A COMPENDIOUS CLASSIFICATION OF THE SCIENCES. 23 in the above diagram. The additional points there figured will be explained in the sequel. The problem now before us is to show how the determina- tions of this series are consequent one on another. Begin- ning with Formal Logic, we may simply posit, as first principles of the science, the Laws of Thought, which, though disclosed by metaphysical investigation, can be stated with perfect intelligibility to those who have not gone through the dialectical process that establishes them. For scientific purposes, it is sufficient that they should be found to be applicable tests of formally valid thought. Nor is the meta- physical problem ever raised by their breaking down. It arises from the theoretical need felt of completing the circle. The circle becomes formally complete when the Theory of Knowledge restores to us with confirmation the principles on which we have hitherto implicitly or explicitly proceeded. Historically, it may be noted, Aristotle arrived at the Laws of Contradiction and of Excluded Middle in his Meta- physics. These and the Law of Identity I hold to be laws of thought, not of things. To take specially the Law of Contradiction, which, according to Aristotle's exact way of putting it, asserts that A cannot be not-A at the same time and in the same relation. The law tells us that thought, if it would be form- ally valid, must not contradict itself ; but it does not enable us to assert a single materially new proposition. Given a subjective world of concepts, we can maintain order among them by this and the other laws ; but we cannot make any assertion that is not implied in what we have already said. Thus, unless we have, beyond the laws of thought, some general proposition or propositions about experience, we can have no science of nature. The laws of thought by them- selves do not allow us to deny, a priori, that what objectively exists is a Heraclitean flux without the reason which Hera- clitus supposed to underlie it, and without the equivalence of measure which he held to be the rule of its transforma- tions. Let us imagine ourselves endowed with the laws of thought and presented with such a flux. The Law of Contradiction is evidently of no avail if nothing remains itself for more than a moment and if there is no constant relation of it to anything else. It is true that we are still obliged to treat the momentary existence of A as inconsistent with its non-existence at that moment ; but, if that is all, there can be no system of experiential knowledge. The formal law does not entitle us to deny the complete absence of perdurability or uniformity. Thus, on the one side, it is
