When one has to refute an argument in which there is faulty generalization, it is often easy to point out that its author had no sufficient time or chance to make observations, or to point out that the instances on which he relied are not fair examples of their class.  In practice the strength of an argument in which this error is to be found lies largely in the positiveness with which it is pronounced; for it is human nature to accept opinions which have an outward appearance of certainty.

A not uncommon form of faulty generalization is to base an argument on a mere enumeration of similar cases.  This is a poor foundation for an argument, especially for a probability in the future, unless the enumeration approaches an exhaustive list of all possible cases.  To have reasoned a few years ago that because Yale had beaten Harvard at rowing almost every year for fifteen years it had a permanent superiority in the strength and skill of its oarsmen would have been dangerous, for when the years before the given period were looked up they would have shown results the other way.  And an enumeration may run through a very long period of time, and still in the end be upset.

To an inhabitant of Central Africa fifty years ago, no fact probably appeared to rest on more uniform experience than this, that all human beings are black.  To Europeans not many years ago, the proposition, ’All swans are white,’ appeared an equally unequivocal instance of uniformity in the course of nature.  Further experience has proved to both that they were mistaken; but they had to wait fifty centuries for this experience.  During that long time, mankind believed in an uniformity of the course of nature where no such uniformity really existed.[37]

Unless you have so wide and complete a view of your subject that you can practically insure your enumeration as exhaustive, it is not safe to reason that because a thing has always happened so in the past, it will always happen so in the future.  The notorious difficulty of proving a negative goes back to this principle.

So closely like hasty generalization that it cannot be clearly separated from it is faulty reasoning that arises from neglecting exceptions to a general principle.  All our generalizations, except those that are so near truisms as to be barren of interest, are more or less rough and ready, and the process of refining them is a process of finding exceptions and restating the principle so that it will meet the case of the exceptions.

Darwin is said to have had “the power of never letting exceptions pass unnoticed.  Every one notices a fact as an exception when it is striking or frequent, but he had a special instinct for arresting an exception."[38] It was this instinct which made him so cautious and therefore so sure in the statement of his hypotheses:  after the idea of natural selection as an explanation of the origin of the species of the natural world had occurred to him, he spent