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

This table contains all the fundamental truths which are rooted in our perceptive or intuitive knowledge a priori, expressed as first principles independent of each other. What is special, however, what forms the content of arithmetic and geometry, is not given here, nor yet what only results from the union and application of those formal principles of knowledge. This is the subject of the "Metaphysical First Principles of Natural Science" expounded by Kant, to which this table in some measure forms the propaedutic and introduction, and with which it therefore stands in direct connection. In this table I have primarily had in view the very remarkable parallelism of those a priori principles of knowledge which form the framework of all experience, but specially also the fact that, as I have explained in § 4 of the first volume, matter (and also causality) is to be regarded as a combination, or if it is preferred, an amalgamation, of space and time. In agreement with this, we find that what geometry is for the pure perception or intuition of space, and arithmetic for that of time, Kant's phoronomy is for the pure perception or intuition of the two united. For matter is primarily that which is movable in space. The mathematical point cannot even be conceived as movable, as Aristotle has shown (" Physics," vi. 10). This philosopher also himselfp. 220 provided the first example of such a science, for in the fifth and sixth books of his "Physics" he determined a priori the laws of rest and motion.

Now this table may be regarded at pleasure either as a collection of the eternal laws of the world, and therefore as the basis of our ontology, or as a chapter of the physiology of the brain, according as one assumes the realistic or the idealistic point of view ; but the second is in the last instance right.

On this point, indeed, we have already come to an understanding in the first chapter ; yet I wish further to illustrate it specially by an example.

Aristotle's book "Be Xenophane" &c, commences with these weighty words of Xenophanes : " AiZiov ewat <f>rj(riv, ei rt eanv, ecirep fir} ei>8e%eTai fyeveaOcu fjbrjBev ex firjSevo?." (JSternum esse, inguit, quicquid est, siquidem fieri non potest, ut ex nihUo quippiam existat.) Here, then, Xenophanes judges as to the origin of things, as regards its possibility, and of this origin he can have had no experience, even by analogy ; nor indeed does he appeal to experience, but judges apodictically, and therefore a priori How can he do this if as a stranger he looks from without into a world that exists purely objectively, that is, independently of his knowledge ?

How can he, an ephemeral being hurrying past, to whom only a hasty glance into such a world is permitted, judge apodictically, a priori and without experience concerning that world, the possibility of its existence and origin ?

The solution of this riddle is that the man has only to do with his own ideas, which as such are the work of his brain, and the constitution of which is merely the manner or mode in which alone the function of his brain can be fulfilled, i.e., the form of his perception.

He thus judges only as to the pluno~ mena of his own brain, and declares what enters into its forms, time, space, and causality, and what does not In this he is perfectly at home and speaks apodictically. In a like sense, then, the following table of the Prcedicabilia a priori of time, space, and matter is to be taken : —

ON KNOWLEDGE A PRIORI.

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PK^EDICABILIA A PRIORI.

Of Time.

(i) There is only one Time, and all different times are parts of it.

(2) Different times are not simultaneous but successive.

(3) Time cannot be thought away, but everything can be thought away from it.

(4) Time has three divisions, the past, the present, and the future, which constitute two directions and a centre of indifference.

(5) Time is infinitely divisible.

(6) Time is homogeneous and a Continuum, i.e., no one of its parts is different from the rest, nor separated from it by anything that is not time.

(7) Time has no beginning and no end, but all beginning and end is in it.

(8) By reason of time we count.

(9) Rhythm is only in time.

(10) We know the laws of time a priori.

Of Space.

(1) There is only one Space, and all different spaces are parts of it.

(2) Different spaces are not successive but simultaneous.

(3) Space cannot be thought away, but everything can be thought away from it.

(4) Space has three dimensions — height, breadth, and length.

(5) Space is infinitely divisible.

(6) Space is homogeneous and a Continuum, i.e., no one of its parts is different from the rest, nor separated from it by anything that is not space.

(7) Space has no limits, but all limits are in it.

(8) By reason of space we measure.

(9) Symmetry is only in space.

(10) We know the laws of space a priori.

Of Matter.

(1) There is only one Matter, and all different materials are different states of matter ; as such it is called Substance.

(2) Different matters (materials) are not so through substance but through accidents.

(3) Annihilation of matter is inconceivable, but annihilation of all its forms and qualities is conceivable.