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.
(7) Hypothetical arguments may be tested by following this outline:
(1) Arrange logically.
(2) Determine antecedent and consequent.
(3) Apply hypothetical rule.
(4) Reduce to categorical form.
(5) Apply categorical rules.
(8) A disjunctive syllogism is one in which the major premise is a disjunctive proposition.
(9) The two kinds of disjunctives are those which “by affirming deny” and those which “by denying affirm.”
(10) In testing disjunctive arguments there are two rules involved: First, “The major premise must assert a logical disjunction.” This necessitates the two requisites “the alternatives must be mutually exclusive” and the “enumeration must be complete.” The two opinions relative to the nature of an alternative assertion are, first, if one is false, the other must be true and vice versa; and second, if one is false, the other must be true, but both may be true. The first is adopted in this discussion.
Second. The second rule involved is “When the minor premise affirms or denies one of the alternatives of a logical disjunctive the conclusion must deny or affirm all of the others.”
(11) Subjecting the disjunctive arguments to the categorical test gives evidence to the close relation existing between the two forms. A logical disjunctive proves to be logical when reduced to the categorical. The reduction entails the two steps, first, reduce to the hypothetical; second, reduce to the categorical.
(12) The logical meaning of the dilemma is suggested by the popular conception. One is said to be in a dilemma when two courses are open to him, neither of which is specially attractive.
A logical dilemma presents two alternatives either one of which might well be avoided.
The major premise of the dilemma is hypothetical; while the minor is disjunctive.
(13) The four forms of the dilemma are the simple constructive, the simple destructive, the complex constructive and the complex destructive.
(14) The dilemma is subject to the hypothetical rule whichis, “The minor premise must either affirm the antecedent or deny the consequent.”
(15) The minor premise need not be a logical disjunctive provided the major conforms to the hypothetical rule.
(16) Frequently when ordinary experiences are reduced to augmentative form they present a disjunctive proposition followed by a hypothetical argument.