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...it was Darwin’s chief contribution, not only to Biology but to the whole of natural science, to have brought to light a process by which contingencies a priori improbable, are given, in the process of time, an increasing probability, until it is their non-occurrence rather than their occurrence which becomes highly improbable. ... Let the reader ... attempt to calculate the prior probability that a hundred generations of his ancestry in the direct male line should each have left at least one son. The odds against such a contingency as it would have appeared to his hundredth ancestor (about the time of King Solomon) would require for their expression forty- four figures of the decimal notation; yet this improbable event has certainly happened.
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Retrospect of criticisms of the theory of natural selection. In Evolution as a Process, eds. J.S.Huxley, A.C.Hardy and E.B.Ford, London: Allen and Unwin, 1954.

 

Ronald Fisher

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Okay, look at it this way: if the evening news has a very high probability of being accurate, then it's highly improbable that they would inaccurately report the numbers chosen in the lottery. That counterbalances any improbability in the choosing of those numbers, so you're quite rational to believe in this highly improbable event.

 

William Lane Craig

 

Faith may be defined briefly as an illogical belief in the occurrence of the improbable.

 

H. L. Mencken

 

What was the Sherlock Holmes principle? 'Once you have discounted the impossible, then whatever remains, however improbable, must be the truth.'
I reject that entirely. The impossible often has a kind of integrity to it which the merely improbable lacks. How often have you been presented with an apparently rational explanation of something that works in all respects other than one, which is just that it is hopelessly improbable? Your instinct is to say 'Yes, but he or she simply wouldn't do that.'

 

Douglas Adams

 

It is a part of probability that many improbable things will happen.

 

Agathon

 

An atheist, like a Christian, holds that we can know whether or not there is a God. The Christian holds that we can know there is a God; the atheist, that we can know there is not. The Agnostic suspends judgment, saying that there are not sufficient grounds either for affirmation or for denial. At the same time, an Agnostic may hold that the existence of God, though not impossible, is very improbable; he may even hold it so improbable that it is not worth considering in practice. In that case, he is not far removed from atheism. His attitude may be that which a careful philosopher would have towards the gods of ancient Greece. If I were asked to prove that Zeus and Poseidon and Hera and the rest of the Olympians do not exist, I should be at a loss to find conclusive arguments. An Agnostic may think the Christian God as improbable as the Olympians; in that case, he is, for practical purposes, at one with the atheists.

 

Bertrand Russell