# Was Lewis Carroll an Amazing Oppositional Geometer? (2014), p. 394

by Moretti, Alessio

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### Caption

- Arrows are more informative than lines (no harm being done to Carroll's logic).

- Aristotelian family
- Classical Sigma-7
- Boolean complexity
- 4
- Number of labels per vertex (at most)
- 1
- Uniqueness of the vertices up to logical equivalence
- No
- Errors in the diagram
- No
- Shape
- Triangle (regular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By some other geometric feature

### Logic

### Geometry

- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- No
- Form
- dots
- Label type
- symbolic
- Symbolic field
- logic
- Contains partial formulas or symbols
- Yes
- Logical system
- predicate logic

### Vertex description

### Edge description

- Diagram is colored
- Yes
- Diagram is embellished
- No
- Tags
- Boolean closed ;
- 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 Greek notation) can be represented as follows:

1000 = $ \alpha\beta\delta $

0100 = $ \alpha\beta\gamma $

0010 = $ \alpha\gamma\delta $

0001 = $ \beta\gamma\delta $

1100 = $ \alpha\beta $

1010 = $ \alpha\delta$

1001 = $ \beta\delta $

0110 = $ \alpha\gamma $

0101 = $ \beta\gamma $

0011 = $ \gamma\delta $

1110 = $ \alpha $

1101 = $ \beta $

1011 = $ \delta $

0111 = $ \gamma $

Note: $\alpha\beta$ means $\alpha\wedge\beta$ (cf. p. 391).

Note that $\alpha$ occurs three times in this diagram (viz., on the three vertices of the large triangle), and that each of $\alpha\beta$, $\alpha\gamma$ and $\alpha\delta$ occurs two times in this diagram (viz., twice on each edge of the large triangle).