The four elements are indicated in the following categorical propositions:
| Quantity sign | Logical subject | Copula | Logical predicate |
| All | fixed stars | are | self-luminous |
| No | wise man | is | going to steal |
| Some | quadrupeds | are | domestic animals |
| Some | glittering things | are not | gold |
| Some | boys | are not | discreet |
| A few | men | are | multi-millionaires |
| Every | citizen | is | duty-bound to vote |
The student must ever keep in mind the fact that to be absolutely logical all categorical propositions must be expressed in terms of the four elements. However, life is too short and man is too busy to speak always in terms of the four elements. Moreover, to be logical may often compel an awkwardness of expression and a lack of euphony which could hardly be tolerated. For these reasons the utterances in ordinary conversation are frequently illogical so far as the four elements are concerned, though not necessarily illogical in meaning. When it is desired to test the validity of any series of statements leading up to some generalization, it may become necessary to express the statement in terms of the four elements. The student should gain some facility in this, otherwise he may be readily led into fallacious reasoning.
The following statements taken at random from newspapers are given in the original and then expressed in terms of the four elements:
| The Original | In Terms of the Four Elements |
| (1) You came too late. | (1) The person is one who came too late. |
| (2) I saw the swell turnout coming along. | (2) The man was one who saw the swell turnout coming along. |
| (3) All of the men walked. | (3) All of the men were those who walked. |
| (4) The robbers cut a hole in this floor. | (4) All the robbers were the ones who cut a hole in this floor. |
| (5) Some of these flew away. | (5) Some birds were those which flew away. |
| (6) The rain interfered with the attendance. | (6) The rain was that which interfered with the attendance. |
| (7) Our habits make or unmake us. | (7) All our habits are forces which make or unmake us. |
| (8) We all had a fine time. | (8) All the party were those who had a fine time. |
In argumentative discourse it is often sufficient to “think the proposition” in terms of the four elements without taking the time to actually express it.
4. LOGICAL AND GRAMMATICAL SUBJECT AND PREDICATE DISTINGUISHED.
The grammatical subject is one word while the logical subject is the grammatical subject with all its modifiers except the quantity sign. For example: in the proposition, “All white men are Caucasians,” men is the grammatical subject, while white men is the logical subject. All being the quantity sign simply indicates the extension of men and is not a part of the logical subject.
The grammatical predicate is the verb-form together with any predicate noun or adjective, while the logical predicate is the predicate word or words and all its modifiers. The grammatical predicate includes the copula, but the logical predicate never includes the copula. The grammatical predicate does not include the object, while the logical predicate always includes what is equivalent to the object and all its modifiers. To illustrate: in the proposition, “Some men are wise,” are wise is the grammatical predicate, while wise is the logical predicate. And in the proposition, “He burned the red house on thehill,” burned is the grammatical predicate, while the one who burned the red house on the hill is the logical predicate.