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

(4) Matter exists, i.e., acts in all the dimensions of space and throughout the whole length of time, and thus these two are united and thereby filled. In this consists the true nature of matter ; thus it is through and through causality.

(5) Matter is infinitely divisible.

(6) Matter is homogeneous and a Continuum, i.e., it does not consist of originally different (homoiomeria) or originally separated parts (atoms) ; it is therefore not composed of parts, which would necessarily be separated by something that was not matter.

(7) Matter has no origin and no end, but all coming into being and passing away are in it.

(8) By reason of matter we weigh.

(9) Equilibrium is only in matter.

(10) We know the laws of the substance of all accidents a priori.

p. 222

FIRST BOOK. CHAPTER IV.

Of Time.

Of Space.

(n) Time can be perceived a priori, although only in the form of a line.

(12) Time has no permanence, but passes away as soon as it is there.

(13) Time never rests.

(14) Everything that exists in time has duration.

(15) Time has no duration, but all duration is in it, and is the persistence of what is permanent in contrast with its restless course.

(16) All motion is only possible in time.

(17) Velocity is, in equal spaces, in inverse proportion to the time.

(18) Time is not measurable directly through itself, but only indirectly through motion, which is in space and time together : thus the motion of the sun and of the clock measure time.

(19) Time is omnipresent. Every part of time is everywhere, i.e., in all space, at ouce.

Of Matter.

(n) Space is immediately perceptible a priori.

(12) Space can never pass away, but endures through all time.

(13) Space is immovable.

(14) Everything that exists in space has a position.

(15) Space has no motion, but all motion is in it, and it is the change of position of what is moved, in contrast with its uubroken rest.

(16) All motion is only possible in space.

(17) Velocity is, in equal times, in direct proportion to the space.

(18) Space is measurable directly through itself, and indirectly through motion, which is in time and space together : hence, for example, an hour's journey, and the distance of the fixed stars expressed as the travelling of light for so many years.

(19) Space is eternal. Every part of it exists always.

(n) Matter can only be thought a priori.

( 12) The accidents change ; the substance remains.

(13) Matter is indifferent to rest and motion ; i.e., it is originally disposed towards neither of the two.

(14) Everything material has the capacity for action.

(15) Matter is what is permanent in time and movable in space ; by the comparison of what rests wiih what is moved we measure duration.

(16) All motion is only possible to matter.

(17) The magnitude of the motion, the velocity being equal, is in direct geometrical proportion to the matter (mass).

(18) Matter as such (mass) is measurable, i.e., determinable as regards its quantity only indirectly, unly through the amount of the motion which it receives and imparts when it is re1 pelled or attracted.

(19) Matter is absolute. That is, it neither conies into being nor passes away, and thus its quantity cau neither be increased not diminished.

ON KNOWLEDGE A PRIORI.

p. 723

Of Time.

(20) In time taken by itself everything would be in succession.

(21) Time makes the change of accidents possible.

(22) Every part of time contains all parts of matter.

(23) Time is the principium in dividuationis.

(24) The now has no duration.

(25) Time in itself is empty and without properties.

(26) Every moment is conditioned by the preceding moment, and is only because the latter has ceased to be. (Principle of sufficient reason of existence in time. — See my essay on the principle of sufficient reason. )

(27) Time makes arithmetic possible.

(28) The simple element in arithmetic is unity.

Of Space.

(20) In space taken by itself everything would be simultaneous.

(21) Space makes the permanence of substance possible.

(22) No part of space contains the same matter as another.

(23) Space is the principium individuation is.

(24) The point has no extension.

(25) Space in itself is em pty and without properties.

(26) By the position of every limit in space with reference to any other limit, its position with reference to every possible limit is precisely determined. (Principle of sufficient reason of existence in space.)

(27) Space makes geometry possible.

(28) The simple element in geometry is the point.

Of Matter.

(20, 21) Matter unites the ceaseless flight of time with the rigid immobility of space ; therefore it is the permanent substance of the changing accidents. Causality determines this change for every place at every time, and thereby combines time and space, and constitutes the whole nature of matter.

(22) For matter is both permanent and impenetrable.

(23) Individuals are material.

(24) The atom has no reality.

(25) Matter in itself is without form and quality, and likewise inert, i.e., indifferent to rest or motion, thus without properties.