These two points being borne in mind, the attention may be concentrated on the Middle Term and its relations with the extremes.
That the predicate may be left unanalysed without affecting the simplicity of the argument or in any way obscuring the exhibition of its turning-point, has an important bearing on the reduction of Modals. The modality may be treated as part of the predicate without in any way obscuring what it is the design of the syllogism to make clear. We have only to bear in mind that however the predicate may be qualified in the premisses, the same qualification must be transferred to the conclusion. Otherwise we should have the fallacy of Four Terms, quaternio terminorum.
To raise the question: What is the proper form for a Modal of Possibility, A or I? is to clear up in an important respect our conceptions of the Universal proposition, "Victories may be gained by accident". Should this be expressed as A or I? Is the predicate applicable to All victories or only to Some? Obviously the meaning is that of any victory it may be true that it was gained by accident, and if we treat the "mode" as part of the predicate term "things that may be gained by accident," the form of the proposition is All S is in P.
But, it may be asked, does not the proposition that victories may be gained by accident rest, as a matter of fact, on the belief that some victories have been gained in this way? And is not, therefore, the proper form of proposition Some S is P?
This, however, is a misunderstanding. What we are concerned with is the formal analysis of propositions as given. And Some victories have been gained by accident is not the formal analysis of Victories may be gained by accident. The two propositions do not give the same meaning in different forms: the meaning as well as the form is different. The one is a statement of a matter of fact: the other of an inference founded on it. The full significance of the Modal proper may be stated thus: In view of the fact that some victories have been gained by accident, we are entitled to say of any victory, in the absence of certain knowledge, that it may be one of them.
A general proposition, in short, is a proposition about a genus, taken universally.
II.—Second Figure.
For testing arguments from general principles, the First Figure is the simplest and best form of analysis.
But there is one common class of arguments that fall naturally, as ordinarily expressed, into the Second Figure, namely, negative conclusions from the absence of distinctive signs or symptoms, or necessary conditions.
Thirst, for example, is one of the symptoms of fever: if a patient is not thirsty, you can conclude at once that his illness is not fever, and the argument, fully expressed, is in the Second Figure.