Immanuel Kant's Critique of Pure Reason — trans. F. Max Müller

In mathematics such subreptions are impos- [p. 792] sible ; and it is true, therefore, that the apagogical proof has its true place there. In natural science, in which everything is based on empirical intuitions, that kind of subreption can generally be guarded against by a repeated comparison of observations ; but even thus, this mode of proof is of little value there. The transcendental endeavours of pure reason, however, are all made within the very sphere of dialectical illusion, where what is subjective presents itself, nay, forces itself upon reason in its premisses as objective. Here, therefore, it can never be allowed, with reference to synthetical propositions, to justify one's assertions by refuting their opposite. For, either this refutation may be nothing but the mere representation of the conflict of the opposite opinion with the subjective conditions under which our reason could alone comprehend it, and this would be of no avail for rejecting the proposition itself, — (thus we see, for instance, that the unconditioned necessity of the existence of a Being cannot possibly be comprehended by us, which sitbjectively bars every speculative proof of a necessary Supreme Being,

636 Discipline of Pure Reason 2but by no means, the possibility of such a Being by itself), — or, on the other hand, it may be that both the affirmative and the negative party have been deceived by the transcendental illusion, and base their arguments on an impossible concept of an object.

In that case the rule applies, non cutis nulla sunt praedicata, that is, [p. 793] everything that has been asserted with regard to an object, whether affirmatively or negatively, is wrong, and we cannot therefore arrive apagogically at the knowledge of truth by the refutation of its opposite.

If, for example, we assume that the world of sense is given by itself in its totality, it is wrong to conclude that it must be either infinite in space, or finite and limited ; for either is wrong, because phenomena (as mere representations) which nevertheless are to be things by thcjns elves (as objects) are something impossible, and the infinitude of this imaginary whole, though it might be unconditioned, would (because everything in phenomena is conditioned) contradict that very unconditioned quantity which is presupposed in its concept.