Mathematics, for all its applications in nature, is a part of ideal philosophy. It is logic applied to certain simple intuitions. These intuitions and many of their developments happen to appear in that efficacious and self-sustaining moiety of being which we call material; so that mathematics is per accidens the dialectical study of nature’s efficacious form. Its use and application in the world rather hide its dialectical principle. Mathematics owes its public success to the happy choice of a simple and widely diffused subject-matter; it owes its inner cogency, however, to its ideality and the merely adventitious application it has to existence. Mathematics has come to seem the type of good logic because it is an illustration of logic in a sphere so highly abstract in idea and so pervasive in sense as to be at once manageable and useful.
The delights and triumphs of mathematics ought, therefore, to be a great encouragement to ideal philosophy. If in a comparatively uninteresting field attention can find so many treasures of harmony and order, what beauties might it not discover in interpreting faithfully ideas nobler than extension and number, concretions closer to man’s spiritual life? But unfortunately the logic of values is subject to voluntary and involuntary confusions of so discouraging a nature that the flight of dialectic in that direction has never been long and, even when short, often disastrous. What is needed, as the example of mathematics shows, is a steadfast intent and an adventurous inquiry. It would not occur to a geometer to ask with trepidation what difference it would make to the Pythagorean proposition if the hypothenuse were said to be wise and good. Yet metaphysicians, confounding dialectic with physics and thereby corrupting both, will discuss for ever the difference it makes to substance whether you call it matter or God. Nevertheless, no decorative epithets can give substance any other attributes than those which it has; that is, other than the actual appearances that substance is needed to support. Similarly, neither mathematicians nor astronomers are exercised by the question whether [Greek: pi] created the ring of Saturn; yet naturalists and logicians have not rejected the analogous problem whether the good did or did not create the animals.
Practical rôle of dialectic.
So long as in using terms there is no fixed intent, no concretion in discourse with discernible predicates, controversy will rage as conceptions waver and will reach no valid result. But when the force of intellect, once having arrested an idea amid the flux of perceptions, avails to hold and examine that idea with perseverance, not only does a flash of light immediately cross the mind, but deeper and deeper vistas are opened there into ideal truth. The principle of dialectic is intelligence itself; and as no part of man’s economy is more vital than intelligence (since intelligence is what makes life aware of its destiny), so no part has a more delightful or exhilarating movement. To understand is pre-eminently to live, moving not by stimulation and external compulsion, but by inner direction and control. Dialectic is related to observation as art is to industry; it uses what the other furnishes; it is the fruition of experience. It is not an alternative to empirical pursuits but their perfection; for dialectic, like art, has no special or private subject-matter, nor any obligation to be useless. Its subject-matter is all things, and its function is to compare them in form and worth, giving the mind speculative dominion over them. It profits by the flux to fix its signification. This is precisely what mathematics does for the abstract form and multitude of sensible things; it is what dialectic might do everywhere, with the same incidental utility, if it could settle its own attitude and learn to make the passions steadfast and calm in the consciousness of their ultimate objects.
Hegel’s satire on dialectic.
The nature of dialectic might be curiously illustrated by reference to Hegel’s Logic; and though to approach the subject from Hegel’s satirical angle is not, perhaps, quite honest or fair, the method has a certain spice. Hegel, who despised mathematics, saw that in other departments the instability of men’s meanings defeated their desire to understand themselves. This insecurity in intent he found to be closely connected with change of situation, with the natural mutability of events and opinions in the world. Instead of showing, however, what inroads passion, oblivion, sophistry, and frivolity may make into dialectic, he bethought himself to represent all these incoherences, which are indeed significant of natural changes, as the march of dialectic itself, thus identified with the process of evolution and with natural law. The romance of an unstable and groping theology, full of warm intentions and impossible ideas, he took to be typical of all experience and of all science.
In that impressionable age any effect of chiaro-oscuro caught in the moonlight of history could find a philosopher to exalt it into the darkly luminous secret of the world. Hegel accordingly decreed that men’s habit of self-contradiction constituted their providential function, both in thought and in morals; and he devoted his Logic to showing how every idea they embraced (for he never treated an idea otherwise than as a creed), when pressed a little, turned into its opposite. This opposite after a while would fall back into something like the original illusion; whereupon a new change of insight would occur and a new thought would be accepted until, the landscape changing, attention would be attracted to a fresh aspect of the matter and conviction would wander into a new labyrinth of false steps and half-meanings. The sum total of these wanderings, when viewed from above, formed an interesting picture. A half-mystical, half-cynical reflection might take a certain pleasure in contemplating it; especially if, in memory of Calvin and the Stoics, this situation were called the expression of Absolute Reason and Divine Will.
We may think for a moment that we have grasped the elusive secret of this philosophy and that it is simply a Calvinism without Christianity, in which God’s glory consists in the damnation of quite all his creatures. Presently, however, the scene changes again, and we recognise that Creator and creation, ideal and process, are identical, so that the glory belongs to the very multitude that suffers. But finally, as we rub our eyes, the whole revelation collapses into a platitude, and we discover that this glory and this damnation were nothing but unctuous phrases for the vulgar flux of existence.
That nothing is what we mean by it is perfectly true when we in no case know what we mean. Thus a man who is a mystic by nature may very well become one by reflection also. Not knowing what he wants nor what he is, he may believe that every shift carries him nearer to perfection. A temperamental and quasi-religious thirst for inconclusiveness and room to move on lent a certain triumphant note to Hegel’s satire; he was sure it all culminated in something, and was not sure it did not culminate in himself. The system, however, as it might strike a less egotistical reader, is a long demonstration of man’s ineptitude and of nature’s contemptuous march over a path paved with good intentions. It is an idealism without respect for ideals; a system of dialectic in which a psychological flux (not, of course, psychological science, which would involve terms dialectically fixed and determinate) is made systematically to obliterate intended meanings.