The Logic of Modality (2016), p. 356
by Strobino, Riccardo; Thom, Paul

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Caption

Hexadecagon of opposition for alethic and temporal simple propositions on the substantial reading

Legend

Logic

Aristotelian family

Sigma-8 Graph

Number of labels per vertex (at most)

1

Uniqueness of the vertices up to logical equivalence

Yes

Errors in the diagram

No

Geometry

Shape

Octagon (irregular)

Colinearity range

0–2

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

By some other geometric feature

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

Yes

Form

none

Label type

symbolic

Symbolic field

logic

Contains partial formulas or symbols

Yes

Logical system

modal syllogistics

Edge description

Contains definitions of relations

No

Form

dotted lines

,

solid lines

,

none

Has arrowheads

Yes

Overlap

No

Curved

No

Hooked

No

As wide as vertices

No

Contains text

No

Label type

none

Style

Diagram is colored

No

Diagram is embellished

No

Has related diagram

Strobino, Riccardo. 2018. “Ibn Sina’s Logic.” In Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. Stanford, CA: CSLI. (online)

Additional notes

(i) Alethic modalities:
- $L$: substantial necessity
- $M_1$: substantial one-sided possibility

(ii) Temporal modalities:
- $A$: substantial perpetuity
- $X_1$: substantial one-sided absoluteness

(Cf. p. 353.)