logical geometry

2D Aristotelian diagrams

This page provides a number of 2D Aristotelian diagrams that can be constructed with bitstrings of length 4 (the bitstring representation format is introduced here; more details can be found in Paper P7 and Paper P10). Based on the types of bitstrings they contain, we distinguish various families of:

For the visual representation of the Aristotelian relations we use the following two colour and line coding systems: colour codes

Aristotelian squares

balanced classical square
classical square
2 bitstrings of level 1
2 bitstrings of level 3
balanced degenerated square
degenerated square
4 bitstrings of level 2

Aristotelian hexagons

JSB strong hexagon
Sacoby-Sesmat-Blanché hexagon (strong)
2 bitstrings of level 1
2 bitstrings of level 2
2 bitstrings of level 3
JSB weak hexagon
Sacoby-Sesmat-Blanché hexagon (weak)
3 bitstrings of level 1
3 bitstrings of level 3
SC hexagon
Sherwood-Czezowski hexagon
(Moretti-Pellissier)
2 bitstrings of level 1
2 bitstrings of level 2
2 bitstrings of level 3
unconnected-4 hexagon
Unconnected-4 hexagon
(Smessaert-Demey)
1 bitstring of level 1
4 bitstrings of level 2
1 bitstring of level 3
unconnected-12 hexagon
Unconnected-12 hexagon
(Smessaert-Demey)
6 bitstrings of level 2

Aristotelian octagons

Moretti-Pellissier octagon
Moretti-Pellissier octagon
4 bitstrings of level 1
4 bitstrings of level 2
Béziau octagon
Béziau octagon
2 bitstrings of level 1
4 bitstrings of level 2
2 bitstrings of level 3
Buridan octagon
Buridan octagon
2 bitstrings of level 1
4 bitstrings of level 2
2 bitstrings of level 3