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 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 (2) The man was one who saw the swell coming along. turnout coming along.