Often one example seems sufficient to cause belief.  We might believe that all giraffes have long necks, even though we had seen but one; but such a belief would exist because, by many examples of other animals, we have learned that a single specimen will fairly represent all other specimens of the same class.  On the other hand, if this one giraffe should possess one brown eye and one white eye, we should not expect all other giraffes to have such eyes, for our observation of many hundreds of animals teaches us that the eyes of an animal are usually alike in color.  In order to establish a true generalization, the essential characteristics must be selected, and these cannot be determined by rule, but rather by common sense.

+177.  Deductive Reasoning.+—­When once a general principle has been established, we may demonstrate the truth of a specific proposition by showing that the general principle applies to it.  We see a gold ring and say, “This ring is valuable,” because we believe the general proposition, “All articles made of gold are valuable.”  Expressed in full, the process of reasoning would be—­

  A. All articles made of gold are valuable.
  B. This ring is made of gold.
  C. Therefore this ring is valuable.

A series of statements such as the above is called a syllogism.  It consists of a major premise (A), a minor premise (B), and a conclusion (C).

Of course we shall not be called upon to prove so simple a proposition as the one given, but with more difficult ones the method of reasoning is the same.  The process which applies a general proposition (A) to a specific instance (C), is called deductive reasoning.

+178.  Relation between Inductive and Deductive Reasoning.+—­Deductive reasoning is shorter and seems more convincing than inductive reasoning, for if the premises are true and the statement is made in correct form, the conclusions are irresistible.  Each conclusion carries with it, however, the weakness of the premises on which it is based, and as these premises are general principles that have been themselves established by inductive reasoning, the conclusions of deductive reasoning can be no more sure than those of inductive reasoning.  Each may prove only that the proposition is probably true rather than that it is surely true, though in many cases this probability becomes almost a certainty.

+179.  The Enthymeme.+—­We seldom need to state our argument in the syllogistic form.  One of the premises is usually omitted, and we pass directly from one premise to the conclusion.  If we say, “Henry will not succeed as an engineer,” and when asked why he will not, we reply, “Because he is not good in mathematics,” we have omitted the premise, “A knowledge of mathematics is necessary for success in engineering.”  A shortened syllogism, that is, a syllogism with one premise omitted, is called an enthymeme.