Square of Opposition in Aristotelian Logic

radius of S

radius of P

contradictories

contraries

subcontraries

subalternation

Aristotelian logic, or the traditional study of deduction, deals with four so-called categorical (or subject-predicate) propositions, which can be defined by:

SaP

⇔ all

S

is

P

(universal affirmative or A proposition),

SiP

⇔ some

S

is

P

(particular affirmative or I proposition),

SeP

⇔ no

S

is

P

(universal negative or E proposition),

SoP

⇔ some

S

is not

P=

(particular negative or O proposition).

S

is called a subject (or minor) term and

P

is called a predicate (or major) term of the proposition. We could think of

S

and

P

as one-place nonempty predicates or sets.