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Leonardi.DB
a logical geometry project

# Was Lewis Carroll an Amazing Oppositional Geometer? (2014), p. 398 by Moretti, Alessio

### Caption

Carrollâ€“Richards' tetrahedron is in fact an oppositional tetrahexahedron.

### 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
Yes
Errors in the diagram
No

### Geometry

Shape
Tetrahedron (regular)
Colinearity range
1
Coplanarity range
1
Cospatiality range
0
By diametric opposition (but no central symmetry)

### Vertex description

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

### 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 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).

3 of the 14 vertices are not explicitly drawn.