§ 46. The Systematic Order.
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Schopenhauer, Arthur and Hillebrand, Karl, Mme.
The order of succession in which I have stated the various forms of the Principle of Sufficient Reason in this treatise, is not systematic; it has been chosen for the sake of greater clearness, in order first to present what is better known and least presupposes the rest. In this I have followed Aristotle's rule: καὶ μαθήσεως οὐκ ἀπὸ τοῦ πρώτου, καὶ τῆς τοῦ πράγματος ἀρχῆς ἐνίοτε ἀρκτέον, ἀλλ' ὅθεν ῥᾷστ' ἂν μάθοι (et doctrina non a primo, ac rei principio aliquando inchoanda est, sed unde quis facilius discat).[156] But the systematic order in which the different classes of reasons ought to follow one another is the following. First of all should come The Principle of Sufficient Reason of Being; and in this again first its application to Time, as being the simple schema containing only what is essential in all the other forms of the Principle of Sufficient Reason, nay, as being the prototype of all finitude. The Reason of Being in Space having next been stated, the Law of Causality would then follow; after which would come the Law of Motives, and last of all the Principle of Sufficient Reason of Knowing; for the other classes of reasons refer to immediate representations, whereas this last class refers to representations derived from other representations.
The truth expressed above, that Time is the simple schema which merely contains the essential part of all the forms of the Principle of Sufficient Reason, explains the absolutely perfect clearness and precision of Arithmetic, a point in which no other science can compete with it. For all sciences, being throughout combinations of reasons and consequences, are based upon the Principle of Sufficient Reason. Now, the series of numbers is the simple and only series of reasons and consequences of Being in Time; on account of this perfect simplicity—nothing being omitted, no indefinite relations left—this series leaves nothing to be desired as regards accuracy, apodeictic certainty and clearness. All the other sciences yield precedence in this respect to Arithmetic; even Geometry: because so many relations arise out of the three dimensions of Space, that a comprehensive synopsis of them becomes too difficult, not only for pure, but even for empirical intuition; complicated geometrical problems are therefore only solved by calculation; that is, Geometry is quick to resolve itself into Arithmetic. It is not necessary to point out the existence of sundry elements of obscurity in the other sciences.