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_.

The mediate element of the inference in a Hypothetical Syllogism
consists in asserting, or denying, the fulfilment of a given condition;
just as in a C