The essential characteristics of a proposition are the following. First, it must be expressed in language; an unspoken judgement is not yet a proposition. Second, it must take the form of an assertion that affirms or denies one term of another. Third, it must be capable of truth or falsity — questions, commands and exclamations are not propositions because they cannot be true or false. Fourth, it must be analysable into a definite subject, a definite predicate and a copula.

Every standard proposition has three parts: (i) the subject, the term about which something is stated; (ii) the predicate, the term that is stated about the subject; and (iii) the copula, the sign of the relation between subject and predicate, which must be the verb ‘to be’ in the present tense and which indicates either affirmation or denial. For example, in “All men are mortal”, ‘all men’ is the subject, ‘mortal’ is the predicate and ‘are’ is the copula. By rewriting ordinary sentences in this strict subject–copula–predicate form, the logician makes them ready for the formal operations of opposition, conversion and syllogism.

Proposition and sentence: Every proposition is necessarily a sentence, because it is expressed in words. But every sentence is not a proposition. A sentence is the unit of grammar; it may be assertive, interrogative, imperative, optative or exclamatory. Out of these, only the assertive sentence corresponds to a proposition. “The door is closed” is both a sentence and a proposition. “Is the door closed?” is a sentence but not a proposition because it neither affirms nor denies. Again, a sentence is judged correct by the rules of grammar, but a proposition is judged true or false by the rules of logic. A sentence need not stand in the strict subject–copula–predicate form, while a proposition must.

Proposition and judgement: A judgement is a mental act in which the mind compares two ideas and either combines or separates them. A proposition is that very judgement put into words. Judgement is the inner thought, proposition is its outer expression. Judgement is studied by psychology, while proposition is studied by logic. Judgement may exist silently in the mind, but a proposition cannot exist without language. The same judgement, e.g., that fire is hot, may be expressed in many languages, giving many propositions, but the underlying judgement is one. Thus a proposition is a sentence that has the logical form of an assertion, and it is also a judgement that has been verbally expressed.

Classification by quality: Quality depends on the copula. If the copula affirms the predicate of the subject, the proposition is affirmative: “All flowers are beautiful.” If the copula denies the predicate of the subject, the proposition is negative: “No flowers are eternal.” Thus quality refers to whether the proposition affirms or denies.

Classification by quantity: Quantity depends on the subject. If the predicate is affirmed or denied of the whole subject, the proposition is universal: “All birds are animals”, “No birds are fish.” If the predicate is affirmed or denied of only a part of the subject, the proposition is particular: “Some birds are black”, “Some birds are not migratory.” Thus quantity refers to how much of the subject is taken into the assertion.

Four-fold combination: By combining the two divisions we obtain four standard categorical propositions, named by the vowels A, E, I and O after the Latin words AffIrmo (I affirm) and nEgO (I deny):
(i) A — Universal Affirmative: “All men are mortal.” Predicate affirmed of the whole subject.
(ii) E — Universal Negative: “No men are perfect.” Predicate denied of the whole subject.
(iii) I — Particular Affirmative: “Some men are wise.” Predicate affirmed of part of the subject.
(iv) O — Particular Negative: “Some men are not wise.” Predicate denied of part of the subject.

This A E I O scheme is the cornerstone of the entire traditional theory of opposition, conversion and the categorical syllogism.

Categorical proposition: A categorical proposition is one in which the predicate is affirmed or denied of the subject directly, without any condition or alternative. The relation is asserted absolutely. Examples: “Honey is sweet”, “No man is perfect”, “Some flowers are red.” All A, E, I and O propositions are categorical.

Hypothetical proposition: A hypothetical (or conditional) proposition is one in which the relation between subject and predicate is asserted only on a condition expressed by ‘if-then’. It is composed of two parts: the antecedent (the ‘if’ clause, stating the condition) and the consequent (the ‘then’ clause, stating what follows). Example: “If it rains, the ground gets wet.” Here the wetness of the ground is asserted only on the condition that it rains. A hypothetical proposition does not state that either part is actually true; it only states the connection between them.

Disjunctive proposition: A disjunctive proposition asserts an alternative between two or more predicates connected by ‘either-or’. Example: “Either he is mad or he is drunk.” This proposition asserts that at least one of the alternatives must be true, though it does not say which. Disjunctive propositions are useful in arguments by elimination, where we deny one alternative to affirm the other.

Categorical propositions are simple and unconditional, while hypothetical and disjunctive propositions are compound, because each of them is composed of two simple propositions joined by a logical connective (‘if-then’ or ‘either-or’).

A singular proposition is one whose subject denotes a single, definite individual — a person, place or thing — and not a class. Examples: “Socrates is wise”; “Mount Everest is the highest peak in the world”; “Delhi is the capital of India.” At first sight a singular proposition seems to be neither universal (because the subject is one individual, not a class) nor particular (because we do not say ‘some’).

Reduction: Traditional logic resolves this difficulty by treating a singular proposition as equivalent to a universal proposition. The reasoning is as follows: in a singular proposition the predicate is affirmed or denied of the whole of its subject, since the subject denotes only one individual and the assertion exhausts that individual completely. Now the very definition of a universal proposition is that the predicate is affirmed or denied of the whole subject. Hence a singular proposition fulfils the definition of a universal proposition and is logically reduced to one. If the copula is affirmative, the singular proposition is reduced to A (Universal Affirmative): “Socrates is wise” becomes “Socrates is a wise man” and is treated as A. If the copula is negative, it is reduced to E (Universal Negative): “Ravana is not virtuous” is treated as E. This reduction enables singular propositions to take their place in the standard machinery of opposition and the categorical syllogism.