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Leonardi.DB
a logical geometry project

Aristotelian Logic (1991), p. 172
by Parry, William T.; Hacker, Edward A.

Caption

"Modern" Square of Opposition for A priori Categoricals

Logic

Aristotelian family
Sigma-0 Graph
Boolean complexity
1
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
linguistic
Language
English
Lexical field
categorical
Contains partial sentences or single words
No
Contains abbreviations
No

Edge description

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
,
symbolic
Language
English
Contains partial sentences or single words
Yes
Contain abbreviations
No
Symbolic field
logic
Contains partial formulas or symbols
Yes
Logical system
propositional logic

Style

Diagram is colored
No
Diagram is embellished
No
Tags
Boolean closed
;
non-contingent formulas

Additional notes

'All men are animals' and 'Some men are animals' are tautological (under the assumption of existential import), while 'No men are animals' and 'Some men are not animals' are contradictory (under that same assumption). Hence this diagram contains only non-contingent formulas, and is thus a sigma-0 diagram.

The edges are labeled with propositional connectives corresponding to the Aristotelian relations (cf. Theorem 1 of Smessaert & Demey, 2014, Logical Geometries and Information in the Square of Oppositions, Journal of Logic, Language and Information 23 : 527 - 565).
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