opposite concepts) are indistinguishable, and on the other hand all
identities, such as that of concept, definition and demonstration,
appear differentiated or capable of differentiation, we can deduce the
impossibility of constructing logical Science by means of an analysis
of the verbal form. The condemnation of all _formal_ Logic is thus
pronounced.
[Sidenote: _Its nature._]
This Logic has been variously called _Aristotelian, peripatetic,
scholastic,_ after its authors and historical representatives;
_syllogistic,_ from the doctrine that forms its principal content;
_formal,_ from its pretensions to philosophic purity; _empirical,_ by
those who tried to drive it back to its place; and although this last
name is correct, it would be better to call it _formal,_ and still
better, _verbal,_ to indicate of what the empiricism to which it is
desired to allude, chiefly consists. Indeed, if empiricism be marked
by its limiting itself to single representations, regrouping them in
types and arranging them in classes, there is no doubt that that method
of treatment is empirical, which takes the logical function, not in
the eternal peculiarity of its character as thought of the universal,
but only in its various particular translations or manifestations, in
which it acquires contingent characteristics. Since these contingent
characteristics come to it, in the first place, from the verbal form,
it can well be called verbalism. Owing to its verbalism, too, it has
happened, that over and above the grammars of individual languages,
there has been conceived as existing a _general, rational_ and
_logical_ Grammar; and this hybrid science, which is no longer grammar
and arose from logical assumptions, has developed in such a way as to
be indistinguishable from empirical or verbal Logic.
[Sidenote: _Its partial justification._]
Certainly, as mere empiricism, this so-called Logic could not be
condemned. And Hegel was not wrong in remarking that if people are
interested in establishing that there are sixty species of parrots
and one hundred and thirty-seven of veronica, it is not clear why
it should be of less interest to establish the various forms of the
judgment and of the syllogism. That discipline has its utility as mere
empiricism, and it may be useful to any one to employ in certain cases
the terminology in which an affirmation is characterized as positive
or as merely negative, as particular or as universal, as a judgment
that awaits reasoning and demonstration, as an immediate inference,
enthymeme or sorites, as a conclusive or an inconclusive, or as a
correct or an incorrect syllogism, and so on. It is also comprehensible
how, as mere empiricism, it assumed a _normative_ character, and was
translated into _rules_; rules, which are valid within their own
sphere, neither more nor less than are all empirical rules.
[Sidenote: _Its error._]
But it does not limit itself to acting simply as an empirical
description, nor even as a simple technique; it usurps a much more
lofty office. Just as Rhetoric and Grammar, innocent and useful so
long as they limit themselves to the functions of convenient grouping
and convenient terminology, become false and harmful when they assume
the attitude of sciences of absolute values, and must then be resolved
into, and replaced by Æsthetic; so empirical or verbal Logic becomes
transformed into error when it claims to give the laws of thought, or
the thought of thought, which cannot be other than the concept of the
concept. It is not, then, _formal,_ as it boasts itself to be, because
the only logical form is the universal, and this alone is the object of
logical investigation; but it is falsely formal, since it relies upon
contingencies, and must, therefore, be called _formalist._ We reject it
here exclusively in its formalist aspect; that is to say, in so far as
it is a complex of empirical distinctions that wish to pass as rational
and usurp the place of true rationality.
[Sidenote: _Its traditional constitution._]
Several of such empirical distinctions, such as the distinction between
thought and principle of thought, truth and reason of truth, judgments
and syllogisms, and such-like, have been recorded and criticized; we
shall proceed to mention others, when suitable opportunities occur.
Here it will be well to refer to the general physiognomy and structure
of that Logic, as it was embodied for centuries in the schools and
still persists in treatises.
[Sidenote: _The three logical forms._]
Its point of departure is the external distinction between words and
connections of words, which belongs properly to Grammar. But words
are then treated by it as concepts, and connections of words, as
judgments. Thus it obtains the identification of the concept with the
abstract and mutilated grammatical word and arrives at the monstrous
determination of the concepts as things which are not in themselves
either true or false. Thus, again, by constantly calling upon the
connections of the concepts for succour, it succeeds in distinguishing
the judgment from the mere proposition. A double criterion is
constantly adopted in establishing these and other fundamental forms:
the verbal and the logical; and formalist Logic oscillates equivocally
between the two different determinations; whence the alternating
appearance of truth and of falsehood, with which its distinctions
present themselves. The syllogism, which should be the third
fundamental form, is conceived as the connection of three distinct
judgments; but if it yet retains its importance and preponderance
over two-membered forms or over serial forms of more than three
propositions and judgments, this is really because to the distinction
and enumeration of the three propositions there is added the criterion
of the concept as a nexus, or as a triunity of universal, particular
and singular.
[Sidenote: _The theories of the concept and of the judgment._]
The three fundamental forms have been reduced by some logicians to
two, by others; amplified to four or to five, by adding to them
the perceptive form or the definitive and systematic form. These
restrictions and amplifications have always encountered resistance,
because it was justly felt that in this way one form of empiricism was
being mingled with another: the verbal form with empirical distinctions
drawn from other presuppositions. But in determining in particular the
three fundamental forms, formalist Logic has not been able to restrict
itself to the mere distinction of words and propositions, artificially
placed in relation with the pure concept; but has been obliged to draw
from other sources. The concepts are variously classified, sometimes
from the verbal point of view, as _identical, equivalent, equivocal,
anonymous_ and _synonymous_; sometimes from the logical point of view,
as _distinct, disparate, contrary_ or _contradictory_; sometimes
from the psychological point of view, as _incomplete_ and _complete,
obscure_ and _clear,_ the concepts further always being understood
as names, so that, for example, distinct concepts are indifferently
philosophically distinct concepts, and empirically distinct concepts;
and the contraries are both the philosophical contraries and those
empirically so-called. The same has occurred in the classification
of judgments where sometimes the determinations of the concept are
taken as foundation and the judgments distinguished as _universal
particular_ and _individual;_ sometimes the intrinsic dialectic nature
of the concept, and they are distinguished as _affirmative, negative_
and _indeterminate_ or _infinite_; sometimes the stages passed through
in the search for truth, and they are distinguished into _categorical,
hypothetical_ and _disjunctive,_ or _apodeictic, assertory_ and
_problematic._ And these forms have further always been understood
verbally. "Universality" is the "totality" empirically designated
by the word, and not true universality; and "individuality," on the
contrary, is not only the individuality of the representation, but
also the single particularity of the distinct concept; "affirmative"
is differentiated from "negative" by accidental grammatical form, and
not because that unique act which is thought, at once affirmation and
negation (as the will is both love and hatred) can be truly divided.
[Sidenote: _The theory of the syllogism._]