The World as Will and Idea, Vol. I — Arthur Schopenhauer, trans. Haldane & Kemp
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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.
SO that in some there is more subordination, in others more co-ordination ; and in this respect, the former make greater claims upon the judgment, the latter upon the memory. It was known to the schoolmen,^ that, as the syllogism requires two premises, no science can proceed from a single first principle which cannot be the subject of further deduction, but must have several, at least two.
The specially classifying sciences: Zoology, Botany, and also Physics and Chemistry, inasmuch as they refer all inorganic action to a few fundamental forces, have most subordination ; history, on the other hand, has really none at all ; for the general in it consists merely in the survey of the principal periods, from which, however, the particular events cannot be deduced, and are only subordinated to them according to time, but according to the concept are co-ordinate with them.
Therefore, histoiy, strictly speaking, is certainly rational knowledge, but is not science. In mathematics, according to Euclid’s treatment, the axioms alone are indemonstrable first principles, and all demonstrations are In gradation strictly subordinated to them.
But this method of treatment is not essential to mathematics, and in fact each proposition introduces quite a new space construction, which in itself is independent of those which precede it, and indeed can be completely comprehended from itself, quite independently of them, in the pure intuition or perception of space, in which the most complicated construction is just as directly evident as the axiom ; but of this more fully hereafter.
Meanwhile every mathematical proposition remains always a universal truth, which is valid for innumerable particular cases ; and a graduated process from the simple to the complicated propositions which are to be deduced from them, is also essential to mathematics; therefore, in every respect mathematics is a science.
The completeness of a science as such, that is, in respect of form, consists in there being as much subordination and as little ^ Suarez, Disput. Metaphysics, disp. iii. sect. 3, tit. .3.
co-ordination of the principles as possible.
Scientific talent in general is, therefore, the faculty of subordinating the concept-spheres according to their different determinations, so that, as Plato repeatedly counsels, a science shall not be constituted by a general concept and an indefinite multiplicity immediately under it, but that knowledge shall descend by degrees from the general to the particular, through intermediate concepts and divisions, according to closer and closer definitions.
In Kantian language this is called satisfying equally the law of homogeneity and that of specification.
It arises from this peculiar nature of scientific completeness, that the aim of science is not greater certainty — for certainty may be possessed in just as high a degree by the most disconnected particular knowledge — but its aim is rather the facilitating of rational knowledge by means of its form, and the possibility of the completeness of rational knowledge which this form affords.
It is therefore a very prevalent but perverted opinion that the scientific character of knowledge consists in its greater certainty, and just as false is the conclusion following from this, that, strictly speaking, the only sciences are mathematics and logic, because only in them, on account of their purely a priori character, is there unassailable certainty of knowledge.
This advantage cannot he denied them, hut it gives them no special claim to be regarded as sciences ; for the special characteristic of science does not lie in certainty but in the systematic form of knowledge, based on the gradual descent from the general to the particular.
The process of knowledge from the general to the particular, which is peculiar to the sciences, involves the necessity that in the sciences much should be established by deduction from preceding propositions, that is to say, by demonstration ; and this has given rise to the old mistake that only what has been demonstrated is absolutely true, and that every truth requires a demonstration; whereas, on the contrary, every demonstration requires an undemonstrated truth, which ultimately supports it, or it may be, its own demonstration. Therefore a directly established truth is as much to be preferred to a truth established by demonstration as water from the spring is to water from the aqueduct.
Perception, partly pure a priori, as it forms the basis of mathematics, partly empirical a posterioi'i, as it forms the basis of aU the other sciences, is the source of all truth and the foundation of all science. (Logic alone is to be excepted, which is not founded upon perception but yet upon direct knowledge by the reason of its own laws.) Not the demonstrated judgments nor their demonstrations, but judgments which are created directly out of perception, and founded upon it rather than on any d(‘monstrations, are to science what the sun is to the world ; for all light proceeds from them, endTiglited by their light the others .giye light also.
To stablish the truth of such primary judgments directly from perception, to raise such strongliolds of science from the innumerable multitude of real objects, that is the work of the faculty of judyment, which consists in the power of rightly and accurately carrying over into abstract consciousness what is known in perception, and judgment is consequently the mediator between understanding and reason.
Only extraordinary and exceptional strength of judgment in the individual can actually advance science ; but every one who is possessed of a liealthy reason is able to deduce propositions from i)ropositions, to demonstrate, to draw conclusions.
To lay down and make permanent for reflection, in suitable concepts, what is known through perception, so that, on the one hand, wliat is common to many real objects is thought through OTie concept, and, on the other hand, their points of difference are each thought through one concept, so tliat the different shall be known and thought as different in spite of a partial agreement, and the identical shall be known and thought as identical in spite of a partial difference, all in accordance with the end and intention which in each case
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