In our thinking these two processes cannot be separated, for some elements in the phe nomena under observation appear immediately illuminated by our knowledge, others again are not so illuminated, but when properly tested are found to emit the light which is in them; these various elements are so closely joined together that the two processes must ever run parallel.
The form of inference which best illustrates the deductive reasoning, although by no means exclusively, is that of the Syllogism (q.v.). The syllogism is that method of reasoning which combines two judgments so as to pro duce a third; as for example: Whatever turns blue litmus paper red is an acid. This compound turns blue litmus paper red. Therefore, it is an acid.
It will be observed that the two judgments which combine to produce the third have a term in common; this is called the middle term of the syllogism. Moreover, the third judg ment or conclusion is proved by the process of eliminating the middle term, and taking as the subject and predicate of the conclusion the remaining terms of the given judgments. The subject of the conclusion is called the minor term; the predicate, the major term, and of the two given judgments, the one containing the major term is called the major premise, and the one containing the minor term, the minor premise. It is the peculiar function of the major premise to exhibit some aspect of our general knowledge, and of the minor prem ise to exhibit a more particular phase of our general knowledge, or as it more frequently occurs some special case embodied in a con crete experience. It is the combined function of the two together to apply some portion of our general knowledge to a special case so as to yield its true interpretation. It is impos sible to discuss here at length the various rules by which the validity of the syllogism may be tested. It may be said, however, that the rules of the syllogism depend upon the fundamental principle that if a special case can be proved to fall within the area of a uni versal, then the inference follows that the spe cial case becomes invested with the essential characteristics of the universal itself. But if the special case falls outside the scope of the universal, either wholly or in part, then the inference does not follow. For instance, in all
cases at law the special case is referred to some law principle, that is, to a universal which completely covers its essential signifi cance and thereby determines the issues of the trial with the kttending damages or punishment. Whenever a judicial decision is reversed by a superior court it is because the special case under investigation did not properly come under the law principle to which it was re ferred. It is obvious that the syllogistic method of reasoning admits of abuse by con necting premises in a merely formal manner which have no real connection. Such an arti ficial and mechanical treatment of the syllogism leads naturally to empty subtleties and weak sophistries. It was this exclusive emphasis upon the formal and technical side of the syllo gism that brought the writings of the school men to such ill repute, so that the term scholas tic has become suggestive of a complete divorce of thought from reality. Aristotle, to whom we owe the formulation of the syllogistic method of reasoning, placed supreme stress upon the real connection which must underlie all formal relationship in the structure of the syllogism. Thus he states that °the middle term must express the real cause,' TO /Lev yap aIraiv re picrov. Anal. Post. ii. 2, 90A 6.
The force of Aristotle's observation will be appreciated if we trace the usual process of thought whenever any judgment of ours is questioned. Suppose that one asserts that there is going to be a storm within a few hours, and he is asked concerning the ground of his opinion. The reply would be that there is a rapidly falling barometer, and also that a rapidly falling barometer indicates an ap proaching storm. Here the middle term, °rap idly falling barometer,' serves to unite the uni versal judgment to the special case as observed and at the same time to connect the two parts of the reasoning process by a real tie repre senting the underlying cause upon which they are based. Inference, indeed, is often defined as the process by which the ground of a judg ment is explicitly disclosed.