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

Since necessity is the same thing as following from given grounds, it must appear in a special way in the case of every form of the principle of sufficient reason, and also have its opposite in the possibility and impossibility which always arises only through the application of the abstract reflection of the reason to the object Therefore the four kinds of necessity mentioned above stand opposed to as many kinds of impossibility, physical, logical, mathe matical, and practical. It may further be remarked that if one remains entirely within the province of abstract concepts, possibility is always connected with the more general, and necessity with the more limited concept ; for example, " An animal may be a bird, a fish, an amphibious creature, &c." " A nightingale must be a bird, a bird must be an animal, an animal must be an organism, an organism. must be a body." This is because logical necessity, the expression of which is the syllogism, proceeds from the general to the particular, and never conversely. In the concrete world of nature (ideas of the first class), on the j contrary, everything is really necessary through the law of causality ; only added reflection can conceive it as also contingent, comparing it with that which is not its cause, and also as merely and purely actual, by disregarding all causal connection. Only in this class of ideas does the conception of the actual properly occur, as is also shown by the derivation of the word from the conception of causality. In the third class of ideas, that of pure mathematical perception or intuition, if we confine ourselves strictly to it, there is only necessity. Possibility occurs here also only

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through relation to the concepts of reflection : for example, " A triangle may be right-angled, obtuse-angled, or equiangular ; its three angles must be equal to two right- angles." Thus here we only arrive at the possible through the transition from the perceptible to the abstract

After this exposition, which presupposes the recollection of what was said both in the essay on the principle of sufficient reason and in the first book of the present work, there will, it is hoped, be no further doubt as to the true and very heterogeneous source of those forms which the table of judgments lays before us, nor as to the inadmissibility and utter groundlessness of the assumption of twelve special functions of the understanding for the explanation of them. The latter point is also supported by a number of special circumstances very easily noted. Thus, for example, it requires great love of symmetry and much trust in a clue derived from it, to lead one to assume that an affirmative, a categorical, and an assertatory judgment are three such different things that they justify the assumption of an entirely special function of the understanding for each of them.

Kant himself betrays his consciousness of the untenable nature of his doctrine of the categories by the fact that in the third chapter of the Analytic of Principles (phenomena et noumena) several long passages of the first edition (p. 241, 242, 244-246, 248-253) are omitted in the second — passages which displayed the weakness of that doctrine too openly. So, for example, he says there (p. 241) that he has not defined the individual categories, because he could not define them even if he had wished to do so, inasmuch as they were susceptible of no definition. In saying this he forgot that at p. 82 of the same first edition he had said : " I purposely dispense with the definition of the categories although I may be in possession of it." This then was, sit venia verbo, wind. But this last passage he has allowed to stand. And so all those passages wisely omitted afterwards betray the fact thatp. 76 nothing distinct can be thought in connection with the categories, and this whole doctrine stands upon a weak foundation.