# Thinking Outside the Square of Opposition Box (2012), p. 86

by Jacquette, Dale

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### Caption

- Revised and Expanded Square of Opposition with A(V) and O(V) Inversions

- Aristotelian family
- Degenerate Sigma-3 with Unconnectedness 4
- Boolean complexity
- 4
- 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
- Yes
- Errors in the diagram
- No
- Shape
- Hexagon (irregular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By central symmetry

### Logic

### Geometry

- 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
- Contains definitions of relations
- No
- Form
- solid lines
- Has arrowheads
- Yes
- Overlap
- No
- Curved
- No
- Hooked
- No
- As wide as vertices
- No
- Contains text
- Yes
- Label type
- linguistic
- Language
- English
- Contains partial sentences or single words
- Yes

### Vertex description

### Edge description

- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- subject negation

### Style

### Additional notes

- We assume that the extension of P is not the entire domain, so that A and A(V) are contraries. Furthermore, we assume that it is possible that S is the complement of P, so that E and A(V) are unconnected. Under these assumptions, this diagram is a U4 sigma3.