In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle's tractate On Interpretation and its distinction between two oppositions: contradiction and contrariety. However, Aristotle did not draw any diagram; this was done several centuries later.

In traditional logic, a proposition (Latin: propositio) is a spoken assertion (oratio enunciativa), not the meaning of an assertion, as in modern philosophy of language and logic. A categorical proposition is a simple proposition containing two terms, subject (S) and predicate (P), in which the predicate is either asserted or denied of the subject.

Every categorical proposition can be reduced to one of four logical forms, named A, E, I, and O based on the Latin affirmo (I affirm), for the affirmative propositions A and I, and nego (I deny), for the negative propositions E and O. These are:

In tabular form:

*Proposition A may be stated as "All S is P." However, Proposition E when stated correspondingly as "All S is not P." is ambiguous because it can be either an E or O proposition, thus requiring a context to determine the form; the standard form "No S is P" is unambiguous, so it is preferred. Proposition O also takes the forms "Some S is not P." and "A certain S is not P." (Latin 'Quoddam S nōn est P.')

** ${\displaystyle Sx}$ in the modern forms means that a statement ${\displaystyle S}$ applies on an object ${\displaystyle x}$. It may be simply interpreted as "${\displaystyle x}$ is ${\displaystyle S}$" in many cases. ${\displaystyle Sx}$ can be also written as ${\displaystyle S(x)}$.

Aristotle states (in chapters six and seven of the Peri Hermēneias (Περὶ Ἑρμηνείας, Latin De Interpretatione, English 'On Interpretation')), that there are certain logical relationships between these four kinds of proposition. He says that to every affirmation there corresponds exactly one negation, and that every affirmation and its negation are 'opposed' such that always one of them must be true, and the other false. A pair of an affirmative statement and its negation is, he calls, a 'contradiction' (in medieval Latin, contradictio). Examples of contradictories are 'every man is white' and 'not every man is white' (also read as 'some men are not white'), 'no man is white' and 'some man is white'.

The below relations, contrary, subcontrary, subalternation, and superalternation, do hold based on the traditional logic assumption that things stated as S (or things satisfying a statement S in modern logic) exist. If this assumption is taken out, then these relations do not hold.