conception of the judgment as the copulation of a _subject_ and a
_predicate_ affords a suitable parallel to this method of treatment of
the judgment; subject and predicate being understood in an empirical
and grammatical manner, whence they are also discovered in those
verbal affirmations, in which they are not distinct, because they are
identical, as in the case of the judgment of definition. For empirical
Logic, in the judgment: "The will is the practical form of the spirit,"
"will" is subject and "practical form" predicate in the same way as in
"Peter is a man," "Peter" is subject, and "man" predicate. From the
distinction between subject and predicate, arise the four _figures_
of the syllogism; the criterion being the position of the middle term
in the two premisses of the three propositions of which the syllogism
is formed. If the middle term be subject in the first premiss and
predicate in the second, we have the first figure; if it be predicate
in both, the second; if it be subject in both, the third; if it be
predicate in the first and subject in the second, the fourth figure
("_sub-prae,_ turn _prae-prae,_ turn _sub-sub,_ turn _prae-sub")._
But in order to deduce the moods of each figure recourse is then had
to another criterion, indeed to two other criteria; that is, to the
empirical distinctions of judgments into universal and particular, and
into affirmative and negative, with the four consequent determinations
into universal-affirmative judgments (A), universal-negative (E),
particular-affirmative (I), and particular-negative (O). Thus, in the
first figure, two universal affirmative premisses constitute the first
mood, and the conclusion is universal affirmative _(Barbara)_; two
premisses, both universal, but one affirmative and the other negative,
constitute the second, and the conclusion is universal negative
_(celarent)_; two premisses, one universal affirmative and the other
particular affirmative, constitute the third mood, and the conclusion
is particular affirmative _(darii);_ two premisses, one universal
negative and one particular affirmative, constitute the fourth mood,
and the conclusion is particular negative _(ferio)._ And so on.
[Sidenote: _Spontaneous reductions to the absurd of formal Logic._]
This is not the occasion to go on expounding in its other particulars
this construction, of which we have given an example, for it is
very well known: nor to attach importance to criticizing it, since'
its foundations themselves have already been shown to be false and
its hybrid genesis explained. Verbal Logic, which vaunts itself as
rational, carries its own caricature in itself, namely the creation of
_Sophisms_; because, since it seeks the force of thought in words, it
cannot prevent sophistical ability from making use, in its turn, of
words, in order capriciously to create thoughts and forms of thought.
Thus verbal Logic, in order to combat sophisms, is constrained hastily
and eagerly to abandon simple verbal connections, and to take refuge in
concepts and connections of concepts thought in words; that is to say,
neither more nor less than to negate the formalist point of view. And
with analogous self-irony it renounces that point of view and dissolves
itself, when it tries to refute the fourth figure of the syllogism, or
to reduce the second, third and fourth to the first, as the only real
figure, and then the first to a connection of three concepts; not to
mention the permanent self-irony and patent demonstration of falsity
involved in the logical deduction of the figures of the syllogism which
it makes from a series of moods, recognized as _not conclusive._
[Sidenote: _Mathematical Logic or Logistic._]
Formalist Logic has been the object of many violent attacks from the
Renaissance onwards; but it cannot be said that it has been struck in
its essential part, because up to the present, the principle itself, or
the incoherence from which it springs, has not been attacked. Several
attempts at reform have followed and still follow; they have all of
them the same defect, which is the wish to reform formal Logic without
issuing from its circle, and without refuting its tacit presumption--
the pretension of obtaining thought in words, concepts in
propositions. The most considerable attempt of the kind that has been
made, which has many zealous followers in our day, is _mathematical
Logic,_ also called _calculatory, algebraical, algorhythmic, symbolic,
a new analytic,_ or a _Logical calculus or Logistic._
[Sidenote: _Its non-mathematical character._]
It is admitted by those who profess it and is for the rest evident
from the definitions of Logistic that have been given, that it has
nothing in common with mathematics, for although the majority of its
