beyond their immediate statement. If A is either B or not B, and it is shown not to be B, it is left uncertain what A may be. The class of propositions referred to do more than this, inasmuch as they present alternative conceptions, mutually exhaustive, each the privative of the other. Of these two contraries, the one always evokes the other; neither can be thought except in relation to the other. They do not arise from the dichotomic process of classification, but from the polar relations of things. Their relation is not in the mind but in themselves, a real externality. The distinction between such as spring from the former and the latter is the most important question in philosophy.
To illustrate by examples, we familiarly speak of heat and cold, and to say a body is not hot is as much as to say it is cold. But every physicist knows that cold is merely a diminution of heat, not a distinct form of force. The absolute zero may be reached by the abstraction of all heat, and then the cold cannot increase. So, life and death are not true contraries, for the latter is not anything real but a mere privative, a quantitative diminution of the former, growing less to an absolute zero where it is wholly lost.
Thus it is easy to see that the Unconditioned exists only as a part of the idea of the Conditioned, the Unknowable as the foil of the Knowable; and the erecting of these mere privatives, these negatives, these shadows, into substances and realities, and then setting them up as impassable barriers to human thought, is one of the worst pieces of work that metaphysics has been guilty of.
The like does not hold in true contrasts. Each of them has an existence as a positive,and is never lost in a zero of the other. The one is always thought in relation to the other. Examples of these are subject and object, absolute and relative, mind and matter, person and consciousness, time and space. When any one of these is thought, the other is assumed. It is vain to attempt their separation. Thus those philosophers who assert that all knowledge is relative, are forced to maintain this assertion, to wit, All knowledge is relative, is nevertheless absolute, and thus they falsify their own position. So also, those others who say all mind is a property of matter, assume in this sentence the reality of an idea apart from matter. Some have argued that space and time can be conceived independently of each other; but their experiments to show it do not bear repetition.
All true contraries are universals. A universal concept is one of “maximum extension,” as logicians say, that is, it is without limit. The logical limitation of such a universal is not its negation, but its contrary, which is itself also a universal. The synthesis of the two can be in theory only, yet yields a real product. To illustrate this by a geometrical example, a straight line produced indefinitely is, logically considered, a universal. Its antithesis or true contrary is not a crooked line, as might be supposed, but the straight line which runs at right angles to it. Their synthesis is not the line which bisects their angle but that formed by these contraries continually uniting, that is, the arc of a circle, the genesis of which is theoretically the union of two such lines. Again, time can only be measured by space, space by time; they are true universals and contraries; their synthesis is motion, a conception which requires them both and is completed by them. Or again, the philosophical extremes of downright materialism and idealism are each wholly true, yet but half the truth. The insoluble enigmas that either meets in standing alone are kindred to those which puzzled the old philosophers in the sophisms relating to motion, as, for instance, that as a body cannot move where it is and still less where it is not, therefore it cannot move at all. Motion must recognise both time and space to be comprehensible. As a true contrary constantly implies the existence of its opposite, we cannot take a step in right reasoning without a full recognition of both.
This relation of contraries to the higher conception which logically must include them is one of the well-worn problems of the higher metaphysics.
The proper explanation would seem to be, as suggested above, that the synthesis of contraries is capable of formal expression only, but not of interpretation. In pursuing the search for their union we pass into a realm of thought not unlike that of the mathematician when he deals with hypothetical quantities, those which can only be expressed in symbols—, √1 for example—but uses them to good purpose in reaching real results. The law does not fail, but its operations can no longer be expressed under material images. They are symbolic and for speculative thought alone, though pregnant with practical applications.
As I have hinted, in all real contraries it is theoretically possible to accept either the one or the other. As in mathematics, all motion can be expressed either under formulas of initial motion (mechanics), or of continuous motion (kinematics), or as all force can be expressed as either static or as dynamic force; in either case the other form assuming a merely hypothetical or negative position; so the logic of quality is competent to represent all existence as ideal or as material, all truth as absolute or all as relative, or even to express the universe in formulæ of being or of not-being. This perhaps was what Heraclitus meant when he propounded his dark saying: “All things are and are not.” He added that “All is not,” is truer than “All is.” Previous to his day, Buddha Sakyamuni had said: “He who has risen to the perception of the not-Being, to the Unconditioned, the Universal, his path is difficult to understand, like the flight of birds in the air.”37–1 Perhaps even he learned his lore from some older song of the Veda, one of which ends, “Thus have the sages, meditating in their souls, explained away the fetters of being by the not-being.”37–2 The not-being, as alone free from space and time, impressed these sages as the more real of the two, the only absolute.
The error of assigning to the one universal a preponderance over the other arose from the easy confusion of pure with applied thought. The synthesis of contraries exists in the formal law alone, and this is difficult to keep before the mind. In concrete displays they are forever incommensurate. One seems to exclude the other. To see them correctly we must there treat them as alternates. We may be competent, for instance, to explain all phenomena of mind by organic processes; and equally competent to explain all organism as effects of mind; but we must never suppose an immediate identity of the two; this is only to be found in the formal law common to both; still less should we deny the reality of either. Each exhausts the universe; but at every step each presupposes the other; their synthesis is life, a concept hopelessly puzzling unless regarded in all its possible displays as made up of both.
This indicates also the limits of explanation. By no means every man’s reason knows when it has had enough. The less it is developed, the further is it from such knowledge. This is plainly seen in children, who often do not rest satisfied with a really satisfactory explanation. It is of first importance to be able to recognize what is a good reason.
I may first say what it is not. It is not a cause. This is nothing more than a prior arrangement of the effect; the reason for an occurrence is never assigned by showing its cause. Nor is it a caprice, that is, motiveless volition, or will as a motor. In this sense, the “will of God” is no good reason for an occurrence. Nor is it fate, or physical necessity. This is denying there is any explanation to give.
The reason can only be satisfied with an aliment consubstantial with itself. Nothing material like cause, nor anything incomprehensible like caprice, meets its demands. Reason is allied to order, system and purpose above all things. That which most completely answers to these will alone satisfy its requirements. They are for an ideal of order. Their complete satisfaction is obtained in universal types and measures, pure abstractions, which are not and cannot be real. The formal law is the limit of explanation of phenomena, beyond which a sound intellect will ask nothing. It fulfils all the requirements of reason, and leaves nothing to be desired.
Those philosophers, such as Herbert Spencer, who teach that there is some incogitable “nature” of something which is the immanent “cause” of phenomena, delude themselves with words. The history and the laws of a phenomenon are its nature, and there is no chimerical something beyond them. They are exhaustive. They fully answer
