Traditional Logic II: Chapter 13 - Complex Syllogisms (The Dilemma)

Rule #3:

(concerning the *conclusion*): The conclusion must be exclusive. (In other words, it should be the only one that can be inferred from the premises.)

Rule #1:

(concerning the *major premise*): The consequents in the major premise must follow legitimately from the antecedents. (In other words, the major premise must be true.)

Rule #2:

(concerning the *minor premise*): The disjunction in the minor premise must be complete. (In other words, there must be no third possibility.)

There are four different forms of the dilemma:

-The simple constructive dilemma -The simple destructive dilemma -The complex constructive dilemma -The complex destructive dilemma

What is a Dilemma?

A dilemma is a *two-horned* or *two-edged* argument which presents as the major premise a complex conjunctive proposition in which each of the conjuncts (the *horns*) is a conditional statement, as well as a minor premise, a disjunctive proposition in which either the antecedents of the major premise are confirmed, or its consequents are denied.

Response #3:

Counter Dilemma (if there is a violation of Rule #3)

Simple Constructive Dilemma

Either P or R If P, then Q; and if R, then Q Therefore, Q

Complex Constructive Dilemma

Either P or R If P, then Q; and if R, then S Therefore, either Q or S

Simple Destructive Dilemma

If P, then Q; and if P, then R Either not Q or not R Therefore, not P

Complex Destructive Dilemma

If P, then Q; and if R, then S Either not Q or not S Therefore, not P or not R

Procedure #1:

If the dilemma is constructive, then the consequents of the major premise may be switched and negated.

Procedure #2:

If the dilemma is destructive, then the antecedents of the major premise may be switched and negated.

Rules for the Dilemma

There are three rules that must be followed in order for a dilemma to be considered properly constructed, each pertaining to a distinct part of the syllogism.

Grasping a Dilemma by the horns

We must attack one of the conditional statements in the major premise.

Escaping between the horns of a Dilemma

We must attack one of the disjunctive statements in the minor premise.