That theoretical error is always at bottom logical error. This is an important proposition, which merits explicit statement, because it is customary to speak of æsthetic, naturalistic, mathematical and historical errors side by side with those that are properly logical or philosophical. We too have spoken and will speak thus, when more subtle distinctions and more precise determinations are not necessary. But in truth, a fact like _humano capiti cervicem equinam jungere,_ or _simulare cupressum_ in the sea where the shipwrecked struggles in the waves, does not constitute in itself that practical act, called æsthetic error, unless there be added to it the false affirmation that the object produced is an æsthetic object, that is to say, unless there be added a logical affirmation, so that the practical act becomes, by means of it, logical error. Taken in itself, the union of a human head with a horse's neck, or of a cypress with the sea is a sort of play of the imagination, such as occurs in fancy, in idleness and in dream. The extrinsic combination of a fancy and a concept is also altogether innocent, as in the case of allegory, which, in itself, is not unsuccessful art, but becomes so only when it is affirmed that the two heterogeneous elements form only one; or rather, it then becomes, not unsuccessful art, but bad philosophy. In the same way, a mathematical error (for example, the formula 4 x 4 = 20) is nothing but a _flatus vocis,_ such as is made in jest or to loosen the tongue. Only when we add the logical affirmation that in this _flatus vocis_ an effectual multiplication has been expressed, do we have a mathematical error, which is therefore a logical error. It is not possible to consider and to condemn as a theoretical error a combination which does not intend to deceive any one as to its proper nature; neither those to whom it is shown, nor him who has made it. Thus, among æsthetic, naturalistic, mathematical, historical, logical and practical productions, combinations without cognitive content are quite possible and constantly to be found; but they do not become theoretical errors unless they are crowned with an improper logical affirmation, or rather with an arbitrary judgment formed upon a logical affirmation. Indeed, even illogical combinations of philosophic concepts are not, as such, logical or theoretical errors, since they can be made tentatively, in order to see whether the two concepts combine or no. To make them errors, the arbitrariness of a special act of judgment is necessary. That arbitrariness consists in a lying to others or to ourselves, in order to satisfy an interest of our merely individual life, and it is impossible to lie without employing an affirmation, which is always a logical product. [Sidenote: _History of errors and phenomenology of error._]