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

1 That the three-toed sloth has yet Owen still states this, " Osttologit nine must be regarded as a mistake ; Comp.," p. 405.

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the conception of the subject in the mind of the person judging is more or less complete. The conception "cat" contains in the mind of a Cuvier a hundred times more than in that of his servant; therefore the same judgments about it will be synthetical for the latter, and only analytical for the former. But if we take the conceptions objectively, and now wish to decide whether a given judgment is analytical or synthetical, we must change the predicate into its contradictory opposite, and apply this to the subject without a cupola. If this gives a contradictio in adjecto, then the judgment was analytical ; otherwise it was synthetical.

That Arithmetic rests on the pure intuition or perception of time is not so evident as that Geometry is based upon that of space.1 It can be proved, however, in the following manner. All counting consists in the repeated affirmation of unity. Only for the purpose of always knowing how often we have already affirmed unity do we mark it each time with another word : these are the numerals. Now repetition is only possible through succession. But succession, that is, being after one another, depends directly upon the intuition or perception of time. It is a conception which can only be understood by means of this ;

1 This, however, does not excuse the end to condemn without cerea professor of philosophy who, sitting mony the fundamental teaching of in Kant's chair, expresses himself a great genius in a tone of peremptory thus : "That mathematics as such decision, just as if it were Hegelian contains arithmetic and geometry is foolery. We must not, however, fail correct. It is incorrect, however, to notice that these little people to conceive arithmetic as the science struggle to escape from the track of of time, really for no other reason great thinkers. They would therethan to give a pendant (sic) to fore have done better not to attack geometry as the science of space" Kant, but to content themselves (Rosenkranz in the " Dculschen with giving their public full details Museum," 1857, May 14, No. 20). about God, the soul, the actual freeThiB is the fruit of Hegelism. If dom of the will, and whatever bathe mind is once thoroughly de- longs to that sort of thing, and then bauched with its senseless jargon, to have indulged in a private luxury serious Kantian philosophy will no in their dark back-shop, the philolonger enter it. The audacity to sophical journal ; there they may talk at random about what one does do whatever they like without c> nnot understand has been inherited straint. for no one sees it. from the master, and one comes in

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and thus counting also is only possible by means of time. This dependence of all counting upon time is also betrayed by the fact that in all languages multiplication is expressed by "time," thus by a time- concept : sexies, e£a/«?, sixfois, sex mal. But simple counting is already a multiplication by one, and for this reason in Pestalozzi's educational establishment the children are always made to multiply thus : " Two times two is four times one." Aristotle already recognised the close relationship of number and time, and expounded it in the fourteenth chapter of the fourth book of the " Physics." Time is for him " the number of motion " (" 6 xpovo? apiO/uo? ea-rc tcw7/o-ecD<?"). He very profoundly suggests the question whether time could be if the soul were riot, and answers it in the negative. If arithmetic had not this pure intuition or perception of time at its foundation, it would be no science a priori, and therefore its propositions would not have infallible certainty.

Although time, like space, is the form of knowledge of the subject, yet, just like space, it presents itself as independent of the subject and completely objective. Against our will, or without our knowledge, it goes fast or slow. We ask what o'clock it is ; we investigate time, as if it were something quite objective. And what is this objective existence ? Not the progress of the stars, or of the clocks, which merely serve to measure the course of time itself, but it is something different from all things, and yet, like them, independent of our will and knowledge. It exists only in the heads of percipient beings, but the uniformity of its course and its independence of the will give it the authority of objectivity.