100 THE WORLD AS IDEA.
pure a priori perception, with the same right and certainty as in arithmetic. It is in fact always this necessity, known through perception in accordance with the principle of sufficient reason of being, which gives to geometry its principal evidence, and upon which in the consciousness of every one, the certainty of its propositions rests. The stilted logical demonstration is always foreign to the matter, and is generally soon forgotten, without weakening our conviction. It might indeed be dispensed with altogether without diminishing the evidence of geometry, for this is always quite independent of such demonstration, which never proves anything we are not convinced of already, through another kind of knowledge. So far then it is like a cowardly soldier, who adds a wound to an enemy slain by another, and then boasts that he slew him himself.[1]
Alter all this we hope there will be no doubt that the evidence of mathematics, which has become the pattern and symbol of all evidence, rests essentially not upon demonstration, but upon immediate perception, which is thus here, as everywhere else, the ultimate ground and source of truth. Yet the perception which lies at the basis of mathematics has a great advantage over all other perception, and therefore over empirical perception. It is a priori, and therefore independent of experience, which is always given only in successive parts; therefore everything is equally near to it, and we can start either from the reason or from the consequent, as we please. Now this makes it absolutely reliable,
- ↑ Spinoza, who always boasts that he proceeds more geometrico, has actually done so more than he himself was aware. For what he knew with certainty and decision from the immediate, perceptive apprehension of the nature of the world, he seeks to demonstrate logically without reference to this knowledge. He only arrives at the intended and predetermined result by starting from arbitrary concepts framed by himself (substantia causa sut, &c.), and in the demonstrations he allows himself all the freedom of choice for which the nature of the wide concept-spheres afford such convenient opportunity. That his doctrine is true and excellent is therefore in his case, as in that of geometry, quite independent of the demonstrations of it. Cf. ch. 13 of supplementary volume.
