Multiple Quantification and the Use of Special Quantifiers in Early Sixteenth Century Logic (1978), p. 602
by Ashworth, E. Jennifer
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- Aristotelian family
- Classical Sigma-2
- Boolean complexity
- 3
- Number of labels per vertex (at most)
- 1
- 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
- none
- Label type
- linguistic
- Language
- English
- Lexical field
- syllogistics ,
- quantifiers
- Contains partial sentences or single words
- No
- Contains abbreviations
- Yes
Vertex description
Edge description
- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- supposition theory
Style
Additional notes
- The letter 'a' is used to indicate that the term following it has merely confused supposition; the letter 'b' is used to indicate that the term following it has determinate supposition (cf. p. 601 - 602).
"Every A is b.B" can be formalized as: $\exists x (Bx \wedge \forall y(Ay \to y = x))$.
"a.A is not B" can be formalized as: $\forall x (Bx \to \exists y(Ay \wedge y \neq x))$.
(Note that there is a typo in the example formalization at the bottom of p. 601: the two highest-level disjunction signs should actually be conjunction signs.)