62. Dilemma. -- The dilemma is the combination of a disjunctive proposition, serving as major, with two or more conditional propositions forming a minor. First, partial conclusions exclude the members of the disjunction one after another; then it is concluded in a general manner that the disjunctive proposition taken as a whole is inadmissible.

This method of arguing is lively and cogent. An alternative is presented to one's opponent: he is left the choice between two positions; then it is proved that in either case he is wrong.

The validity of the dilemma requires a punctual observance of the rules of the disjunctive and of the conditional syllogisms.

First rule: The disjunction of the major admits of no intermediary proposition, but must be complete.

Second rule: Each of the two conditional syllogisms which together form the minor of the dilemma must be conclusive, and must lead to the same conclusion.

Example (from Père Félix) : "If we supposed that Jesus Christ, in spite of His own assertions, is not God, we should be led to one of these two insulting conclusions: that He is a madman; or that He is an impostor. Now, supposing Jesus Christ to be insane, how can we reconcile with insanity the lofty wisdom manifested in His life and doctrine? Supposing Him an impostor, how make His humility and abnegation agree with such ambitious designs? Both these hypotheses, therefore, are equally inadmissible: Jesus Christ is the Christ. the Son of the living God."^{1}

It is easy to show that the syllogisms are fundamentally reducible to the categorical syllogism.

{1} The dilemma must not be confounded with reasoning "by successive parts", which consists in enumerating all the species of a genus, to take them up afterwards one by one and finally enunciate of all the conclusion which is valid for each of the parts.