If it is a premise, then the argument may have to be given two separate tests. For example, consider the argument:
Everyone who saw the game was at the dance. Not quite all the students were at the dance. So some students didn't see the game.
Its first premise and its conclusion are categorical propositions, which are easily translated into standard form. Its second premise, however, is an exceptive proposition, not simple but compound. To discover whether its premises imply its conclusion, first test the syllogism composed of the first premise of the given argument, the first half of its second premise, and its conclusion. In standard form, we have
All persons who saw the game are persons who were at the dance. Some students are persons who were at the dance. Therefore some students are not persons who saw the game.
The standard-form categorical syllogism is of form AIO-2 and commits the fallacy of the undistributed middle, violating Rule 2. However, the original argument is not yet proved to be invalid, because the syllogism just tested contains only part of the premises of the original argument. We now have to test the categorical syllogism composed of the first premise and the conclusion of the original argument together with the second half of the second premise. In standard form we then get a very different argument:
All persons who saw the game are persons who were at the dance. Some students are not persons who were at the dance. Therefore some students are not persons who saw the game. This is a standard-form categorical syllogism in Baroko , AOO-2 , and it is easily shown to be valid. Hence the original
argumentThis is a standard-form categorical syllogism in Baroko , AOO-2 , and it is easily shown to be valid. Hence the original argument is valid, because the conclusion is the same, and the premises of the original argument include the premises of this valid standard-form syllogism. Thus, to test the validity of an argument, one of whose premises is an exceptive proposition, may require testing two different standard-form categorical syllogisms.