Part 10

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._]

The classification of syllogisms, founded exactly upon the empirical 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._]