Subalternation and existence presuppositions in an unconventionally formalized canonical square of opposition (2016), p. 199
by Jacquette, Dale
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Caption
- Existential expansions of A and E categoricals
- Aristotelian family
- Classical Sigma-2
- Boolean complexity
- 3
- 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
- Yes
- 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 ...)
- 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
- 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
- Assuming that we are working relative to standard first-order logic (FOL), this diagram contains the following errors:
- $\exists x Sx \wedge \forall x [Sx \to Px]$ and $\exists x [Sx \wedge \neg Px]$ are said to be contradictory, but they are actually contrary
- $\exists x Sx \wedge \forall x [Sx \to \neg Px]$ and $\exists x [Sx \wedge Px]$ are said to be contradictory, but they are actually contrary
- $\exists x [Sx \wedge Px]$ and $\exists x [Sx \wedge \neg Px]$ are said to be subcontrary, but they are actually unconnected (independent)
(The contrariety and the two subalternations in this diagram are correct.) - $\exists x Sx \wedge \forall x [Sx \to Px]$ and $\exists x [Sx \wedge \neg Px]$ are said to be contradictory, but they are actually contrary