The Fallacy of Accident
No rule is so general, which admits not some exception.
Source: Robert Burton, The Anatomy of Melancholy
Xs are normally Ys.
Birds normally can fly.
The fallacy of Accident, one of Aristotle's thirteen fallacies, has been interpreted in various ways by subsequent logicians, perhaps because of the obscurity of The Philosopher's account. I will discuss only one of these interpretations here, due to its relation to recent developments in logic.
Consider the generalization "birds can fly" from the example. Now, it isn't true that all birds can fly, since there are flightless birds. "Some birds can fly" and "many birds can fly" are too weak. "Most birds can fly" is closer to what we mean, but in this case "birds can fly" is a "rule of thumb", and the fallacy of Accident is a fallacy involving reasoning with rules of thumb.
Common sense is full of rules of thumb which do not hold universally, but which hold "generally" or "as a general rule", as is sometimes said. Logicians have tended to ignore rules of thumb, probably because of their unscientific vagueness. However, in the past couple of decades, primarily due to research in artificial intelligence, which has shown the importance of such general rules for practical reasoning, there has been growing interest in so-called "default" or "defeasible" reasoning, of which rules of thumb are a part. As a consequence, there has also been a rebirth of interest in the fallacy of Accident.
The difference between rules of thumb and universal generalizations, is that the former have exceptions. For instance, flightless birds are exceptions to the rule of thumb that birds can fly. One might hope to represent this rule of thumb by the universal generalization "all non-flightless birds can fly", but even this is not correct, for flighted birds with broken wings cannot fly. One might still hope that some lengthy list of exceptions would do the trick. However, one can imagine many different scenarios in which a bird would not be able to fly: its feet are stuck in quicksand, all of the air around it has suddenly rushed into space, it has developed a phobia about flying, etc. One might then try to sum up this diversity of cases under the rubric of "untypical", or "abnormal", and say: "All typical or normal birds can fly". This is exactly what a rule of thumb is.
Rules of thumb differ from statistical generalizations such as "90% of birds can fly" in that there is no specific proportion of flighted to flightless birds that determines normality. The rule of thumb doesn't even necessarily imply that the majority of birds can fly, though it would be unusual if this didn't hold. We can imagine, for instance, that there might be so many penguins in Antarctica that the majority of birds would be flightless. However, our notion of normality applies to the familiar, everyday birds we see in our backyards, rather than "exotics" on distant continents. Clearly, then, rules of thumb are specific to a cultural and temporal context.
The fallacy of Accident occurs when one either attempts to apply such a rule of thumb to an obviously abnormal instance, or when one treats the rule itself as if it were an exceptionless universal generalization, rather than a defeasible rule of thumb.
S. Morris Engel, With Good Reason: An Introduction to Informal Fallacies (5th Edition), (St. Martin's, 1994).
The penguin photo comes from the poster collection at AllPosters.