Hypothetically considered, the minor premise affirms the consequent and thus the argument is fallacious; when changed to the categorical we find the fallacy of undistributed middle. If other examples were taken, it could be proved that the hypothetical fallacy of denying the antecedent is usually equivalent to the categorical fallacy of illicit major; whereas the hypothetical fallacy of affirming the consequent amounts to undistributed middle.
In reducing some hypotheticals it is necessary to make use of such expressions as, “the case of” or “the circumstances that.” The attending argument will illustrate this:
If Jefferson was right, man was created free and equal;
(but) Man was not created free and equal,
∴ Jefferson was not right.
Reduced to the categorical:
The G
case of Jefferson being right is the case of manbeing created M
free and equal;
S
Man was not created M
free and equal,
∴ A
Jefferson (this man) was not G
right.
The argument is valid in both cases.