"The arch fountain of the human spirit," says Dittes, "is perception.... Whether perception as such discloses to us the true nature of things, or whether it makes us familiar only with their phenomena, this is not to be discussed by logic." The practical pedagogue who confines himself to the education of children's brains or who wishes at most to influence such teachers as educate children's brains, is quite right in being satisfied with the old traditional Aristotlean logic. But in the school of the human race, this logic has not been sufficient. For this reason the philosophers have broached the question whether perception, "the arch fountain of the human spirit," is a true or a deceptive fountain. The product of the philosophical investigation which we here offer amounts to the declaration that the logicians are greatly mistaken about the "arch fountain." It is a cardinal error of ancient logic to regard perception as the ultimate source from which the human mind dips its knowledge. It is nature which is the ultimate source, and our perception is but the mediator of understanding. And its product, recognized truth, is not truth itself, but merely a formal picture of it. Universal nature is the arch fountain, is the eternal and imperishable truth itself, and our perception, like every other part of universal existence, is only an attribute, a particle of absolute nature. The human mind, with whose nature logic is dealing, is no more an independent thing than any other, but simply a phenomenon, a reflex or predicate of nature.
To confound true perceptions or perceived truths with general truth, with the non plus ultra of all truths, is equivalent to regarding a sparrow as the bird in general, or a period of civilization as civilization itself, which would mean the closing of the door to all further development.
Modern philosophy, beginning with Bacon of Verulam and closing with Hegel, carries on a constant struggle with the Aristotlean logic. The product of this struggle, the outcome of philosophy, does not deny the old rules of traditional logic, but adds a new and decidedly higher circle of logical perception to the former ones. For the sake of better understanding it may be well to give to this circle a special title, the special name of "theory of understanding," which is sometimes called "dialectics."
In order to demonstrate the essential contents of this philosophical product by an investigation of the fundamental laws of traditional logic and to explain it thereby, I refer once more to the teacher of elementary logic, Dittes.
Under the caption of "Principles of Judgment" he teaches: "Since judging, like all thinking, aims at the perception of truth, the rules have been sought after by which this purpose might be accomplished. As universally applicable rules, as principles or laws of thought, the following four have been named:
(1) The law of uniformity (identity).
(2) The law of contradiction.
(3) The law of the excluded third.
(4) The law of adequate cause."
So much scholastic talk has been indulged in over these four "principles," that I can hardly bring myself to discuss them further. But since my purpose, the demonstration of the positive outcome of philosophy, consists in throwing a new light on the logic contained in these four so-called principles or laws, I am compelled to lay bare their inmost kernel.
The first principle, then, declares that A is A, or to speak mathematically, every quantity is equal to itself. In plain English: a thing is what it is; no thing is what it is not. "Characters which are excluded by any conception must not be attributed to it." The square is excluded from the conception of a circle, therefore the predicate "square" must not be given to a circle. For the same reason a straight line must not be crooked, and a lie must not be true.
Now this so-called law of thought may be well enough for household use, where nothing but known quantities are under consideration. A thing is what it is. Right is not left and one hundred is not one thousand. Whoever is named Peter or Paul remains Peter or Paul all his life. This, I say, is all right for household use.
But when we consider matters from the wider point of view of cosmic universal life, then this famous law of thought proves to be nothing but an expedient in logic which is not adequate to the nature of things, but merely a means of mutual understanding for us human beings. Hence the left bank of the Rhine is not the right, because we have agreed that in naming the banks of a river we will turn our backs to the source and our faces to the mouth of the river and then designate the banks as right and left. Such a way of distinguishing, thinking, and judging is good and practical, so long as this narrow standpoint is accompanied by the consciousness of its narrowness. Hitherto this has not been the case. This determined logic has overlooked that the perception which is produced by its rules is not truth, not the real world, but only gives an ideal, more or less accurate, reflection of it. Peter and Paul, who according to the law of identity are the same all their lives, are in fact different fellows every minute and every day of their lives, and all things of this world are, like those two, not constant, but very variable quantities. The mathematical points, the straight lines, the round circles, are ideals. In reality every point has a certain dimension, every straight line, when seen through a magnifying glass, is full of many crooked turns, and even the roundest circle, according to the mathematicians, consists of an infinite number of straight lines.