The subjective constraint which prevents one from contradicting here, is a biological constraint: the instinct which makes us see the utility of concluding as we do conclude, is in our blood, we are almost this instinct.... But what simplicity it is to attempt to derive from this fact that we possess an absolute truth! ... The inability to contradict anything is a proof of impotence but not of "truth."
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....