For example—
Denial of the Antecedent.
If you repent, then only are you forgiven.
You do not repent.
.'. You are not forgiven.
Affirmation of the Consequent.
If you repent, then only are you forgiven.
You are forgiven.
.'. You repent.
CHAPTER XXI.
Of the Reduction of the Partly Conjunctive Syllogism.
§ 744. Such syllogisms as those just treated of, if syllogisms they are to be called, have a major and a middle term visible to the eye, but appear to be destitute of a minor. The missing minor term is however supposed to be latent in the transition from the conjunctive to the simple form of proposition. When we say 'A is B,' we are taken to mean, 'As a matter of fact, A is B' or 'The actual state of the case is that A is B.' The insertion therefore of some such expression as 'The case in hand,' or 'This case,' is, on this view, all that is wanted to complete the form of the syllogism. When reduced in this manner to the simple type of argument, it will be found that the constructive conjunctive conforms to the first figure and the destructive conjunctive to the second.
Constructive Mood. Barbara.
If A is B, C is D. \ / All cases of A being B are cases 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.
Destructive Mood. Camestres.
If A is B, C is D. \ / All cases of A being B are cases 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.