The World as Will and Idea, Vol. II — Arthur Schopenhauer, trans. Haldane & Kemp
The text is shown on its own: no facing layer is held for this issue.
The translator’s English as printed (R. B. Haldane & J. Kemp). The original-language text is not held; names are romanised as the translator printed them.
The same law lies at the foundation of the theory of the lever and of the balance. For here also the smaller mass, on the longer arm of the lever or beam of the balance, has a greater velocity in falling; and multiplied by this it may be equal to, or indeed exceed, the quantity of motion or the momentum of the greater mass at the shorter arm of the lever. In the state of rest brought about by equilibrium this velocity exists merely in intention or virtually, potentid, not actu ; but it acts just as well as actu, which is very remarkable.
The following explanation will be more easily understood now that these truths have been called to mind.
The quantity of a given matter can only be estimated in general according to its force, and its force can only be known in its expression. Now when we are considering matter only as regards its quantity, not its quality, this expression can only be mechanical, i.e., it can only consist in motion which it imparts to other matter. For only in motion does the force of mutter become, so to speak, alive; hence the expression vis viva for the manifestation of force of matter in motion. Accordingly the only measure of the quantity of a given matter is the quantity of its motion, or its momentum. In this, however, if it is given, the quantity of matter still appears in oonON KNOWLEDGE A PRIORI. 227 junction and amalgamated with its other factor, velocity. Therefore if we want to know the quantity of matter (the mass) this other factor must be eliminated.
Now the velocity is known directly ; for it is ~ But the other factor, which remains when this is eliminated, can always be known only relatively in comparison with other masses, which again can only be known themselves by means of the quantity of their motion, or their momentum, thus in their combination with velocity.
"We must therefore compare one quantity of motion with the other, and then subtract the velocity from both, in order to see how much each of them owed to its mass. This is done by weighing the masses against each other, in which that quantity of motion is compared which, in each of the two masses, calls forth the attractive power of the earth that acts upon both only in proportion to their quantity. Therefore there are two kinds of weighing.
Either we impart to the two masses to be compared equal velocity, in order to find out which of the two now communicates motion to the other, thus itself has a greater quantity of motion, which, since the velocity is the same on both sides, is to be ascribed to the other factor of the quantity of motion or the momentum, thus to the mass (common balance).
Or we weigh, by investigating how much mart velocity the one mass must receive than the other has, in order to be equal to the latter in quantity of motion or momentum, and therefore allow no more motion to be communicated to itself by the other ; for then in proportion as its velocity must exceed that of the other, its mass, i.e., the quantity of its matter, is less than that of the other (steelyard).
This estimation of masses by weighing depends upon the favourable circumstance that the moving force, in itself, acts upon both quite equally, and each of the two is in a position to communicate to the other directly its surplus quantity of motion or momentum, so that it becomes visible.
The substance of these doctrines has long ago been expressed by Newton and Kant, but through the connection and the clearness of this exposition I believe I have made it more intelligible, so that that insight is possible for nil which I regarded as necessary for the justification of proposition No. 18.
( 228 )
Second fâatf.
THE DOCTRINE OF THE ABSTRACT IDEA, OR THINKING.
CHAPTER V.i
ON THE IRRATIONAL INTELLECT.
It must be possible to arrive at a complete knowledge of the consciousness of the brutes, for we can construct it by abstracting certain properties of our own consciousness. On the other hand, there enters into the consciousness of the brute instinct, which is much more developed in all of them than in man, and in some of them extends to what we call mechanical instinct.
The brutes have understanding without having reason, and therefore they have knowledge of perception but no abstract knowledge. They apprehend correctly, and also grasp the immediate causal connection, in the case of the higher species even through several links of its chain, but they do not, properly speaking, think. For they lack conceptions, that is, abstract ideas. The first consequence of this, however, is the want of a proper memory, which applies even to the most sagacious of the brutes, and it is just this which constitutes the principal difference between their consciousness and that of men. Perfect intelligence depends upon the distinct consciousness of thf
1 This chapter, along with the one which follows it, is connected wit! § 8 and 9 of the first book.
p. 229
No commentary for this page under the selected tracks.
There is commentary on page 1.