All that passes for knowledge can be arranged in a hierarchy of degrees of certainty, with arithmetic and the facts of perception at the top.

Almost all great advances have sprung originally from disinterested motives. Scientific discoveries have been made for their own sake and not for their utilization, and a race of men without a disinterested love of knowledge would never have achieved our present scientific technique. … Faraday, Maxwell, and Hertz, so far as can be discovered, never for a moment considered the possibility of any practical application of their investigations.

Gradually, … the aspect of science as knowledge is being thrust into the background by the aspect of science as the power of manipulating nature. It is because science gives us the power of manipulating nature that it has more social importance than art. Science as the pursuit of truth is the equal, but not the superior, of art. Science as a technique, though it may have little intrinsic value, has a practical importance to which art cannot aspire.

I conclude that, while it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable, must be attained by scientific methods; and what science cannot discover, mankind cannot know.

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.

Persecution is used in theology, not in arithmetic, because in arithmetic there is knowledge, but in theology there is only opinion. So whenever you find yourself getting angry about a difference of opinion, be on your guard, you will probably find, on examination, that your belief is going beyond what the evidence warrants?

Philosophy is that part of science which at present people chose to have opinions about, but which they have no knowledge about. Therefore every advance in knowledge robs philosophy of some problems which formerly it had …and will belong to science.

Science is what we know, and philosophy is what we don't know.

Science may set limits to knowledge, but should not set limits to imagination.

The degree of one’s emotions varies inversely with one’s knowledge of the facts—the less you know the hotter you get.

The examination system, and the fact that instruction is treated mainly as a training for a livelihood, leads the young to regard knowledge from a purely utilitarian point of view as the road to money, not as the gateway to wisdom.

The good life is one inspired by life and guided by knowledge.

The scientific attitude of mind involves a sweeping away of all other desires in the interest of the desire to know.

The significance of a fact is relative to [the general body of scientific] knowledge. To say that a fact is significant in science, is to say that it helps to establish or refute some general law; for science, though it starts from observation of the particular, is not concerned essentially with the particular, but with the general. A fact, in science, is not a mere fact, but an instance. In this the scientist differs from the artist, who, if he deigns to notice facts at all, is likely to notice them in all their particularity.

There is much pleasure to be gained from useless knowledge.

Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind.

Throughout the last four hundred years, during which the growth of science had gradually shown men how to acquire knowledge of the ways of nature and mastery over natural forces, the clergy have fought a losing battle against science, in astronomy and geology, in anatomy and physiology, in biology and psychology and sociology. Ousted from one position, they have taken up another. After being worsted in astronomy, they did their best to prevent the rise of geology; they fought against Darwin in biology, and at the present time they fight against scientific theories of psychology and education. At each stage, they try to make the public forget their earlier obscurantism, in order that their present obscurantism may not be recognized for what it is.

Vagueness is very much more important in the theory of knowledge than you would judge it to be from the writings of most people. Everything is vague to a degree you do not realize till you have tried to make it precise, and everything precise is so remote from everything that we normally think, that you cannot for a moment suppose that is what we really mean when we say what we think.

We know very little, and yet it is astonishing that we know so much, and still more astonishing that so little knowledge can give us so much power.

What men want is not knowledge, but certainty.

While the dogmatist is harmful, the sceptic is useless …; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or of ignorance. Knowledge is not so precise a concept as is commonly thought. Instead of saying ‘I know this’, we ought to say ‘I more or less know something more or less like this’. … Knowledge in practical affairs has not the certainty or the precision of arithmetic.

With equal passion I have sought knowledge. I have wished to understand the hearts of men. I have wished to know why the stars shine. And I have tried to apprehend the Pythagorean power by which numbers holds sway above the flux. A little of this, but not much, I have achieved.