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Therefore, it will not be successful in cities of four hundred thousand or larger, which is a reductio ad absurdum. The folly of the attempt is shown by the very statement of the conclusion. The Dilemma. One special form of the syllogism is at times so strong an argument that it deserves special mention here, namely, the dilemma.
"I am very curious to know just how they got rid of labor unions in Altruria." "We had syndicates, too, and finally we had the reductio ad absurdum we had a federation of labor unions find a federation of syndicates, that divided the nation into two camps. The situation was not only impossible, but it was insupportably ridiculous."
"I'm very much obliged, Father. I'm sorry I was stupid just now; but you know it's extraordinarily bewildering to me. I still don't seem to be able to grasp all you said about Democracy." The old priest smiled reassuringly. "Well, you see, the universal franchise reduced Democracy ad absurdum fifty years ago. Even the uneducated saw that.
In the same way one may refute by reductio ad absurdum all such arguments as, "Custom has rendered the spoils system desirable"; "The prevalency of the high license law shows its superiority to prohibition"; and "Since in the past all college students were required to study Latin and Greek, these subjects should be required at the present time."
After 1854, and for ten years, the political history of Canada is a reductio ad absurdum of the older party system. Government succeeded government, only to fall a prey to its own lack of a sufficient majority, and the unprincipled use by its various opponents of casual combinations and alliances. Apart from a little group of Radicals, British and French, who advocated reforms with an absence of moderation which made them impossible as ministers of state, there were not sufficient differences to justify two parties, and hardly sufficient programme even for one. The old Tories disappeared from power with their leader, Sir Allan MacNab, in 1856. The Baldwin-Hincks reformers had distributed themselves through all the parties Canadian Peelites they may be called. The great majority of the representatives of the French followed moderate counsels, and were usually sought as allies by whatever government held office. The broader principles of party warfare were proclaimed only by the Clear-Grits of Upper Canada and the Rouges of Lower Canada. The latter group was distinct enough in its views to be impossible as allies for any but like-minded extremists: "Le parti rouge," says La Minerve, "s'est formé
If this kind of demonstration is not permitted, the process of reasoning called deductio ad absurdum, which even the severity of geometry does not reject, could not be employed at all in legislative discussions. One of our strongest weapons against folly acting with authority would be lost.
Warned by the unanswerable arguments of Zeno against infinitesimals, mathematicians substituted for this the statement that, by continuing the construction, we can inscribe a polygon approaching equality with the circle as nearly as we please. The method of exhaustion used, for the purpose of proof by reductio ad absurdum, the lemma proved in Eucl.
Armor and projectiles must soon bring each other to a standstill; as when, in the Italian wars of the fifteenth century, offence and defence reached the reductio ad absurdum of the incapacity of men-at-arms to inflict serious injury upon each other, or even to pick themselves up when the weight of their armor, with some aid from the clumsy blows of an antagonist, had overthrown them.
The armament argument for peace has been given its reductio ad absurdum; but it is by no means clear that the world-wide war will free the nations from the burdensome folly of keeping enormous armies and navies. As Christians we must protest without ceasing that international relations, based on mutual fear and maintained by the use of brute force, can never furnish the peace of Christ.
This reductio ad absurdum of legalism is exactly paralleled, in many of our elementary schools, in the answers to arithmetical questions given by the children.
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