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Leonardi.DB
a logical geometry project

# Was Lewis Carroll an Amazing Oppositional Geometer? (2014), p. 402 by Moretti, Alessio

### Caption

Six Carrollian strong oppositional hexagons (indicial and vernacular reading).

### Logic

Aristotelian family
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
Hexagon (regular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
By central symmetry

### Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
dots
Label type
linguistic
Language
English
Lexical field
syllogistics
Contains partial sentences or single words
No
Contains abbreviations
Yes

### Style

Diagram is colored
Yes
Diagram is embellished
No
Tags
Boolean closed
;
existential import

Consider the following partition:
1) A! (all x are y, and there is at least one x)
2) I $\wedge$ O (some x are y and some x are not y)
3) E! (no x are y, and there is at least one x)
4) there are no x

With the bitstrings based on this partition, the formulas of this diagram (in vernacular notation) can be represented as follows:

1000 = all x are y
0100 = some x are y and some x are y'
0010 = all x are y'
0001 = there are no x
1100 = some x are y
1010 = all x are y or all [x] are y'
1001 = no x are y'
0110 = some x are y'
0101 = not all x are y nor are all y' [not all x are y and not all x are y']
0011 = no x are y
1110 = some x exist
1101 = not all x are y'
1011 = no x are y or none [i.e. no x] are y'
0111 = not all x are y