The Logical Square and the Table of Oppositions. Five Puzzles about the Traditional Square of Opposition Solved by Taking up a Hint from Frege (2012), p. 409
by Kienzler, Wolfgang

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Logic

Aristotelian family

Classical Sigma-2

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

Square (regular)

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 ...)

No

Form

none

Label type

linguistic

Language

English

Lexical field

syllogistics

Contains partial sentences or single words

No

Contains abbreviations

Yes

Edge description

Style

Diagram is colored

No

Diagram is embellished

No

Tags

duality

Additional notes

Contradiction is on the vertical edges, rather than on the diagonals. Subcontrariety and subalternation are not explicitly visualized.