Here, forgetting that space of three dimensions is nothing real that can be experienced, but is a mathematical construction, and on the other hand finding it convenient for mathematical reasons to construct spaces of less or more than three dimensions, or of _n_ dimensions, they end by treating these constructions as conceivable realities, and seriously discuss bi-dimensional beings or four-dimensional worlds. [Sidenote: _Dualism, agnosticism and superstition of mathematicism._] With affirmations such as those of infinites incomprehensible to thought, and of real but not experienceable spaces, mathematicism also creates a dualism of thought and of reality superior to thought, or (what amounts to the same thing) of thought which meets its equivalent in experience and thought without a corresponding experience. The unknowable here too lies in wait and falls upon the imprudent mathematicist philosopher, who feels himself lost before a second, third, fourth and infinite worlds, excogitated by himself, superior or inferior worlds to those of man, underworlds and overworlds and over-over worlds. He then becomes even spiritualist and asks with Zollner, why spiritualist facts should not possess reality and be produced in the fourth dimension of space, shut off from us. The contradiction of the mathematicist attempt, like that of the æsthetic and empiricist, is clearly revealed in the dualistic, agnostic and mystical consequences to which, as we shall see more clearly further on, all of them necessarily lead. III PHILOSOPHISM [Sidenote: _Rupture of the unity of the a priori synthesis._] The three modes of error examined exhaust the possible combinations of the pure concept with the forms of the theoretic or theoretic-practical spirit, anterior or posterior to it. Other modes of error arise from the breaking up of the unity of the concept, from the separation of its constitutive elements. Each one of these elements, abstracted from the other, and finding that other before it, annuls, instead of recognizing the other as an organic part of itself; that is to say, substitutes for it its own abstract existence. The concept, as we know, is the logical _a priori_ synthesis, and so the unity of subject and predicate, unity in distinction and distinction in unity, affirmation of the concept and judgment of the fact, at once philosophy and history. In pure and effective thought, the two elements constitute an indissoluble organism. A fact cannot be affirmed without thinking; it is impossible to think without affirming a fact. In logical thought, the representation without the concept is blind, it is pure representation deprived of logical right, it is not the subject of a judgment; the concept without representation is void. [Sidenote:_Philosophism, logicism or panlogism._]