Page:The World as Will and Idea - Schopenhauer, tr. Haldane and Kemp - Volume 2.djvu/275

(Greek characters)" (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 Infinito 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 De Cælo, 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 defined 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 therefore 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 no 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