cultivators are mathematicians and use is made of the phraseology usual
in Mathematics, and it is directed toward Mathematics, in certain of
its practical intentions, there is nothing intrinsically mathematical
in it. Logistic is a science which deals, not with quantity alone, but
with _quantity and quality together_; it is a science of _things in
general_; it is _universal mathematics,_ containing also, subordinated
to itself, the mathematical sciences properly so-called, but not
coinciding with these. It means to be, not mathematics, but _a general
science of thought._
[Sidenote: _Example of its mode of treatment._]
But the "thought" of Logistic is nothing but the "verbal proposition,"
which, in fact, supplies its starting-point. What the proposition is;
whether it be possible truly to distinguish the proposition we call
"verbal" from all the others, poetical, musical, pictorial; whether
the verbal proposition does not bear indistinctly in itself, a series
of very diverse spiritual formations, from poetry to mathematics, from
history and philosophy to the natural sciences; what language is and
what the concept is--these and all other questions concerning the forms
of the spirit and the nature of thought, remain altogether extraneous
to Logistic and do not disturb it in its work. The propositions (the
concept of the proposition remaining an unexplained presupposition)
can be indicated by _p, q,_ etc.; the relation of implication of one
proposition in another can be indicated by the sign _⊃,_ hence an
isolated proposition is "that which implies itself" _(p.⊃.q.)._ By
following a method such as this, many distinctions of the traditional
formalist Logic are eliminated, and in compensation for this, new ones
are added and old and new are dressed in a new phraseology. The logical
_sum a + b_ is the smallest concept, which contains the other two _a_
and _b_ and is what was previously called the "sphere of the concept";
the logical _product a x b_ indicates the greater concept contained
in _a_ and in _b,_ and answers to that which was previously called
"comprehension." There are also new or renovated laws, like the law
of _identity,_ by force of which, in Logic (differently from Algebra),
_a + a + a ... = a;_ by which it is desired to signify this profound
truth, that the repetition of one and the same concept as many times as
one wishes, always gives the same concept;--the law of _commutation,_
by which _ab = ba_;--or that of absorption, by which _a(a + b) = a;_
or--(the convention being that the negation of a concept is indicated
by placing against it a vertical line) the other beautiful laws and
formulæ: _a + a | = a| (a | )a = a; aa | = o._ This is a charming
amusement for those who have a taste for it.
[Sidenote: _Identity of nature of Logistic with formalist Logic._]
Thus it is seen that if the words and the formulæ be somewhat
different, the nature of mathematical Logic in no respect differs from
that of formalist Logic. Where the new Logic contradicts the old, it is
not possible to say which of the two is right; as of two people walking
side by side over insecure ground, it is impossible to say which of
the two walks securely. The very doctrine of the _quantification
of the predicate_ (which has been the leaven of the reform) in no
wise alters the traditional manner of conceiving the judgment, with
the corresponding arbitrary manner of distinguishing subject and
predicate. It simply establishes a convention with the object of being
able to symbolize, with the sign of equality, the subject and the
predicate:--the subject being included in the predicate, is part of it:
"men are mortal" equals: "men are some mortals"; and so, "men" being
indicated with _a_ and "some mortals" with _b,_ the judgment can be
symbolized: _a = b._ For us, it is indifferent whether the modes of
the syllogism be the 64 and the 19 recognized as valid by traditional
Logic, or the 12 affirmative and the 24 negative of Hamilton's Logic,
which distinguishes four classes of affirmative and four of negative
propositions. It is indifferent whether the methods of conversion
be three or two or one. It is indifferent whether logical laws or
principles be enumerated as two, three, five or ten. Since we do not
accept the point of departure, it is impossible for us, far from
admitting the development, even to discuss it; save to demonstrate
that from capricious choice comes capricious choice, as we have made
sufficiently clear in our treatment of formalist Logic. Mathematical
Logic is a new manifestation of this formalist Logic, involving a great
change in traditional formulæ, but none in the intimate substance of
that pretended science of thought.
