Subalternation and existence presuppositions in an unconventionally formalized canonical square of opposition (2016), p. 203
by Jacquette, Dale
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Caption
- Unconventional logical square of opposition 1
- Aristotelian family
- Non-Sigma
- Boolean complexity
- 4
- Number of labels per vertex (at most)
- 3
- 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
- Rectangle (irregular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- N.A.
Logic
Geometry
- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- Yes
- Form
- none
- Label type
- linguistic ,
- symbolic
- Language
- English
- Lexical field
- syllogistics
- Contains partial sentences or single words
- No
- Contains abbreviations
- Yes
- Symbolic field
- logic
- Contains partial formulas or symbols
- Yes
- Logical system
- syllogistics ,
- predicate logic
- Contains definitions of relations
- No
- Form
- solid lines ,
- none
- Has arrowheads
- Yes
- Overlap
- No
- Curved
- No
- Hooked
- No
- As wide as vertices
- No
- Contains text
- Yes
- Label type
- linguistic
- Language
- English
- Contains partial sentences or single words
- Yes
- Contain abbreviations
- No
Vertex description
Edge description
- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- existential import
Style
Additional notes
- The negation closure of this diagram is a Buridan sigma-4 (of Boolean complexity 4).
Note that $\exists x[Sx \to (\neg)Px]$ is not the correct formalization of the natural language statement `Some S is (not) P'.