Certain erroneous doctrines take their origin from the undue separation of demonstration and definition, conspicuously that particular error which places a difference of degree between truth and reason of truth, and consequently admits that a truth can be known without its reason being known. But a truth, of which the reason is not known, is not even truth; or it is truth only in preparation and in hypothesis. We hear much about the intuition with which men of genius are equipped, and which enables them to go straight to the truth, even when they are not capable of demonstrating it. But this intuition, when it is not that truth in preparation, or that orientation towards a truth still quite hypothetical, must of necessity be thought and thus also be demonstration of truth; it must be truth and also reason of truth; thought and reasoning performed no doubt with lightning rapidity, which is expressed in brief propositions and needs going over again and rethinking, in order that it may afford a more ample and, from the didactic point of view, a more persuasive, exposition; but it is always thought and reasoning.
Things are still worse, when not only is a diversity of degree admitted, but the complete indifference of demonstration to truth is proclaimed, so that many or infinite possible demonstrations of one identical truth would be possible. If by this it were meant merely that one identical truth, or one identical concept, can assume infinite verbal or expressive forms, and if demonstration were understood as "exposition" or "expression," there would be nothing to object. But if by demonstration be meant something truly logical, that which is properly called by that name in Logic, this thesis leads directly to the negation of truth, making the demonstration of truth, or truth itself, an illusion, a sophistical appearance created simply to persuade. Those acquainted with courts of law know that very often when a magistrate has made his decision and pronounced sentence he deputes to a younger colleague the task of "reasoning" it, or of providing an appearance of reasoning to what is indeed not a logical product, but simply the voluntas of a certain provision. But though this procedure be intelligible and useful when it occurs in the field of practice and of law, it cannot be admitted in the theoretical field, where it would be the ruin of thought and indirectly of the will itself.
Difference between truth and reason of truth in the pseudoconcepts.
Naturally, all that has been said as to the definition and the syllogism has reference to the true and proper concept, or the pure concept. In the case of pseudoconcepts, where practical motives enter, definition is a simple command (a nominalist definition), and demonstration has no place, save for those of its elements that are derived from the pure concept: given the definitions, the reasoning must logically proceed in a determinate manner. In pseudoconcepts, then, definitions are separate from demonstrations: the first do not spring from the second and are not all one with them; the second presuppose the first and do not produce them. Of these definitions infinite demonstrations are possible, precisely because in reality none is possible, for the definitions themselves are infinite; and when a demonstration is given, this is done only pro forma; it is a deception, to conceal a practical convenience, or rather a logical reasoning employed to make it clear. It is for this reason also that the definitions employed in those demonstrations seem to be obtained by means of an act of faith in the irrational; and here faith signifies, not the confidence of thought in itself, but the making a virtue of necessity, accepting as true what is not known as such.—For the rest, pseudoconcepts and concepts have the same relation with the verbal form; that is to say, all are expressed in the most various ways, and there is no obligatory form of language, which can be called the literary form of logical character. The style of the Civil Code, which aroused the admiration of Stendhal, is not the eternal style of laws, for laws were once even put into verse; as in like barbaric times the sciences used to be put into verse. In the life of the word, concepts and pseudoconcepts rush forward in such a way that it is vain to seek there for distinction among them.
[1] Mentioned in Hegel, Wiss. d. Logik 2, iii. 370 n.