Thinking Outside the Square of Opposition Box (2012), p. 78
by Jacquette, Dale

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Caption

Noncanonical Alternative Square of Opposition 2

Logic

Aristotelian family

Classical Sigma-2

Boolean complexity

3

Number of labels per vertex (at most)

3

Equivalence between (some) labels of the same vertex

No

Analogy between (some) labels of the same vertex

No

Uniqueness of the vertices up to logical equivalence

No

Errors in the diagram

No

Geometry

Shape

Rectangle (irregular)

Colinearity range

0

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

By some other geometric feature

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

Yes

Form

none

Label type

linguistic

,

symbolic

Language

English

Lexical field

syllogistics

Contains partial sentences or single words

No

Contains abbreviations

Yes

Symbolic field

logic

Contains partial formulas or symbols

Yes

Logical system

syllogistics

,

predicate logic

Edge description

Style

Diagram is colored

No

Diagram is embellished

No

Additional notes

This is a 'twisted square': the contradiction relations are on the vertical edges, rather than on the diagonals.