CONCERNING THE ULTIMATE GROUND OF THE DIFFERENTIATION OF DIRECTIONS IN SPACE (1768)

Summary

The celebrated Leibniz possessed many genuine insights, and by their means he enriched the sciences. But he also entertained projects which were of still greater importance. The world, however, was to wait in vain for their realisation. It is not my purpose here to decide what the reason for this failure may have been. Leibniz may have regarded his efforts as too imperfect – a reservation which is typical of men of great merit, and one which has constantly deprived learning of many valuable fragments. Or it may have been with him, as Boerhaave supposed that it was with great chemists: they often claimed to possess the ability to perform certain feats as if they had already executed them, whereas in fact they merely possessed the conviction and the assurance that they could do so, and that they could not fail in the undertaking if only they set their minds to the performance. At any rate, it looks as if a certain mathematical discipline, which Leibniz called analysis situs, and the loss of which was lamented by Buffon among others when he was considering the foldings together of nature in the seeds' – it looks as if this discipline was never more than a thought in Leibniz's mind. I do not know exactly to what extent the object which I propose examining here is related to what the great Leibniz had in mind. But to judge by the meaning of the term, what I am seeking to determine philosophically here is the ultimate ground of the possibility of that of which Leibniz was intending to determine the magnitudes mathematically. For the positions of the parts of space in reference to each other presuppose the direction in which they are ordered in such a relation. In the most abstract sense of the term, direction does not consist in the reference of one thing in space to another – that is really the concept of position – but in the relation of the system of these positions to the absolute space of the universe.