Page:The World as Will and Idea - Schopenhauer, tr. Haldane and Kemp - Volume 2.djvu/213

Rh more or fewer than seven cervical vertebra, or horns and upper incisors in the same animal. But only logical impossibility is a contradiction, not physical, and just as little mathemathical. Equilateral and rectangled do not contradict each other (they coexist in the square), nor does either of them contradict a triangle. Therefore the incompatibility of the above conceptions can never be known by mere thinking, but is only discovered by perception – merely mental perception, however, which requires no experience, no real object. We should also refer here to the proposition of Giordano Bruno, which is also found in Aristotle: "An infinitely large body is necessarily immovable" – a proposition which cannot rest either upon experience or upon the principle of contradiction, since it speaks of things which cannot occur in any experience, and the conceptions "infinitely large" and "movable" do not contradict each other; but it is only pure perception that informs us that motion demands a space outside the body, while its infinite size leaves no space over. Suppose, now, it should be objected to the first mathematical example that it is only a question of how complete a conception of a triangle the person judging has: if the conception is quite complete it will also contain the impossibility of a triangle being rectangular and also equilateral. The answer to this is: assume that his conception is not so complete, yet without recourse to experience he can, by the mere construction of the triangle in his imagination, extend his conception of it and convince himself for ever of the impossibility of this combination of these conceptions. This process, however, is a synthetic judgment a priori, that is, a judgment through which, independently of all experience, and yet with validity for all experience, we form and perfect our conceptions. For, in general, whether a given judgment is analytical or synthetical can only be determined in the particular case according as