Logica Universalis 10 (2-3):233-292 (2016)

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams and four kinds of metalogical decorations.
Keywords Aristotelian diagram  duality diagram  metalogic  opposition geometry  implication geometry  contrariety
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DOI 10.1007/s11787-015-0136-6
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References found in this work BETA

The Power of the Hexagon.Jean-Yves Béziau - 2012 - Logica Universalis 6 (1-2):1-43.
Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
Sur l'opposition des concepts.Robert Blanche - 1953 - Theoria 19 (3):89-130.
On the 3d Visualisation of Logical Relations.Hans Smessaert - 2009 - Logica Universalis 3 (2):303-332.
“Setting” N-Opposition.Régis Pellissier - 2008 - Logica Universalis 2 (2):235-263.

View all 18 references / Add more references

Citations of this work BETA

Using Syllogistics to Teach Metalogic.Lorenz Demey - 2017 - Metaphilosophy 48 (4):575-590.
Duality in Logic and Language.Lorenz Demey, and & Hans Smessaert - 2016 - Internet Encyclopedia of Philosophy.

View all 11 citations / Add more citations

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