The result of the preceding enquiries into the constitution of the cognitive spirit can be resumed, for mnemonic purposes, by saying that there are two pure theoretic forms, the intuition and the concept, the second of which is subdivided into judgment of definition and individual judgment, and that there are two modes of practical elaboration of knowledge, or of formation of pseudoconcepts, the empirical concept and the abstract concept, from which are derived the two subforms of judgment of classification and of judgment of enumeration. If the methods in use in the mediæval schools or in those of Port-Royal (which were not without their utility) were still in vogue, we should be able to embody these results in a few mnemonic verses, which would render the distinctions we have made easy to impart.

Easy to impart, but not understood, or worse, ill understood; because, as we know, both the scheme of classification here adopted and the arithmetical determination of two or more forms are not truly logical thoughts adequate to the representation of the process of the real and of thought. Our grouping constructed to help the memory must therefore be interpreted with the aid of the developments offered above, and not only corrected, but altogether resolved in them. In these developments, the intuition and the concept have appeared as two forms, not capable of co-ordination, but both distinct and united. The judgment of definition and the individual judgment have appeared as logically identical, divisible only from an external or literary point of view, that is to say, by the greater or less importance attached either to the predicate or to the subject. Further, the formation of the pseudoconcepts is outside theory, although founded upon theoretic elements; it belongs essentially, not to the cognitive spirit, but to the practical spirit. And if their subdivision into empirical and abstract concepts is necessary, the necessity is founded upon the fact, that only in these two modes can the concept be practically developed, when its synthetic unity is arbitrarily split up into two one-sided forms. Finally, the two fundamental forms of the spirit themselves, the theoretic and the practical, are not co-ordinate with one another, nor capable of arithmetical enumeration. The one is in the other, the one is correlative to the other, because the one presupposes the other.

Non-existence of technical forms, and of composite forms.

No other cognitive or practical-cognitive forms, or other subforms, beyond those which we have defined, are conceivable. The technical knowledge, which is discussed in some treatises on Logic, is nothing but knowledge itself, which is always and entirely technical, preceding and conditioning the action and practice of life. The same may be said of normative knowledge, by which, as with technical, it is especially meant in ordinary language to designate the whole of the pseudoconcepts. But this is erroneous, when we consider that such knowledge constitutes the true immediate precedent condition of action. The pseudoconcepts must be retranslated into individual judgments, in order that they may be able to form the basis of action, for which, as is justly remarked, we require direct and concrete perceptions of actual situations. Formulæ and abstractions aid perception only in an indirect and subsidiary manner.

The so-called combined or composite forms in which two or more original forms are brought together, must also be rejected, for the reason already given, that composite concepts do not exist in pure Logical thought, and consequently cannot exist in the Science of Logic, which is the science of that thought. The composite form, then, is an empirical and arbitrary determination, as may be observed, for instance, in the case in which we speak of an empirico-philosophic concept, that is, of the union (which is a successive enunciation) of an empirical concept and a philosophic concept.

Identity of cognitive forms and forms of knowledge. Objections to it.

The cognitive forms having thus been established, we pass on to the question, what and how many and of what kind are the forms of knowledge. The reply must be that the forms of knowledge (for example, History and the natural Sciences) cannot be anything but identical with the cognitive forms, and of the same kind and same number as they. The first of these statements finds itself at once at issue with common thought, in which a profound distinction is drawn between the ordinary and the scientific man, the profane and the philosopher, the poet and the non-poet, the ignorant and the learned, layman and clergy; and again, between conversation and science, effusion of the soul and art, collection of facts and history, good sense and philosophy. It is thought that acquaintance belongs to all: every one communicates his sentiments, narrates his experiences and those of others, reasons, classifies and calculates. But art, philosophy, history and science are believed to belong to the few. That alone deserves those solemn names, which is the result of exceptional moments, when man is more than man, or at least when he is no longer one of the crowd, but belongs to an aristocracy.

Empirical distinctions and their limits.