[Sidenote: _Practical aspect of Logistic._]
As the _science of thought,_ Logistic is a laughable thing; worthy, for
that matter, of the brains that conceive and advocate it, which are the
same that are promulgating a new Philosophy of language, indeed a new
Æsthetic, with their insipid theories of the _universal Language._ As a
formula of _practical utility_ it is not incumbent upon us to examine
it here; all the more since we have already had occasion to give our
opinion upon this subject. In the time of Leibnitz, fifty years later
in the last days of Wolffianism; a century ago in Hamilton's time;
forty years ago in the time of Jevons and of others; and finally now,
when Peano, Boole, and Couturat are flourishing, these new arrangements
are offered on the market. But every one has always found them too
costly and complicated, so that they have not hitherto been generally
used. Will they be so in the future? The practical work of persuasion,
proper to the commercial traveller seeking purchasers of a new product,
and the foresight of the merchant or manufacturer as to the fortune
that may await that product, are not pertinent to Philosophy; which,
being disinterested, could here, at the most, reply with words of
benevolent patience: "If they be roses, they will bloom."
IV
THE INDIVIDUAL JUDGMENT AND PERCEPTION
[Sidenote: _Reaction of the concept upon the representation._]
Problems of a widely different nature from these formalist playthings
await exploration in the depths of the Science of Logic. And resuming
what we have called the descent of the universal into the individual,
it is of importance, after having established the relation between
concept and form of expression, to examine in what way the concept
reacts upon the representation, from which it appears to be at a stroke
and altogether separated.
In more precise terms: Beyond doubt the concept is thought only in
so far as it becomes concrete in an expressive form and itself also
becomes, from this point of view, representative. Thus, a logical
affirmation, or one that presents itself as logical, can be viewed
under a twofold aspect, as logical and as æsthetic. It can be regarded
as well thought-out, and so also very well expressed, perfectly
æsthetic because perfectly logical; or as very well expressed but ill
thought, or not truly thought, and so not logical, and yet sentimental,
passionate and imaginative. But this expression-representation,
in which the concept lives (and which is, for example, the tone,
the accent, the personal form, the style, which I am employing in
this book to expound Logic), is a _new_ representation, conditioned
by the concept. We now ask, not indeed the character of this
representation (which is sufficiently clear), but of what kind are
those representations, about and upon which, the thought of the concept
has been kindled. Do they remain apart, excluded from the light of
the concept, obscure as before, that is, logically obscure? Does the
concept illuminate only itself in a sort of egoistic satisfaction,
without irradiating with its light the representations upon which it
has arisen?
[Sidenote: _Logicization of the representations._]
That would be inconceivable and contrary to the unity of the spirit;
and indeed, such separation and indifference do not exist. The
appearance of the concept transfigures the representations upon which
it arises, making them _other_ than they formerly were; from being
indiscriminate it makes them discriminate; from fantastic, logical;
from clear but indistinct (as used to be said), clear and distinct.
I am, for example, in such a condition of soul as prompts me to sing
or to versify, and thus to make myself objective and known to myself;
but I am objective and known only to fancy, so much so, that at the
moment of poetical or musical expression I should not be able to say
what was really happening in me: whether I wake or dream, whether I
see clearly, or catch glimpses, or see wrongly. When from the variety
of the multitude of representations, which have preceded and which
follow it, I pass on to enquire as to the truth of them all (that is
to say, the reality, which does not pass), and rise to the concept,
those representations themselves must be revised in the light of the
concept that has been attained, but no longer with the same eyes as
formerly,--they must not be _looked at,_ but henceforth, _thought._
My state of soul then becomes determinate; and I shall say, for
example: "What I have experienced (and sung and made poetry of), was
an absurd desire; it was a clash of different tendencies that needed
to be overcome and arranged; it was a remorse, a pious desire," and
so on. Thus by means of the concept is formed a _judgment_ of that
representation.
