The World as Will and Idea, Vol. II — Arthur Schopenhauer, trans. Haldane & Kemp

Cogito, ergo sum, is an analytical judgment. Indeed Parmenides held it to be an identical judgment : " to yap avTo voeiv eo-rt re /cat eivai " (nam intelligere et esse idem est, Clem. Alex. Strom., vi 2, § 23). As such, however, or indeed even as an analytical judgment, it cannot contain any special wisdom; nor yet if, to go still deeper, we seek to deduce it as a conclusion from the major premise, non-entis nulla sunt prcedicata. But with this proposition what Descartes really wished to express was the great truth that immediate certainty belongs only to selfconsciousness, to what is subjective. To what is objective, on the other hand, thus to everything else, only indirect certainty belongs ; for it is arrived at through selfconsciousness ; and being thus merely at second hand, it is to be regarded as problematical. Upon this depends the value of this celebrated proposition. As its opposite we may set up, in the sense of the Kantian philosophy, cogito, ergo est, that is, exactly as I think certain relations in things (the mathematical), they must always occur in*>2 FIRST BOOK. CHAPTER IV. all possible experience ; — this was an important, profound, and a late appergu, which appeared in the form of the problem as to the possibility of synthetic judgments a priori, and has actually opened up the way to a deeper knowledge. This problem is the watchword of the Kantian philosophy, as the former proposition is that of the Cartesian, and shows e£ oicov e*9 ola.

Kant very fitly places his investigations concerning time and space at the head of all the rest. For to the speculative mind these questions present themselves before all others : what is time ? — what is this that consists of mere movement, without anything that moves it? — and what is space? this omnipresent nothing, out of which nothing that exists can escape without ceasing to be anything at all ?

That time and space depend on the subject, are the mode in which the process of objective apperception is brought about in the brain, has already a sufficient proof in the absolute impossibility of thinking away time and space, while we can very easily think away everything that is presented in them. The hand can leave go of everything except itself. However, I wish here to illustrate by a few examples and deductions the more exact proofs of this truth which are given by Kant, not for the purpose of refuting stupid objections, but for the use of those who may have to expound Kant's doctrine in future.

" A right-angled equilateral triangle " contains no logical contradiction ; for the predicates do not by any means cancel the subject, nor are they inconsistent with each other. It is only when their object is constructed in pure perception that the impossibility of their union in it appears. Now if on this account we were to regard this as a contradiction, then so would every physical impossibility, only discovered to be such after the lapse of centuries, be a contradiction; for example, the composition of a metal from its elements, or a mammal with

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more or fewer than seven cervical vertebra,1 or horns and upper incisors in the same animal. But only logical impossibility is a contradiction, not physical, and just as little mathematical. Equilateral and rectangled do not contradict each other (they coexist in the square), nor does either of them contradict a triangle.

Therefore the incompatibility of the above conceptions can never be known by mere thinking, but is only discovered by perception— merely mental perception, however, which requires no experience, no real object.

We should also refer here to the proposition of Giordano Bruno, which is also found in Aristotle : " An infinitely large body is necessarily immovable"— a proposition which cannot rest either upon experience or upon the principle of contradiction, since it speaks of things which cannot occur in any experience, and the conceptions " infinitely large " and " movable " do not contradict each other ; but it is only pure perception that informs us that motion demands a space outside the body, while its infinite size leaves no space over.

Suppose, now, it should be objected to the first mathematical example that it is only a question of how complete a conception of a triangle the person judging has : if the conception is quite complete it will also contain the impossibility of a triangle being rectangular and also equilateral.

The answer to this is : assume that his conception is not so complete, yet without recourse to experience he can, by the mere construction of the triangle in his imagination, extend his conception of it and convince himself for ever of the impossibility of this combination of these conceptions.

This process, however, is a synthetic judgment a priori, that is, a judgment through which, independently of all experience, and yet with validity for all experience, we form and perfect our conceptions. For, in general, whether a given judgment is analytical or synthetical can only be determined in the particular case according as