Logic as the Science of the Pure Concept

by Benedetto Croce

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.

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.

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.

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.

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.