In considering the definition of a universal proposition it is necessary to keep in mind the distinction between a logical and a grammatical subject, as in the second proposition the logical predicate, “cook their food,” refers to only a part of the grammatical subject, _men_, and, therefore, the proposition might fallaciously be termed a particular proposition rather than a universal. _A particular proposition is one in which the predicate refers to only a part of the logical subject._ ILLUSTRATIONS: (1) Some men are wise. (2) Some animals are not quadrupeds. (3) Most elements are metals. (4) Many children are mischievous. In the foregoing propositions _some_, _most_ and _many_ are quantity signs and, therefore, must not be considered as a part of the logical subjects. Considering the logical subjects and predicates in order, the term _wise_ refers to only a part of the _men_ in the world, _quadrupeds_ to only a part of the _animals_, _metals_ to only a part of the _elements_ and _mischievous_ to only a part of the _children_. _An affirmative proposition is one which expresses an agreement between subject and predicate._ _A negative proposition is one which expresses a disagreement between subject and predicate._ Affirmative propositions conjoin terms, negative propositions disjoin terms. In the first the agreement is affirmed; in the second the agreement is denied. ILLUSTRATIONS: None of the captives escaped. Negative. Some teachers are just. Affirmative. All trees grow towards heaven. Affirmative. Some people are not companionable. Negative. No person is above criticism. Negative. Dividing both universal and particular propositions as to quality, gives four kinds; namely, universal affirmative, universal negative, particular affirmative and particular negative. No topic in logic demands greater familiarity than these four types, as every proposition must be reduced to one of the four before it can be used as a basis of reasoning. For the sake of brevity the symbols A, E, I and O are used to designate respectively the universal affirmative, the universal negative, the particular affirmative and the particular negative. A and I, symbolizing the affirmative propositions, are the first and second vowels in _Affirmo_, while E and O, symbolizing the negatives, are the vowels in _Nego_. The common sign of the universal affirmative, or the A proposition is _all_; of the universal negative, or E proposition _no_; of the particular affirmative, or I proposition _some_; of the particular negative, or O proposition _some_ with _not_ as a part of the copula. The accompanying classification summarizes these facts, S and P being used to symbolize the terms “_subject_” and “_predicate_.” _Illustrations_