Here we see that the denial of the antecedent amounts to illicit process of the major term.
§ 7481 Affirmation of Consequent.
If A is B, C is D. \ / All Cases of A being B are cases of C
| = | being D.
C is D. / \ This is a case of C being D.
Here we see that the affirmation of the consequent amounts to undistributed middle.
§ 749. If we confine ourselves to the special rules of the four figures, we see that denial of the antecedent involves a negative minor in the first figure, and affirmation of the consequent two affirmative premisses in the second. Or, if the consequent in the major premiss were itself negative, the affirmation of it would amount to the fallacy of two negative premisses. Thus—
If A is B, C is not D. \ / No cases of A being B are cases of C
| = | being D.
C is not D. / \ This is not a case of C being D.
§ 750. The positive side of the canon of the conjunctive syllogism—'To affirm the antecedent is to affirm the consequent,' corresponds with the Dictum de Omni. For whereas something (viz. C being D) is affirmed in the major of all conceivable cases of A being B, the same is affirmed in the conclusion of something which is included therein, namely, 'this case,' or 'some cases,' or even 'all actual cases.'
§ 751. The negative side—'to deny the consequent is to deny the antecedent'—corresponds with the Dictum de Diverse (§ 643). For whereas in the major all conceivable cases of A being B are included in C being D, in the minor 'this case,' or 'some cases,' or even 'all actual cases' of C being D, are excluded from the same notion.
§ 752. The special characteristic of the partly conjunctive syllogism lies in the transition from hypothesis to fact. We might lay down as the appropriate axiom of this form of argument, that 'What is true in the abstract is true—in the concrete,' or 'What is true in theory is also true in fact,' a proposition which is apt to be neglected or denied. But this does not vitally distinguish it from the ordinary syllogism. For though in the latter we think rather of the transition from a general truth to a particular application of it, yet at bottom a general truth is nothing but a hypothesis resting upon a slender basis of observed fact. The proposition 'A is B' may be expressed in the form 'If A is, B is.' To say that 'All men are mortal' may be interpreted to mean that 'If we find in any subject the attributes of humanity, the attributes of mortality are sure to accompany them.'