On the Aristotelian Roots of the Modal Square of Opposition (2021), p. 335
by Geudens, Christophe; Demey, Lorenz
Copyright according to our policy
Caption
- The relations from T1-T10 mapped onto the modal quadrants (rearranged)$^{36}$
- Aristotelian family
- Classical Sigma-2
- Boolean complexity
- 3
- Number of labels per vertex (at most)
- 5
- Equivalence between (some) labels of the same vertex
- Yes
- Analogy between (some) labels of the same vertex
- No
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Rectangle (irregular)
- 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
- rectangular
- Label type
- linguistic ,
- generic placeholders
- Language
- English
- Lexical field
- modalities
- Contains partial sentences or single words
- Yes
- Contains abbreviations
- No
- Contains definitions of relations
- No
- Form
- solid lines ,
- none ,
- dashed lines
- Has arrowheads
- Yes
- Overlap
- No
- Curved
- No
- Hooked
- No
- As wide as vertices
- No
- Contains text
- No
- Label type
- none
Vertex description
Edge description
- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- Leuven ;
- duality
Style
Additional notes
- Footnote 36 (cf. caption) reads as follows: "As opposed to Fig. 1 and Fig. 2, arrows in Fig. 6 indicate entailment relations, not subalternation relations. Also note that within each quadrant, we do not display those entailments that follow (by transitivity) from the entailments that are displayed, in order to optimize visual clarity. This concretely means that (i) the entailment from the predicate of possibility to the predicate of impossibility and (ii) the entailments from the predicates of possibility and contingency to the predicate of necessity in each quadrant are not displayed." (Pp. 335-336.)