Chapter IV. On Knowledge A Priori.
Project Gutenberg EPUB3 edition
Schopenhauer, Arthur, Haldane, R. B. Haldane (Richard Burdon Haldane), Viscount, and Kemp, J. (John)
(14) Everything material has the capacity for action.
(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.
(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 unbroken rest.
(15) Matter is what is permanent in time and movable in space; by the comparison of what rests with what is moved we measure duration.
(16) All motion is only possible in time.
(16) All motion is only possible in space.
(16) All motion is only possible to matter.
(17) Velocity is, in equal spaces, in inverse proportion to the time.
(17) Velocity is, in equal times, in direct proportion to the space.
(17) The magnitude of the motion, the velocity being equal, is in direct geometrical proportion to the matter (mass).
(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.
(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.
(18) Matter as such (mass) is measurable, i.e., determinable as regards its quantity only indirectly, only through the amount of the motion which it receives and imparts when it is repelled or attracted.
(19) Time is omnipresent. Every part of time is everywhere, i.e., in all space, at once.
(19) Space is eternal. Every part of it exists always.
(19) Matter is absolute. That is, it neither comes into being nor passes away, and thus its quantity can neither be increased nor diminished.
(20) In time taken by itself everything would be in succession.
(20) In space taken by itself everything would be simultaneous.
(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.
(21) Time makes the change of accidents possible.
(21) Space makes the permanence of substance possible.
(22) Every part of time contains all parts of matter.
(22) No part of space contains the same matter as another.
(22) For matter is both permanent and impenetrable.
(23) Time is the principium individuationis.
(23) Space is the principium individuationis.
(23) Individuals are material.
(24) The now has no duration.
(24) The point has no extension.
(24) The atom has no reality.
(25) Time in itself is empty and without properties.
(25) Space in itself is empty and without properties.
(25) Matter in itself is without form and quality, and likewise inert, i.e., indifferent to rest or motion, thus 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.)
(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.)
(26) Every change in matter can take place only on account of another change which preceded it; and therefore a first change, and thus also a first state of matter, is just as inconceivable as a beginning of time or a limit of space. (Principle of sufficient reason of becoming.)
(27) Time makes arithmetic possible.
(27) Space makes geometry possible.
(27) Matter, as that which is movable in space, makes phoronomy possible.
(28) The simple element in arithmetic is unity.