[Sidenote: _The individual judgment and its difference from the
definitive judgment._]
We have already studied the judgment, which is proper to the concept,
and called it definitive judgment or judgment of definition. We have
shown how in it there is no distinction of subject and predicate,
so much so that it may be said, with regard to it, that there is
neither subject nor predicate, but the complete identity of the two:
a predicate or universal, which is subject to itself. However, the
judgment which is now being discussed is not a simple definition and
does not coincide with the first. It certainly has as its base a
concept and therefore a definition; but it contains something more,
a representative or individual element, which is transformed into
logical fact, but does not lose individuality on that account; indeed
it reaffirms its individuality with more precise distinction. This
judgment is connected with the first, but it represents a further stage
of thought. If the first form be a conceptual or _definitive_ judgment,
the second may be called an _individual_ judgment.
[Sidenote: _Distinction of subject and predicate in the individual
judgment_]
Owing to this new element, which the individual judgment contains,
and the judgment of definition does not contain, we eventually find
fully justified in the former that distinction between subject and
predicate which verbal Logic in vain claims to discover in all
judgments, including those of universal character (and even in simple
propositions); so that it ends by attributing to that distinction, of
which later we shall perceive the capital philosophical importance, a
purely grammatical or verbal significance. Subject and predicate can
be distinguished only in so far as the one is not and the other is
universal, in so far as the one is not and the other is concept, that
is to say, only in so far as the one is representation and the other
concept. A particular or singular concept (for example, the will) is
always also a universal concept; and therefore not adapted to function
as a subject to which a predicate is applied; because that predicate,
that universal, is already explicitly in the pretended subject itself
which is net thinkable, save by means of that predicate. Only the
_representation_ can be truly _subject;_ and only the _concept_ can
be _predicate._ This takes place plainly in the individual judgment,
where the two elements are connected. "Peter is good," an individual
judgment, implies the subject "Peter" and the predicate "good," the one
not to be confounded with the other; whereas, in the definition "the
will is the practical form of the spirit," "practical form" and "will"
are identical.
[Sidenote: _Reasons for the variety of definitions of the judgment and
of certain of its divisions._]
When the attempt was made to define the judgment as differing both
from the concept and from the definition, what was aimed at was
the individual judgment. But, if this be so, then the definitions
which conceive the judgment either as relation of representations
or as relation of concepts (the subsumption of one concept under
another, etc.), must be termed false, since it is henceforth clear
that, as individual judgment, it must be conceived as a _relation
of representation and concept._ On the other hand, some celebrated
divisions of the judgment find their origin in the distinction made
by us (which, we again repeat, is given at this point provisionally
with the intention of seeking the definite formula further on),
between the judgment of the concept and the judgment of the
representation, between definition and individual judgment. In this
way the _analytic_ judgment, defined as that in which the concept of
predicate was obtained from the subject, reveals itself as nothing
but the definition, the identity of subject and predicate; the
_synthetic_ judgment, which adds to the subject something which was
not there previously, is the individual judgment, logical thinking
of the intuition, at first only intuited and not thought. We shall
examine further on the true meaning and the definite formula of this
distinction also.
[Sidenote: _The individual judgment and intellectual intuition._]
To ignore the form of the individual judgment, and to recognize only
that of the concept and of the definition, is an impossible position,
though occasionally there appears a tendency in that direction.
We perceive it, for instance, in those who seek for definitions
of everything, and limit themselves to syllogizing, when there is
certainly a case for thinking, but also one for looking, or for
thinking while we look, and for looking while we think. This may be
said truly to represent knowledge, that complete knowledge in which
all anterior forms unite, and which is the result of all of them. To
know is to know reality; and knowledge of reality is translated into
representations, penetrated with thought. That famous _intellectual
intuition,_ which has sometimes been described as the faculty to which
man aspires, but does not possess, and sometimes as a prodigious
faculty, superior to knowledge itself, should be declared, with the
full rigour of letter and concept, to be nothing but the individual
judgment; which is, in truth, intellectual intuition or intuited
intellection.
