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

by Moretti, Alessio

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### Caption

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

- 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
- Shape
- Square (regular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By central symmetry

### Logic

### Geometry

- 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

### Vertex description

### Edge description

- Diagram is colored
- Yes
- Diagram is embellished
- No
- Tags
- existential import

### Style

### 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