On the Aristotelian Roots of the Modal Square of Opposition (2021), p. 332
by Geudens, Christophe; Demey, Lorenz

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Caption

Aristotle's modal diagram at $\textit{De int.}$ 13, 22a14-22b28

Logic

Aristotelian family

Classical Sigma-2

Boolean complexity

3

Number of labels per vertex (at most)

5

Equivalence between (some) labels of the same vertex

Yes

Analogy between (some) labels of the same vertex

No

Uniqueness of the vertices up to logical equivalence

Yes

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 ...)

No

Form

none

Label type

linguistic

,

generic placeholders

Language

English

Lexical field

modalities

Contains partial sentences or single words

Yes

Contains abbreviations

No

Edge description

Contains definitions of relations

No

Form

none

Has arrowheads

No

Overlap

No

Curved

No

Hooked

No

As wide as vertices

No

Contains text

No

Label type

none

Style

Diagram is colored

No

Diagram is embellished

No

Tags

Leuven

;

duality