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.  Sec. 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: 

    Modus tollens. Camestres.

If A is B, C is D;      The case of A being B is a case of C being D: 
C is not D:                This is not a case of C being D: 
.’.  A is not B.             .’.  This is not a case of A being B.

But if, instead of this, we deny the antecedent, to form the new minor premise,

    This is not a case of A being B,

there arises a syllogism in the First Figure with a negative minor premise, and therefore the fallacy of illicit process of the major term.

By thus reducing the Hypothetical Syllogism to the Categorical form, what is lost in elegance is gained in intelligibility.  For, first, we may justify ourselves in speaking of the hypothetical premise as the major, and of the categorical premise as the minor; since in the categorical form they contain respectively the major and minor terms.  And, secondly, we may justify ourselves in treating the Hypothetical Syllogism as a kind of Mediate Inference, in spite of the fact that it does not exhibit two terms compared by means of a third; since in the Categorical form such terms distinctly appear:  a new term (’This’) emerges in the position of the minor; the place of the Middle is filled by the antecedent of the major premise in the Modus ponens, and by the consequent in the Modus tollens.