O
A
E in the first figure. There is one negative premise (O), and the conclusion is negative. There is one particular premise (O), but the conclusion is not particular. This makes the argument invalid according to rule 8; viz.: “A particular premise necessitates a particular conclusion.” Carrying the test still further it will be seen that there is likewise the fallacy of undistributed middle.
Other arguments where one of the premises is partitive.
“All scholars are not wise and, therefore, Aristotlewas not wise.” “All democrats are not free-traders, but most of the men of this particular club are democrats, and hence they are of a different faith (not free-traders).”
“All the members of the club are not good players, and James belongs to the club.”
“All educated men do not write good English; therefore, you ought not to express surprise when informed that X, though an educated man, uses poor English.”
The major premise in each of the foregoing is partitive in nature and should be changed to the following form before the argument is tested; taking these in order we have: “Some scholars are not wise”; “Some democrats are not free-traders”; “Some of the members of the club are not good players”; “Some educated men do not write good English.” Let us test the validity of the last one:
(6) O Some educated men do not write good English,
A X is an educated man,
E ∴ X does not write good English (uses poor English).
Like the first one of the list, this is invalid inasmuch as a particular premise should yield a particular conclusion, not one which is universal. The argument also contains the fallacy of undistributed middle.