_What constitutes a Proposition._--All reasoning deals with propositions, which are judgments expressed. Every proposition involves two distinct conceptions, and expresses the relation between them; affirms the agreement or disagreement of the one with the other. As when I say, Snow is white, the conception of snow is before my mind, and also of whiteness; I perceive that the latter element enters into my notion of snow, and constitutes one of the qualities of the substance so called; I affirm the relation of the two, accordingly, and this gives the proposition enunciated. Every proposition then consists of these several parts, a word or words expressing some conception, a word or words expressing some other conception, a word or words expressing the relation of the two. The words which designate these two conceptions are called the _terms_ of the proposition, and, according to the above analysis, there are, in every proposition, always two terms. That term or conception of which something is affirmed, is called the _subject_, that which is affirmed of the same, the _predicate_, and the word which expresses the relation of the two, the _copula_. In the above proposition, snow is the subject, white, the predicate, and is, the copula. _Quality and Quantity._--Propositions are distinguished as to _quality_ and _quantity_. The former has reference to the affirmative or negative character of the proposition, the latter to its comprehensiveness. Every proposition is either affirmative or negative, which is called its quality. As to quantity, every proposition is either _universal_, affirming something of the whole of the subject--as, All men are mortal; or else _particular_, affirming something of only a part of the subject--as, Some tyrants are miserable. _Four kinds of categorical Propositions._--We have, then, four kinds of categorical propositions, viz., universal affirmative, universal negative, particular affirmative, particular negative. That is, with the same subject and predicate, it is always possible to state four distinct propositions; as, every A is B, no A is B, some A is B, some A is not B. For the sake of convenience, logicians designate these different kinds of propositions severally by the letters A, E, I, O. Propositions that thus differ in quantity and quality are said to be opposed to each other. Of these, the two universals, A and E, are called contraries; the two particulars, I and O, sub-contraries; the universal affirmative, and the particular affirmative, A and I, also the universal negative and the particular negative, E and O, are respectively subalterns; while the universal affirmative and the particular negative, A and O, as also the universal negative and particular affirmative, E and I, are contradictories.