Logic as the Science of the Pure Concept

by Benedetto Croce

Universals, particulars, and singulars. Intension and extension.

But the distinction of concepts into universal, particular, and singular deserves elucidation, for the reason that we are now giving. Concepts, which are only universal, or only particular, or only singular, or to which any one of these determinations is wanting, are not conceivable. Indeed, universality only means that the distinct concept is also the unique concept, of which it is a distinction and which is composed of such distinctions; particularity means that the distinct concept is in a determinate! relation with another distinct concept; and singularity that in this particularity and in that universality it is also itself. Thus the distinct concept is always singular, and therefore universal and particular; and the universal concept would be abstract were it not also particular and singular. In every concept there is the whole concept, and all other concepts; but there is also one determinate concept. For example, beauty is spirit (universality), theoretic spirit (particularity), and intuitive spirit (singularity); that is to say, the whole spirit, in so far as it is intuition. Owing to this distinction into universal, particular, and singular, it is self-evident that intension and extension are, as the phrase is, in inverse ratio, since this amounts to repeating that the universal is universal, the particular particular, and the singular singular.

Logical definition.

The interest of this distinction of universality, particularity, and singularity lies in this, that upon it is founded the doctrine of definition, since it is not possible to define, that is, to think a concept, save by thinking its singularity (peculiarity), nor to think this, save by determining it as particularity (relation with the other distinct concepts) and universality (relation with the whole). Conversely, it is not possible to think universality without determining its particularity and singularity; otherwise that universal would be empty. The distinct concepts are defined by means of the one, and the one by means of the distinct. This doctrine, thus made clear, is also in harmony with that of the nature of the concepts.

Unity, distinction as circle.

But the theory of the distinct concepts and that of their unity still present something irrational and give rise to a new difficulty. Because, if it be true that the distinct concepts constitute an ideal history or series of grades, it is also true that in such a history and series there is a first and last, the concept a, which opens the series, and, let us say, the concept d, which concludes it. Commencement and end thus remain both without motive. But in order that the concept be unity in distinction and that it may be compared to an organism, it is necessary that it have no other commencement save itself, and that none of its single distinct terms be an absolute commencement. For, in fact, in the organism no member has priority over the others; but each is reciprocally first and last. Now this means that the symbol of linear series is inadequate to the concept; and that its true symbol is the circle, in which a and d function, in turn, as first and last. And indeed the distinct concepts, as eternal ideal history, are an eternal going and returning, in which a, b, c, d arise from d, without possibility of pause or stay, and in which each one, whether a or b or c or d, being unable to change its place, is to be designated, in turn, as first or as last. For example, in the Philosophy of Spirit it can be said with equal truth or error that the end or final goal of the spirit is to know or to act, art or philosophy; in truth, neither in particular, but only their totality is the end; or only the Spirit is the end of the Spirit. Thus is eliminated the rational difficulty, which might be urged in relation to this part.

Distinction in the pseudoconcepts.

It is still better eliminated, and the whole doctrine of the pure concepts which we have been expounding is thereby illumined and thrown into clearer outline when we observe the transformation (which we will not call either inversion or perversion), to which it is submitted in the doctrine of the pseudoconcepts. It is therefore expedient to refer rapidly to this for the sake of contrast and emphasis.

Above all, certain distinctions, which in the doctrine of the pure concepts have been seen to be without significance or importance, find their significance in the doctrine of the pseudoconcepts. We understand, for instance, how and why identical concepts can be discussed; since, in the field of caprice, one and the same thing, or one and the same not-thing, can be defined in different ways and give rise to two or more concepts which, owing to the identity of their matter, are thus identical. The concept of a figure having three angles, or that of a figure having three sides, are identical concepts, alike applicable to the triangle; the concept of 3 x 4 and that of 6 x 2 are identical, since both are definitions of the number 12; the concept of a feline domestic animal and that of a domestic animal that eats mice are identical, both being definitions of the cat. It is likewise clear how and why primary and derived, simple and compound concepts are discussed; for our arbitrary choice, by forming certain concepts and making use of these to form others, comes to posit the first as simple and primitive in relation to the second, which are, in their turn, to be considered as compound or secondary.

The subordination and co-ordination of the empirical concepts.