The Roots of (Scalar) Implicature (2014), p. 21
by Horn, Laurence

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Caption

Jespersen's three-sided square (a.k.a. tripartition) of opposition

Logic

Aristotelian family

Contrariety 3-clique

Boolean complexity

3

Number of labels per vertex (at most)

1

Uniqueness of the vertices up to logical equivalence

Yes

Errors in the diagram

No

Geometry

Shape

Triangle (irregular)

Colinearity range

0

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

N.A.

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

No

Form

none

Label type

symbolic

Symbolic field

logic

Contains partial formulas or symbols

Yes

Logical system

syllogistics

Edge description

Style

Diagram is colored

No

Diagram is embellished

No

Additional notes

The current annotation focuses on the triangle 'in the background'. The annotation for the square 'in the foreground' can be found here.

A and C are identical to the canonical A and E, respectively. B is equivalent to I $\wedge$ O.

The negation closure of this diagram is a JSB sigma-3.