Caramuel's Theory of Opposition (2017), p. 366
by Lenzen, Wolfgang
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Caption
- Caramuel's "Cube of opposition"
- Aristotelian family
- Buridan Sigma-4
- Boolean complexity
- 6
- Number of labels per vertex (at most)
- 2
- Equivalence between (some) labels of the same vertex
- No
- Analogy between (some) labels of the same vertex
- No
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Cube (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
- none
- Label type
- linguistic ,
- symbolic
- Language
- Latin
- Lexical field
- syllogistics
- Contains partial sentences or single words
- No
- Contains abbreviations
- No
- Symbolic field
- logic
- Contains partial formulas or symbols
- No
- Logical system
- predicate logic
- 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
- Yes
- Diagram is embellished
- No
- Tags
- oblique terms ;
- composed operator duality
Style
Additional notes
- DQ1: $\forall x\forall y E(x,y)$
DQ2: $\exists x\forall y E(x,y)$
DQ3: $\forall x\exists y E(x,y)$
DQ4: $\exists x\exists y E(x,y)$
DQ5: $\exists x\exists y \neg E(x,y)$
DQ6: $\forall x\exists y \neg E(x,y)$
DQ7: $\exists x\forall y \neg E(x,y)$
DQ8: $\forall x\forall y \neg E(x,y)$
Cf. p. 360.