(1) If A is not B, C is D;
(2) If A is not B, C is not D.
But since the quality of a Hypothetical Proposition is determined by the quality of its consequent, not at all by the quality of its antecedent, we cannot get from these two major premises any really new Moods, that is to say, Moods exhibiting any formal difference from the four previously expounded.
It is obvious that, given the hypothetical major premise—
If A is B, C is D—
we cannot, by denying the antecedent, infer a denial of the consequent. That A is B, is a mark of C being D; but we are not told that it is the sole and indispensable condition of it. If men read good books, they acquire knowledge; but they may acquire knowledge by other means, as by observation. For the same reason, we cannot by affirming the consequent infer the affirmation of the antecedent: Caius may have acquired knowledge; but we cannot thence conclude that he has read good books.
To see this in another light, let us recall [chap. v. § 4], where it was shown that a hypothetical proposition may be translated into a categorical one; whence it follows that a Hypothetical Syllogism may be translated into a Categorical Syllogism. Treating the above examples thus, we find that the Modus ponens (with affirmative major premise) takes the form of Barbara, and the Modus tollens the form of Camestres:
| Modus ponens. | Barbara. |
| If A is B, C is D; | The case of A being B is a case of C being D; |
| A is B: | This is a case of A being B: |
| ∴ C is D. | ∴ This is a case of C being D. |
Now if, instead of this, we affirm the consequent, to form the new minor premise,
This is a case of C being D,
there will be a Syllogism in the Second Figure with two affirmative premises, and therefore the fallacy of undistributed Middle. Again: