Quotes on Probability

The incomplete knowledge of a system must be an essential part of every formulation in quantum theory. Quantum theoretical laws must be of a statistical kind. To give an example: we know that the radium atom emits alpha-radiation. Quantum theory can give us an indication of the probability that the alpha-particle will leave the nucleus in unit time, but it cannot predict at what precise point in time the emission will occur, for this is uncertain in principle.

All knowledge resolves itself into probability. ... In every judgment, which we can form concerning probability, as well as concerning knowledge, we ought always to correct the first judgment deriv'd from the nature of the object, by another judgment, deriv'd from the nature of the understanding.

All knowledge degenerates into probability.

We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?

If you trace back all those links in the chain that had to be in place for me to be here, the laws of probability maintain that my very existence is miraculous. But then after however many decades, less than a hundred years, they disburse and I cease to be. So while they're all congregated and coordinated to make me, then-and I speak her on behalf of all those trillions of atoms-I should really make the most of things.

Some reasonable term ought to be allowed to enable aliens to get rid of foreign and acquire American attachments; to learn the principles and imbibe the spirit of our government; and to admit of a probability at least, of their feeling a real interest in our affairs.

We may not be able to get certainty, but we can get probability, and half a loaf is better than no bread.

And human instinct is ancient and reliable, utterly mysterious and possibly capable of great genius. I believe that refined, fluent instincts are a person's most valuable asset. My own instincts have repeatedly guided me against the grain of logic and probability. When I have trusted and followed their direction, they have never been wrong. I don't know how or why. But I know that every significant experience-positive or negative-sharpens them and makes them more accurate.

It was wonderful love that Christ should rather die for us than for the angels that fell. They were creatures of a more noble extract, and in all probability might have brought greater revenues of glory to God; yet that Christ should pass by those golden vessels, and make us clods of earth into stars of glory -- Oh, the hyperbole of Christ's love!

The scientific imagination always restrains itself within the limits of probability.