The Will to Power · Friedrich Wilhelm Nietzsche
516.
We are not able to affirm and to deny one and the same thing: that is a principle of subjective experience--which is not in the least "necessary," _but only a sign of inability._ If, according to Aristotle, the _principium contradictionis_ is the most certain of all principles; if it is the most ultimate of all, and the basis of every demonstration; if the principle of every other axiom lie within it: then one should analyse it all the more severely, in order to discover how many assumptions _already lie_ at its root. It either assumes something concerning reality and Being, as if these had become known in some other sphere--that is to say, as if it were _impossible_ to ascribe the opposite attributes to it; or the proposition means: that the opposites _should_ not be ascribed to it. In that case, logic would be an imperative, _not_ directed at the knowledge of truth, but at the adjusting and fixing of a world _which must seem true to us._ In short, the question is a debatable one: are the axioms of logic adequate to reality, or are they measures and means by which alone we can, _create_ realities, or the concept "reality"?... In order to affirm the first alternative, however, one would, as we have seen, require a previous knowledge of Being; which is certainly not the case. The proposition therefore contains no _criterion of truth,_ but an _imperative_ concerning that which _should_ pass as true.
Supposing there were no such thing as A identical with itself, as every logical (and mathematical) proposition presupposes, and that A is in itself an _appearance,_ then logic would have a mere world _of appearance_ as its first condition. As a matter of fact, we believe in that proposition, under the influence of an endless empiricism which seems to _confirm_ it every minute. The "thing"--that is the real substratum of A; _our belief in things_ is the first condition of our faith in logic. The A in logic is, like the atom, a reconstruction of the thing.... By not understanding this, and by making logic into a criterion of _real being,_ we are already on the road to the classification of all those hypostases, substance, attribute, object, subject, action, etc., as realities--that is to say, the conception of a metaphysical world or a "real world" (--_this is, however, once more the world of appearance..._). The primitive acts of thought, affirmation, and negation, the holding of a thing for true, and the holding of a thing for not true,--in so far as they do not only presuppose a mere habit, but the very _right_ to postulate truth or untruth at all,--are already dominated by a belief, _that there is such a thing as knowledge for us,_ and _that judgments can really hit the truth:_ in short, logic never doubts that it is able to pronounce something concerning truth in itself (--that is to say, that to the thing which is in itself true, no opposite attributes _can_ be ascribed).
In this belief there _reigns_ the sensual and coarse prejudice that our sensations teach us _truths_ concerning things,--that I cannot at the same moment of time say of one and the same thing that it is _hard_ and _soft._ (The instinctive proof, "I cannot have two opposite sensations at once," is quite _coarse_ and _false_.) That all contradiction in concepts should be forbidden, is the result of a belief, that we _are able_ to form concepts, that a concept not only characterises but also _holds_ the essence of a thing.... As a matter of fact, logic (like geometry and arithmetic) only holds good of _assumed existences which we have created._ Logic is _the attempt on our part to understand the actual world according to a scheme of Being devised by ourselves; or, more exactly, it is our attempt at making the actual world more calculable and more susceptible to formulation, for our own purposes...._
Text from Project Gutenberg, public domain in the United States.