19. SUMMARY.
(1) Just as there are three kinds of propositions so there are three kinds of arguments; namely, categorical, hypothetical, disjunctive.
(2) Categorical syllogistic arguments are those in which all of the propositions are categorical.
Hypothetical syllogistic arguments are those in which the major premise is hypothetical.
In contradistinction to disjunctives, hypothetical arguments may be referred to as “conjunctive”.
(3) The hypothetical proposition is composed of antecedent and consequent; the former being the limiting condition; while the latter is the direct assertion. As the words indicate the antecedent usually precedes the consequent. The signs of the antecedent are “if,” “though,” “unless,” “suppose,” “granted that,” “when,” etc.
(4) The two kinds of hypothetical syllogisms are the constructive and destructive; the former is involved when the minor premise affirms the antecedent; the latter when the minor premise denies the consequent. These two kinds are sometimes referred to as “modus ponens” and “modus tollens” respectively.
(5) Out of the four possible hypothetical syllogisms only two are valid as investigation proves this rule: The minor premise must affirm the antecedent or deny the consequent. In the case of the hypothetical proposition being co-extensive, the rule does not apply.
(6) Hypothetical arguments may be reduced to the categorical by contracting the antecedent of the hypothetical proposition to form the subject-term, and by contracting the consequent of the hypothetical proposition to form the predicate-term of the major premise of the categorical syllogism. If it is necessary, supply a new minor term.
Denying the antecedent is a matter of illicit major; whereasaffirming the consequent is equivalent to undistributed middle.