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. 413
by Kienzler, Wolfgang

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Caption

UEBERWEG 1857 half-rejects subcontrary, follows Trendelenburg.

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 ...)

Yes

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

Contradiction is on the horizontal edges, rather than on the diagonals.