Definition of the Proposition
The proposition defined as a judgment expressed in terms, with its three elements (subject, predicate, copula), the reduction of propositions to logical form, and the properties of quantity and quality.
A proposition is a judgment expressed in terms: a formula affirming or denying a predicate of a subject by means of the copula. Its three elements are the subject, the predicate, and the copula (always the present indicative of 'to be'); subject and predicate together form the material element, the copula the formal element. Propositions using other verbs and tenses are reducible to this logical form ('John ran away' becomes 'John is one-having-run-away'); negation belongs essentially to the copula even when expressed by a particle prefixed to the subject. Every proposition has 'quality' (affirmative or negative, by its copula) and 'quantity' (universal or particular, by the Extension of its subject).
Chapter II — The Judgment Expressed
Just as the idea is expressed exteriorly by the term, so the judgment is expressed exteriorly by the Proposition. This Chapter studies the nature of the Proposition, defines and classifies it, and sets forth the relative properties of Propositions.
The Chapter is accordingly divided into the following Articles:
- Article 1. Definition of the Proposition
- Article 2. Classification of the Proposition
- Article 3. Relative Properties of Propositions
Article 1. Definition of the Proposition
A proposition is a judgment expressed in terms.
In other words, it is a formula of terms which affirms or denies a predicate of a subject, such affirmation or denial being expressed by the copula. Thus every proposition has three elements:
- subject: a term expressing the idea of which another idea is affirmed or denied;
- predicate: a term expressing the idea which is affirmed or denied of the subject;
- copula: the present tense of the verb “to be,” by which the affirmation or denial is expressed.
The subject and predicate together constitute the material element of the proposition, and the copula (which is the expression of the judgment proper) is the formal element.
The copula is always the present tense, indicative mood, of the verb “to be.” Propositions that contain other verbs and other tenses are reducible to logical form, that is to say, such propositions may be restated in the subject-copula-predicate form. Examples of propositions already in logical form are: “Gold is precious”; “The man is not old.” Examples of reduction to logical form are the following:
| Original Form | Logical Form |
|---|---|
| John ran away | John is one-having-run-away |
| Mary will play | Mary is one-about-to-play |
| Charles has not arrived | Charles is not one-having-arrived |
| Patience brings blessings | Patience is a-thing-bringing-blessings |
| No man has been prejudged | All men are not those-prejudged |
Notice two things here: 1. the mode or manner of reducing a proposition to logical form, and 2. the fact that negative propositions have their negation essentially in the copula, even when the verb is positive and the negative is expressed in a particle prefixed to the subject. The last example given above illustrates the point.
When the verb “to be” is used in the sense of “to exist,” as in the proposition, “God is,” the reduction is effected by substituting “to exist” for “to be” and proceeding as shown above. Thus “God is” becomes, in logical form, “God is one-existing.”
Every proposition has the properties known as “quality” and “quantity.” The quality of a proposition is determined by the copula as affirmative or negative. The quantity of a proposition is determined by the Extension of its subject as universal or particular. Thus the proposition, “All men are mortal” is universal in quantity, and affirmative in quality; while the proposition, “Some men are not wise” is particular in quantity, and negative in quality.
Summary of the Article
This short Article has furnished us the definition of the proposition; has set forth its elements in detail, and has classed these as formal and material. It has furnished us with a short but sufficient account of what is meant by the “quantity” and “quality” of propositions.