The World as Will and Idea, Vol. II — 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.
ness of such subsumption — a method whereby we can arrive by longer or shorter circuits at almost any result we choose to set before us as our goal. Hence this mere abstract reasoning differs only in degree from sophistication strictly so called. But sophistication is in the theoretical sphere exactly what chicanery i3 in the practical.
Yet even Plato himself has very frequently permitted such mere abstract reasoning; and Proclus, as we have already mentioned, has, after the manner of all imitators, carried this fault of his model much further. Dionysius the Areopagite, " Be Divinis Nominibus" is also strongly affected with this.
But even in the fragments of the Eleatic Melissus we already find distinct examples of such mere abstract reasoning (especially § 2-5 in Brandis' Comment. Eleat.) His procedure with the conceptions, which never touch the reality from which they have their content, but, moving in the atmosphere of abstact universality, pass away beyond it, resembles blows which never hit the mark.
A good pattern of such mere abstract reasoning is the " De Diis et Mundo " of the philosopher Sallustius Biichelchen ; especially chaps. 7, 12, and 17. But a perfect gem of philosophical mere abstract reasoning passing into decided sophistication is the following reasoning of the Platonist, Maximus of Tyre, which I shall quote, as it is short: ■ Every injustice is the taking away of a good.
There is no other good than virtue: but virtue cannot be taken away : thus it is not possible that the virtuous can suffer injustice from the wicked. It now remains either that no injustice can be suffered, or that it is suffered by the wicked from the wicked. But the wicked man possesses no good at all, for only virtue is a good ; therefore none can be taken from him. Thus he also can suffer no injustice. Thus injustice is an impossible thing.
The original, which is less concise through repetitions, runs thus : " ASitcia eari a<f>atpecri<; ayadoV to Be ayadov ti av €17) aWo 7] apenj ; — r) Se apery avaipaiperov. Ovk aSiKrjaerac TOivvv 6 ttjv apeTtjv e^top, rj ovk eariv aâiKia afyaipeoK ayaOov' ovBev yap ayaOov a<paiperov, ovB'xcnrofiXrjTov, ovB iXerov, ovBe Xrjiarov. Eiev ovv, ovB' aSi/ceircu 6 XPV°~- ros, ovB viro tov fioy^Orjpov avcKpctipero? yap. AenreTai toivvv 7) fjirjSeva aSi/ceicrdat, KaOaira%, r\ tov fio^Oijpov viro tov ofioiov' aX\a toj p.o^vP'P ovBevo? peTecrTiv ayaOov r) Be aBi/cia nv ayaOov acpaipeais' 6 Be fir) e^wv 6, tl a<paipeaOn, ovBe ei<? o, tl chiicqo-Or], e^ei" (Sermo 2).
I shall add further a modern example of such proofs from abstract conceptions, by means of which an obviously absurd proposition is set up as the truth, and I shall take it from the works of a great man, Giordano Bruno. In his book, "Del Infinite Universo e Mondi" (p. 87 of the edition of A. Wagner), he makes an Aristotelian prove (with the assistance and exaggeration of the passage of Aristotle's Be Ccelo, i.
5) that there can be no space beyond the world. The world is enclosed by the eight spheres of Aristotle, and beyond these there can be no space. For if beyond these there were still a body, it must either be simple or compound. It is now proved sophistically, from principles which are obviously begged, that no simple body could be there ; and therefore, also, no compound body, for it would necessarily be composed of simple ones.
Thus in general there can be no body there — but if not, then no space. For space is denned as " that in which bodies can be ; " and it has just been proved that no body can be there. Thus there is also there no space. This last is the final stroke of this proof from abstract conceptions.
It ultimately rests on the fact that the proposition, " Where no space is, there can be no body " is taken as a universal negative, and therePore converted simply, " Where no body can be there is no space. But the former proposition, when properly regarded, is a universal affirmative : " Everything that has 10 space has no body," thus it must not be converted simply.
Yet it is not every proof from abstract conceptions, with a conclusion which clearly contradicts perception (as here the finiteness of space), that can thus
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be referred to a logical error. For the sophistry does not always lie in the form, but often in the matter, in the premisses, and in the indefiniteness of the conceptions and their extension. "We find numerous examples of this in Spinoza, whose method indeed it is to prove from conceptions. See, for example, the miserable sophisms in his " Ethics," P. iv., prop. 29-31, by means of the ambiguity of the uncertain conceptions convenire and commune habere. Yet this does not prevent the neo-Spinozists of our own day from taking all that he has said for gospel. Of these the Hegelians, of whom there are actually still a few, are specially amusing on account of their traditional reverence for his principle, omnis determinatio est negatio, at which, according to the charlatan spirit of the school, they put on a face as if it was able to unhinge the world ; whereas it is of no use at all, for even the simplest can see for himself that if I limit anything by determinations, I thereby exclude and thus negate what lies beyond these limits.
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