Notes on <On the Fourfold Root of the Principle of Sufficient Reason> - Chapter 6
Chapter 6. On the Third Class of Objects for the Subject, and that form of the Principle of Sufficient Reason which predominates in it
§ 35. Explanation of this Class of Objects.
It is the formal part of complete representations—that is to say, the intuitions given us à priori of the forms of the outer and inner sense, i.e. of Space and of Time—which constitutes the Third Class of Objects for our representative faculty. The form of Causality, on the contrary, which belongs to the Understanding, is not separately and by itself an object for our faculty of representation, nor have we consciousness of it, until it is connected with what is material in our knowledge.
§ 36. Principle of the Sufficient Reason of Being.
Space and Time are so constituted, that all their parts stand in mutual relation, so that each of them conditions and is conditioned by another. We call this relation in Space, position; in Time, succession. The law by which the divisions of Space and of Time determine one another reciprocally with reference to these relations (position and succession) is what I call the Principle of the Sufficient Reason of Being.
§ 37. Reason of Being in Space.
The position of each division of Space towards any other, say of any given line determines also absolutely its totally different position with reference to any other possible line. It is just as impossible to find an end a parte ante in the series of links in the chain of Reasons of Being as in that of Reasons of Becoming, nor can we find any a parte post either, because of the infinity of Space and of the lines possible within Space.
Nothing of all this can be proved; for the truth of these principles is transcendental, they being directly founded upon the intuition of Space given us à priori.
§ 38. Reason of being in Time. Arithmetic.
Every instant in Time is conditioned by the preceding one. The Sufficient Reason of Being, as the law of consequence, is so simple here, because Time has only one dimension, therefore it admits of no multiplicity of relations.
§ 39. Geometry.
The whole science of Geometry likewise rests upon the nexus of the position of the divisions of Space.
In Geometry, it is only in dealing with axioms that we appeal to intuition. All the other theorems are demonstrated: that is to say, a reason of knowing is given, the truth of which everyone is bound to acknowledge. The logical truth of the theorem is thus shown, but not its transcendental truth (v. §§ 30 and 32), which, as it lies in the reason of being and not in the reason of knowing, never can become evident excepting by means of intuition.