1. We are apt, under the influence of prepossession or prejudice, to remember certain coincidences better than others, and so to imagine extra-casual coincidence where none exists. This bias works in confirming all kinds of established beliefs, superstitious and other, beliefs in dreams, omens, retributions, telepathic communications, and so forth. Many people believe that nobody who thwarts them ever comes to good, and can produce numerous instances from experience in support of this belief. 2. We are apt, after proving that there is a residuum beyond what chance will account for on due allowance made for positive frequency, to take for granted that we have proved some particular cause for this residuum. Now we have not really explained the residuum by the application of the principle of chances: we have only isolated a problem for explanation. There may be more than chance will account for: yet the cause may not be the cause that we assign off-hand. Take, for example, the coincidence that has been remarked between race and different forms of Christianity in Europe. If the distribution of religious systems were entirely independent of race, it might be said that you would expect one system to coincide equally often with different races in proportion to the positive number of their communities. But the Greek system is found almost solely among Slavonic peoples, the Roman among Celtic, and the Protestant among Teutonic. The coincidence is greater than chance will account for. Is the explanation then to be found in some special adaptability of the religious system to the character of the people? This may be the right explanation, but we have not proved it by merely discounting chance. To prove this we must show that there was no other cause at work, that character was the only operative condition in the choice of system, that political combinations, for example, had nothing to do with it. The presumption from extra-casual coincidence is only that there is a special cause: in determining what that is we must conform to the ordinary conditions of explanation. So coincidence between membership of the Government and a classical education may be greater than chance would account for, and yet the circumstance of having been taught Latin and Greek at school may have had no special influence in qualifying the members for their duties. The proportion of classically educated in the Government may be greater than the proportion of them in the House of Commons, and yet their eminence may be in no way due to their education. Men of a certain social position have an advantage in the competition for office, and all those men have been taught Latin and Greek as a matter of course. Technically speaking, the coinciding phenomena may be independent effects of the same cause. 3. Where the alternative possibilities are very numerous, we are apt not to make due allowance for the number, sometimes overrating it, sometimes underrating it.