On the theory of the infinite in modern thought

by Eleanor F. Jourdain

W. James’s words ring hollow when he attempts to dissociate such a conception from the reality of which it is the crown and inclusive symbol, and type and essence. “I personally,” he says, “give up the Absolute. I find it entangles me in metaphysical paradoxes that are inacceptable.” He allows that there may be a God, though limited in power and goodness, “one helper amongst others, primus inter pares in the midst of all the shapers of the great world’s fate.” In such a system, as H. Jones has pointed out, “there is neither in the universe nor in God any principle to inspire or guide, or in any way to bring about the amelioration desired. The process is guided by no end. The universe begins by being an aggregate of accidents, pluralistic, discontinuous, irrational, and, of itself, cannot become otherwise. There is nothing actual within to change its character.… God is himself finite, helpless to bring about this great change, a part, and no more, of a universe broken in fragments.”

Another form, and a very scholarly one, of the argument against the existence of an Absolute has been stated by Bax in the “Roots of Reality.” He appears to have reached the conclusion that the telos, the goal of human thought, is not an Absolute involving any notion of fixity, but that it may be conceived of as a “moving synthesis.” He argues that everything of which we are conscious in the universe is seen against a background which itself moves, and is only realisable or distinguishable if it shifts upon something relatively motionless behind it. He concludes, therefore, that by analogy there is no Absolute, since what we perceive always implies something against which we perceive it; thus that there is no goal by which and at which the spirit of man can find rest. On his theory we could never claim to reach the conception of an Absolute, though he admits the progressive character of human thought, and the increasing reach, lucidity, and depth of the human mind. The true answer to this argument is that it proves exactly what it sets out to disprove. As it is acknowledged that only the permanent or the relatively permanent can produce the phenomena of change, so the appearance of the goal of thought as a moving synthesis would presuppose an Absolute as a ground reality.[19]

If in truth we were able to apprehend entirely the source of all life and the background of all experience, we might say that it did not exist for us as an Absolute, but the fact that whatever we perceive postulates an unending series behind it, carries with it the proof of an Absolute Infinite. (This conclusion is led up to by the mathematician’s idea of the series of all finite and transfinite ordinal numbers.) Some part of this argument has been already suggested in Ormond’s “Foundations of Knowledge,” and so far was used by Mr. Illingworth in the “Doctrine of the Trinity.”[20]

“From a deeper metaphysical point of view it is the concept of evolution itself that must submit to the determination of knowledge, for it will be found that in so far as it becomes epistemologically necessary to ground relative processes in an Absolute experience, just so far will it become necessary also to connect the evolutionary aspect of the world itself with a ground reality that is stable, and involves the flux of change only as transcending and including it.”[21]

The further answer that any judgment, even the Pragmatist’s “judgment of value,” implies an Absolute has been stated in his Oxford Lectures[22] by Professor H. Jones.

(b) The next point we should like to work out is the relation of fact to law. The Pragmatist denies scientific law and also logic, and makes his appeal to facts. No conclusion can be drawn from that denial except by the use of logic itself. If he consistently denied logic, his position would be unassailable by logic, but he uses the method he denies, and is thus open to attack. On the subject of the Laws of Science the Pragmatist points out truly that there is no actual continuity between a fact and a law. But laws are concepts, the result of mental activities; they are themselves subject to the laws of logic. “They were means, and you make them ends,” complains the Pragmatist. That is just what nature herself does. She perfects means, such as the means of supporting life, and then these become ends. Language, again, is at first a means, and then becomes an end. So does any science change its character to the onlooker. A law, too, though it generalises facts, is a limit on absolute generalisation. It thus stands midway between the abstraction and the fact. The Pragmatist, however, opposes to law what he calls a new fact—​what should rather be called a hypothesis. He asserts that in every event, action, experiment, there is a margin unseen and unrecognised by us; that at every moment, therefore, the unknown, the unexpected, may take shape and voice and denounce all our careful and reasoned conclusions. “Why should the sun rise to-morrow because he has risen to-day and yesterday?” asks the Pragmatist. “We are making an enormous assumption,” he says, “in claiming the uniformity of Nature and the principle of causality.” The Idealist answers that the Pragmatist makes a larger assumption in doubting the truth of the principles, which though relative and not absolute, still do work out in practice, than the Idealist does in his act of faith. In fact, the act of faith is rational as well as natural; it is the act of doubting that is in this case due to a mere scholastic quibble. It is the Idealist and not the Pragmatist who makes his appeal to the truth of facts. Each day that the sun goes on rising finds the Idealist in a better philosophical position and the Pragmatist in a worse, except on the assumption that the link between man and the external world is a false imagination. Let us emphasise:—It is the Pragmatist who quibbles with logic, and the Idealist who appeals to facts.

(c) Now there are certain facts and certain deductions from facts, well known to mathematicians, which we should like to quote here as having a bearing on the theory of the Absolute, because they deal with aspects of Infinity, and mark a connection between the world as we know it and the concepts of the philosopher. All have the support of science, and furnish the Idealist philosopher with examples which support his theories, and strengthen his position in the face of the Pragmatist attack. They have to do with the theory of Infinity as shown in:—

I. The Indefinite Regress.

II. Infinite series.

III. Dimensions in space and time.