On the Fourfold Root of the Principle of Sufficient Reason

§ 37 Reason of Being in Space

The position of each division of Space towards any other, say of any given line—and this is equally applicable to planes, bodies, and points—determines also absolutely its totally different position with reference to any other possible line; so that the latter position stands to the former in the relation of the consequent to its reason. As the position of this given line towards any other possible line likewise determines its position towards all the others, and as therefore the position of the first two lines is itself determined by all the others, it is immaterial which we consider as being first determined and determining the others, i.e. which particular one we regard as ratio and which others as rationata. This is so, because in Space there is no succession; for it is precisely by uniting Space and Time to form the collective representation of the complex of experience, that the representation of coexistence arises. Thus an analogue to so-called reciprocity prevails everywhere in the Reason of Being in Space, as we shall see in § 48, where I enter more fully into the reciprocity of reasons. Now, as every line is determined by all the others just as much as it determines them, it is arbitrary to consider any line merely as determining and not as being determined, and the position of each towards any other admits the question as to its position with reference to some other line, which second position necessarily determines the first and makes it that which it is. It is therefore 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. All possible relative spaces are figures, because they are limited; and all these figures have their Reason of Being in one another, because they are conterminous. The series rationum essendi in Space therefore, like the series rationum fiendi, proceeds in infinitum; and moreover not only in a single direction, like the latter, but in all directions.

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.