Fallacy of Accident

The logical fallacy of accident, also called destroying the exception or a dicto simpliciter ad dictum secundum quid, is a deductive fallacy occurring in statistical syllogisms (an argument based on a generalization) when an exception to the generalization is ignored. It is one of the thirteen fallacies originally identified by Aristotle. The fallacy occurs when one attempts to apply a general rule to an irrelevant situation.
For instance:

Cutting people with a knife is a crime.
Surgeons cut people with knives.
Surgeons are criminals.

It is easy to construct fallacious arguments by applying general statements to specific incidents that are obviously exceptions.
Generalizations that are weak generally have more exceptions (the number of exceptions to the generalization need not be a minority of cases) and vice versa.
This fallacy may occur when we confuse generalizations ("some") for categorical statements ("always and everywhere"). It may be encouraged when no qualifying words like "some", "many", "rarely" etc. are used to mark the generalization.
For example:

Germans are Nazis

The premise above could be used in an argument concluding that all Germans or current Germans should be held responsible for the actions of the Nazis. Qualifying the first term:

Some Germans are Nazis

This premise may make it more obvious it is making an (extremely weak) generalization and not a categorical rule.
Related inductive fallacies include: overwhelming exception, hasty generalization. See faulty generalization.
The opposing kind of dicto simpliciter fallacy is the converse accident.