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.