[Sidenote: _Identity of the individual judgment with perception or
perceptive judgment._]
But the individual judgment can take another name, much better known
and more familiar: _perception_; and perception, in its turn, should
be called, synonymously, individual judgment, or at least _perceptive
judgment._ Perception does not consist of opening the eyes, of offering
the ear, and of unlocking any of the other senses, which are wont to be
enumerated, nor, in general, of abandoning oneself to sensation. The
world does not enter our spirit by these wide gates; but has itself
announced, in order to be received with due honours. That good folk
(and among the best of folk are to be counted many philosophers) think
otherwise is in truth to be explained by their wonted neglect or lack
of analysis and reflection.
And further, perception is not intuition, _i.e.,_ an impression
theoretically fashioned, or that stage or moment of the spirit which
is represented in an eminent degree by the poet, who intuites and does
not know what he intuites, indeed does not know that he does not know
(because the pertinent question has not arisen, and cannot arise, in
him, as poet). To perceive means to apprehend a given fact as having
this or that nature; and so means to think and to judge it. Not even
the lightest impression, the smallest fact, the most insignificant
object, is perceived by us, save in so far as it is thought.
Hence the supreme importance of the individual judgment, which is that
which embraces all knowledge produced by us at every moment, by means
of which we _possess the world,_ by means of which a _world exists._
[Sidenote: _and with the commemorative or historical judgment._]
In perceptive judgments also, are comprised those judgments which
are called by some _commemorative_ or _historical,_ that is to say,
those by which it is recognized that a given fact has occurred in the
past. This recognition can never be founded upon anything other than
present intuitions, intuitions, that is to say, of our present life,
which contains the past in it, and persuades us of the veracity of a
given piece of evidence, as now apprehended by us. And conversely, all
perceptive judgments are, in some way, commemorative and historical,
because the present, in the very act by which we hold it before our
spirit, becomes a past, that is to say an object of memory and of
history.
[Sidenote: _Erroneous distinction of individual judgments as of fact
and of value._]
On the other hand, it would be erroneous to divide individual
judgments, as has often been attempted, into judgments of _fact_ and
judgments of _value,_ claiming that the judgment, "Peter is a man," is
of a different nature from: "Peter is good." Every judgment of fact, in
so far as it attributes a predicate to a subject, gives to it a value,
declaring it to participate in the universal or in a determination of
the universal. And conversely, every judgment of value, in so far as
it attributes a value, cannot attribute other than the universal or
a determination of the universal, since outside the universal there
is no value. Even judgments of negative form, such as: "Peter is
not good," or "is not-good," or: "Peter is bad," are attributes of
universality and of value; because, as we know, theoretically they do
not affirm anything other than that Peter has a spiritual determination
different from goodness (for example, that he is utilitarian, not yet
moral). Certainly, in judgments such as these which we have selected
as examples, there is mingled (this too has been noted; and at this
point it suffices to recall it) the expression of an _ought to be,_
which, in this case, is revealed in the negative formula adopted; but
the expression of an ought to be or of a desire is not a judgment
either of fact or of value; indeed, it is not a judgment at all; it is
a mere proposition, a logos semanticos, not apophanticos, an optative
or desiderative formula, a _lyricism_ of the spirit directed to the
future.[1]
[Sidenote: _The individual judgment as ultimate and perfect form of
knowledge._]
There is no other cognitive fact to know, beyond perception or
individual judgment. In this, the ultimate and the most perfect
of cognitive facts, the circle of knowledge is completed. Obscure
sensibility, having become clear intuition, and then having made itself
thought of the universal, in the individual judgment is logically
thought, and is, henceforward, knowledge of fact or of event, that is,
of effectual reality. The individual judgment, or perception, is fully
adequate to reality.
[Sidenote: _Error of treating it as the first fact of knowledge._]