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Concept
Square of opposition
Summary
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 by Apuleius and Boethius.
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:
The A proposition, the universal affirmative (universalis affirmativa), whose form in Latin is 'omne S est P', usually translated as 'every S is a P'.
The E proposition, the universal negative (universalis negativa), Latin form 'nullum S est P', usually translated as 'no S are P'.
The I proposition, the particular affirmative (particularis affirmativa), Latin 'quoddam S est P', usually translated as 'some S are P'.
The O proposition, the particular negative (particularis negativa), Latin 'quoddam S nōn est P', usually translated as 'some S are not P'.
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 "Sometimes S is not P." and "A certain S is not P." (literally the Latin 'Quoddam S nōn est P.
Official source
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