3. THE FOUR ELEMENTS OF A CATEGORICAL PROPOSITION.

Every categorical proposition should have four elements; namely, the quantity sign, the logical subject, the copula and the logical predicate. In the foregoing categorical propositions the quantity signs are respectively, every, all and no. In any case the quantity sign is always attached to the subject and indicates its breadth or extension. For example, in the two propositions, “All men are mortal” and “Some men are wise,” the quantity sign all makes the term man much broader than does the quantity sign some.

The logical subject of a categorical proposition is the term of which something is affirmed or denied, whereas the logical predicate of a categorical proposition is the term which is affirmed or denied of the subject. In the two propositions, “All men are mortal” and “No men are immortal,” the term about which something is affirmed or denied is men, while the terms which are affirmed and denied of the subject are respectively mortal and immortal. “Men” is, therefore, the logical subject of each proposition, while “mortal” is the logical predicate of the first and “immortal” the logical predicate of the second. The copula is the connecting word between the logical subject and predicate and denotes whether or not the latter is affirmed or denied of the former. The copula is always some form of “to be” or its equivalent. When the predicate is denied of the subject, “not” may be used with the copula and considered a part of it. To illustrate: in the logical proposition, “Some men are not wise,” “are not” may be regarded as the copula.

The four elements are indicated in the following categorical propositions:

Quantity signLogical subjectCopulaLogical predicate
Allfixed starsareself-luminous
Nowise manisgoing to steal
Somequadrupedsaredomestic animals
Someglittering thingsare notgold
Someboysare notdiscreet
A fewmenaremulti-millionaires
Everycitizenisduty-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.