Logica Universalis 2 (2):235-263 (2008)

Our aim is to show that translating the modal graphs of Moretti’s “n-opposition theory” (2004) into set theory by a suited device, through identifying logical modal formulas with appropriate subsets of a characteristic set, one can, in a constructive and exhaustive way, by means of a simple recurring combinatory, exhibit all so-called “logical bi-simplexes of dimension n” (or n-oppositional figures, that is the logical squares, logical hexagons, logical cubes, etc.) contained in the logic produced by any given modal graph (an exhaustiveness which was not possible before). In this paper we shall handle explicitly the classical case of the so-called 3(3)-modal graph (which is, among others, the one of S5), getting to a very elegant tetraicosahedronal geometrisation of this logic
Keywords Opposition theory  classical modal logic  Blanché’s logical hexagon  Aristotle’s square  logical bisimplexes  logical cube   β-structure  tetraicosahedron   n-opposition   n-partition of the true  strong n-opposition  weak n-opposition  Moretti’fs modal graph  set translation of modal graphs
Categories (categorize this paper)
DOI 10.1007/s11787-008-0038-y
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,247
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Sur l'opposition des concepts.Robert Blanche - 1953 - Theoria 19 (3):89-130.

Add more references

Citations of this work BETA

The Power of the Hexagon.Jean-Yves Béziau - 2012 - Logica Universalis 6 (1-2):1-43.
Metalogical Decorations of Logical Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
On the 3d Visualisation of Logical Relations.Hans Smessaert - 2009 - Logica Universalis 3 (2):303-332.

View all 16 citations / Add more citations

Similar books and articles


Added to PP index

Total views
164 ( #64,215 of 2,448,516 )

Recent downloads (6 months)
3 ( #226,386 of 2,448,516 )

How can I increase my downloads?


My notes