Was Lewis Carroll an Amazing Oppositional Geometer? (2014), p. 387
by Moretti, Alessio

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Caption

The square of opposition revisited by Frege and Peirce. - Frege's own version of the logical square (1879)

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

Yes

Geometry

Shape

Square (regular)

Colinearity range

0

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

By central symmetry

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

No

Form

none

Label type

symbolic

Symbolic field

logic

Contains partial formulas or symbols

No

Logical system

predicate logic

Edge description

Style

Diagram is colored

No

Diagram is embellished

No

Tags

duality

Is a representation of

Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Louis Nebert. (p. 24)

Additional notes

At the bottom edge of the diagram, 'conträr' should be corrected to 'subconträr'.