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Leonardi.DB
a logical geometry project

The Syllogism Revised (1952), p. 4
by Reichenbach, Hans

Caption

CUBE OF OPPOSITION

Logic

Aristotelian family
Moretti-Pellissier Sigma-4
Boolean complexity
5
Number of labels per vertex (at most)
1
Uniqueness of the vertices up to logical equivalence
Yes
Errors in the diagram
No

Geometry

Shape
Cube (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
No
Logical system
syllogistics

Edge description

Contains definitions of relations
No
Form
solid lines
,
none
,
dashed lines
Has arrowheads
No
Overlap
No
Curved
No
Hooked
No
As wide as vertices
No
Contains text
Yes
Label type
linguistic
Language
English
Contains partial sentences or single words
Yes
Contain abbreviations
No

Style

Diagram is colored
No
Diagram is embellished
No
Tags
subject negation
;
generalized Post duality

Additional notes

This diagram contains the 8 formulas of syllogistics with subject negation. Usually, these formulas are used to construct a Keynes-Johnson sigma-4, based on four existential import assumptions (viz.: there is at least one S, at least one non-S, at least one P, at least one non-P). However, Reichenbach additionally makes two 'differential import' assumptions (viz.: S is distinct from P, S is distinct from non-P), thus obtaining a Moretti-Pellissier sigma-4.
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