I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
"But," you might say, "none of this shakes my belief that 2 and 2 are 4." You are quite right, except in marginal cases - and it is only in marginal cases that you are doubtful whether a certain animal is a dog or a certain length is less than a meter. Two must be two of something, and the proposition "2 and 2 are 4" is useless unless it can be applied. Two dogs and two dogs are certainly four dogs, but cases arise in which you are doubtful whether two of them are dogs. "Well, at any rate there are four animals," you may say. But there are microorganisms concerning which it is doubtful whether they are animals or plants. "Well, then living organisms," you say. But there are things of which it is doubtful whether they are living organisms or not. You will be driven into saying: "Two entities and two entities are four entities." When you have told me what you mean by "entity," we will resume the argument.
Bertrand Russell (1872 - 1970)
Source: N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
If I had the power to organize higher education as I should wish it to be, I should seek to substitute for the old orthodox religions - which appeal to few among the young, and those as a rule the least intelligent and the most obscurantist - something which is perhaps hardly to be called religion, since it is merely a focusing of attention upon well-ascertained facts. I should seek to make young people vividly aware of the past, vividly realizing that the future of man will in all likelihood be immeasurably longer than his past, profoundly conscious of the minuteness of the planet upon which we live and of the fact that life on this planet is only a temporary incident; and at the same time with these facts which tend to emphasize the insignificance of the individual, I should present quite another set of facts designed to impress upon the mind of the young the greatness of which the individual is capable, and the knowledge that throughout all the depths of stellar space nothing of equal value is known to us. . . .
A man who has once perceived, however temporarily and however briefly, what makes greatness of soul, can no longer be happy if he allows himself to be petty, self-seeking, troubled by trivial misfortunes, dreading what fate may have in store for him. The man capable of greatness of soul will open wide the windows of his mind, letting the winds blow freely upon it from every portion of the universe. He will see himself and life and the world as truly as our human limitations will permit; realizing the brevity and minuteness of human life, he will realize also that in individual minds is concentrated whatever of value the known universe contains. And he will see that the man whose mind mirrors the world becomes in a sense as great as the world. In emancipation from the fears that beset the slave of circumstance he will experience a profound joy, and through all the vicissitudes of his outward life he will remain in the depths of his being a happy man.