In the first place, what does Kant's doctrine mean for Geometry? Obviously not the aspect of the doctrine which has been attacked by psychologists, the "Kantian machine-shop" as James calls it--at any rate, if this can be clearly separated from the logical aspect. The question whether space is given in sensation, or whether, as Kant maintained, it is given by an intuition to which no external matter corresponds, may for the present be disregarded. If, indeed, we held the view which seems crudely to sum up the standpoint of the Critique, the view that all certain knowledge is self-knowledge, then we should be committed, if we had decided that Geometry was apodeictic, to the view that space is subjective. But even then, the psychological question could only arise when the epistemological question had been solved, and could not, therefore, be taken into account in our first investigation. The question before us is precisely the question whether, or how far, Geometry is apodeictic, and for the moment we have only to investigate this question, without fear of psychological consequences. =53.= Now on this question, as on almost all questions in the Aesthetic or the Analytic, Kant's argument is twofold. On the one hand, he says, Geometry is known to have apodeictic certainty: therefore space must be _à priori_ and subjective. On the other hand, it follows, from grounds independent of Geometry, that space is subjective and _à priori_; therefore Geometry must have apodeictic certainty. These two arguments are not clearly distinguished in the Aesthetic, but a little analysis, I think, will disentangle them. Thus in the first edition, the first two arguments deduce, from non-geometrical grounds, the apriority of space; the third deduces the apodeictic certainty of Geometry, and maintains, conversely, that no other view can account for this certainty[69]; the last two arguments only maintain that space is an intuition, not a concept. In the second edition, the double argument is clearer, the apriority of space being proved independently of Geometry in the metaphysical deduction, and deduced from the certainty of Geometry, as the only possible explanation of this, in the transcendental deduction. In the Prolegomena, the latter argument alone is used, but in the Critique both are employed.