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Leonardi.DB
a logical geometry project

# Was Lewis Carroll an Amazing Oppositional Geometer? (2014), p. 392 by Moretti, Alessio

### Caption

Carroll's mysterious first logical chart seems to contain at least one logical square.

### 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
No

### 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
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
existential import

### Additional notes

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