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][!--Note--]
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][!--Note--] 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 twenty years collecting further facts and verifying observations to test the theory before he gave it to the world. A generalization that the republican form of government produces greater peace and prosperity than the monarchical would neglect the obvious exceptions in the Central American republics; and to make it at all tenable the generalization would have to have some such proviso as, "among peoples of Germanic race." Even then the exceptions would be more numerous than the cases which would fall within the rule.[39][!--Note--] One must cultivate respect for facts in making theories: a theory should always be held so tentatively that any new or unnoticed facts can have their due influence in altering it.
Of the errors in reasoning about a cause none is more common than that known by the older logic as post hoc, ergo propter hoc (after this, therefore on account of it), or more briefly, the post hoc fallacy. All of us who have a pet remedy for a cold probably commit this fallacy two times out of three when we declare that our quinine or rhinitis or camphor pill has cured us; for as a wise old doctor of two generations ago declared, and as the new doctrines of medical research are making clear, in nine cases out of ten nature cures.
Of the same character are the common superstitions of daily life, for example, that if thirteen sit at table together one will die within the year, or that crossing a funeral procession brings misfortune. Where such superstitions are more than playfully held, they are gross cases of calling that a cause which has no relation to the event. Here is another example, from a letter to The Nation:[40][!--Note--]
In the last volume of the Shakespeare controversy, the argument presented "To the Reader" seems fairly to be summarized as follows: The plays are recognized as wonderful; scholars are amazed at the knowledge of the classes in them, lawyers at the law, travelers at the minute accuracy of the descriptions of foreign cities; they show a keen critic of court etiquette and French soldiery; the only possible man of the time with this encyclopedic outlook was Francis Bacon. Both in the original and in the summary there seems a casual connection implied, namely, that the plays are wonderful because of the knowledge, and because of the knowledge Bacon is the author. But, stated thus baldly, the fallacy is obvious. It is not because the author "had by study obtained nearly all the learning that could be gained from books" that the Elizabethans went to see the plays, or that we to-day read them; but it is because there is to be found in them wonderful characterization expressed dramatically, namely, before an audience. And this audience is what the scholars seem to forget. For by it is the dramatist limited, since profundity of thought or skill in allusion is good or bad, artistically, exactly in proportion as the thought is comprehended or the allusion understood.
Sometimes this fallacy is caused by assuming that because a certain result followed an event in the only case known, therefore there was a causal connection. In a hearing before a committee of the Massachusetts legislature on a bill to establish closer relations between Boston and its suburbs, the question was asked of a witness whether he believed that in the case of London "the London police would have been as efficient as they are now if there had been no annexation" of the surrounding towns; he very properly replied: "That's a hard question to answer, because we have only the existing side to look at. We don't know what it would have been as separate communities." Wherever multiple causes are possible for a phenomenon it is unsafe to argue from a single case.
Another form of error in reasoning to a cause is to assume that a fact is simple, when it is really complex, as in the following example:
I do not think I am overstepping the bounds when I say that the headship of no corporation, or state, or even the headship of the United States, requires greater general ability, force of character, or knowledge of administration than the head of administration of a great city like New York or Berlin. The latter we know to be well administered, the former—well, let us say, less so. The whole difference is in the systems. Apply the Berlin system to New York, and you will get Berlin results.