A. All metals are fusible.
B. Thurium is a metal.
C. Therefore thurium is fusible.
Such a series of statements is called a syllogism. A syllogism always consists of a major premise (A), a minor premise (B), and a conclusion (C). The major premise always states a general law; the minor premise shows that the general law applies to the particular case under consideration; and the conclusion is, in the light of the two premises, an established truth.
The strength of deductive argument depends on two things: the truth of the premises and the framing of the syllogism. The syllogism must always be so stated that a conclusion is derived from the application of a general law to some specific instance to which the law obviously applies. In the next place, the premises must be true. If they are only probably correct, the conclusion is a mere presumption; if either one is false, the conclusion is probably false. But if the syllogism is correctly framed, and if both premises are true, the conclusion is irrefutable. As premises are facts that have first been established by induction, the relation between inductive and deductive reasoning is very close. In fact, deduction depends on induction for its very existence. To overthrow a deductive argument all that is necessary is to show the error in the inductive process that built up either one or both of the premises.
The tests for deduction are:—
(1) Are both premises true?
(2) Is the fact stated in the minor premise an instance of the general law expressed in the major premise?
In practical argumentation it is not always necessary or desirable to express a deductive argument in full syllogistic form. One premise is frequently omitted; the syllogism thus shortened is called an enthymeme. The reasoning then takes some such form as, "This man will fail in business because he is incompetent." The major premise, "All incompetent men fail in business," is understood, but is not expressed. The enthymeme constitutes as strong and forceful an argument as the syllogism, provided the suppressed premise is a well- established fact; but whenever this premise is not accepted as true, it must be stated and proved. The argument will then consist of the full syllogistic process.
The following outline illustrates the chief difference between induction and deduction:—