One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.
To such questions no answer can be found in the laboratory.
But if a man is so obstinately teleological as to continue to ask what purpose is served by the Creator, it becomes obvious that his question becomes impious.
He who exercises his reason and cultivates it seems to be both in the best state of mind and most dear to the gods.
On questions of fact, we can appeal to science and scientific methods of observation; but on ultimate questions of ethics there seems to be nothing analogous. Yet, if this is really the case, ethical disputes resolve themselves into contests for power – including propaganda power.
On the one hand the purposes of the community are enforced upon the individual, and, on the other hand the individual, having acquired the habit of viewing his life as a whole, increasingly sacrifices his present to his future.
Plato is perpetually getting into trouble through not understanding relative terms. He thinks that if A is greater than B and less than C, then A is at once great and small, which seems to him a contradiction. Such troubles are among the infantile diseases of philosophy.
Frege’s work it followed that arithmetic, and pure mathematics generally, is nothing but a prolongation of deductive logic. This disproved Kant’s theory that arithmetical propositions are ‘synthetic’ and involve a reference to time. The development of pure mathematics from logic was set forth in detail in Principia Mathematica, by Whitehead and myself.
There is a certain tendency in our practical age to consider that it does not much matter whether religious teaching is true or not, since the important question is whether it is useful.
This piece of scientific history illustrates a general maxim: that any hypothesis, however absurd, may be useful in science, if it enables a discoverer to conceive things in a new way; but that, when it has served this purpose by luck, it is likely to become an obstacle to further advance.
I come now to Berkeley’s empirical arguments. To begin with, it is a sign of weakness to combine empirical and logical arguments, for the latter, if valid, make the former superfluous.1 If I am contending that a square cannot be round, I shall not appeal to the fact that no Square in any known city is round. But as we have rejected the logical arguments, it becomes necessary to consider the empirical arguments on their merits.
To Christians, Mohammedans, and Jews the most fundamental question involved in the truth of religion is the existence of God. In the days when religion was still triumphant the word “God” had a perfectly definite meaning; but as a result of the onslaughts of Rationalists the word has become paler and paler, until it is difficult to see what people mean when they assert that they believe in God.
The mental continuity of a person is a continuity of habit and memory: there was yesterday one person whose feelings I can remember, and that person I regard as myself of yesterday; but, in fact, myself of yesterday was only certain mental occurrences which are now remembered and are regarded as part of the person who now recollects them. All that constitutes a person is a series of experiences connected by memory and by certain similarities of the sort we call habit.
In this book chivalry receives its fair share of attention, not from the romantic point of view, but as an elaborate game which the upper classes invented to beguile the intolerable tedium of their lives. An essential part of chivalry was the curious courtly conception of love as something which it was pleasant to leave unsatisfied.
As civilization progresses, the earthly sanctions become more secure and the divine sanctions less so. People see more and more reason to think that if they steal they will be caught and less and less reason to think that if they are not caught God will nevertheless punish them. Even highly religious people in the present day hardly expect to go to Hell for stealing. They reflect that they can repent in time, and that in any case Hell is neither so certain nor so hot as it used to be.
Most people in civilized communities do not steal, and I think the usual motive is the great likelihood of punishment here on earth. This is borne out by the fact that in a mining camp during a gold rush, or in any such disorderly community, almost everybody steals.
Any system of morals which has a theological basis becomes one of the tools by which the holders of power preserve their authority and impair the intellectual vigor of the young.
Although personal survival after death is an illusion, there is nevertheless something in the human mind that is eternal.
The fanatic fails to recognise that the suppression of a real evil, if carried out too drastically, produces other evils which are even greater.
Those who affirm positively that God exists cannot avoid falling into an impiety. For if they say that God controls everything, they make Him the author of evil things; if, on the other hand, they say that He controls some things only, or that He controls nothing, they are compelled to make God either grudging or impotent, and to do that is quite obviously an impiety.
To formulate any satisfactory modern ethic of human relationships, it will be essential to recognize the necessary limitations of men’s power over the non-human environment, and the desirable limitations of their power over each other.