Some logicians refer to modal propositions as being such as indicate _degrees_ of belief. Such words as “probably,” “certainly,” etc., would indicate their modality. As logic has to do with the pure proposition and not the modal, the difference of opinion is of little import. (3) _Truistic Propositions._ _A truistic proposition is one in which the predicate repeats the words and the meaning of the subject._ Illustrations: “A man is a man,” “A beast is a beast,” “A traitor is a traitor,” “What I have done I have done.” The truistic proposition is of little importance except in cases where the subject is used extensionally while the predicate is used intensionally. In the illustration, “A man is a man,” the subject merely stands for a member of the man family, while the predicate may indicate certain manly qualities. Against such ambiguities the logician must be on guard. =8. THE RELATION BETWEEN SUBJECT AND PREDICATE.= In Chapter 5 the extension and intension of terms was explained. The student recalls, for instance, that the term “man” may be used to denote objects, as “white man,” “black man,” “red man,” etc. In this sense the term “man” is used _extensionally_. But when made to stand for the attributes “rationality,” “power of speech,” etc., the term “man” is used intensionally. In considering the relation between subject and predicate it is customary to employ the terms in an extensional sense only, since such a restriction serves the purpose of syllogistic reasoning and conversion. Let us, then, give attention to the _extension_ of the subject and predicate of the categorical propositions A, E, I, O. (1) _The Universal Affirmative or A Proposition._ _All S is P symbolizes the A proposition._ This may be interpreted as meaning that all of the subject belongs to a part of the predicate, or that all of the subject belongs to all of the predicate. The first interpretation is the usual one and may be illustrated by the following propositions: 1. “All men are mortal.” 2. “All trees grow.” 3. “All metals are elements.” It is obvious that the subjects of these propositions include every specimen of the particular class mentioned. For example: The subject _all men_ includes every specimen of the human family; _all trees_ includes every object of that class; _all metals_ covers everything which the scientist classes as such. In the three propositions, then, reference is made to the _whole_ subject but to only a _part_ of the predicate, as other beings beside men, such as the horse, are mortal; and other plants aside from trees, such as the sun flower, grow; other substances, namely oxygen, are elements. For the sake of making the logical meaning of the four propositions clearer, recourse may be made to Euler’s diagrams, so named because the Swiss mathematician and logician, Leonhard Euler, first used them.