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Accepted on proposition of the following jury: (2009)
BibTeX
@MISC{Moretti09acceptedon,
author = {Alessio Moretti and Jean-yves Béziau Co-supervisor and Daniel Schulthess Co-supervisor and Dominique Luzeaux Examinator and Paul Mcnamara Examinator and Hans Smessaert Examinator},
title = {Accepted on proposition of the following jury:},
year = {2009}
}
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Abstract
geometry of oppositions, n-opposition, square of opposition, logical square, logical hexagon, logical bi-simplexes, logical poly-simplexes, contradiction, modal logic, concept, spatial logics, n-dimensional geometry, central symmetry, simplexes, Aristotelian p q-semantics, Aristotelian p q-lattice, conceptual spaces. Summary: The present work is devoted to the exploration of some formal possibilities suggesting, since some years, the possibility to elaborate a new, whole geometry, relative to the concept of “opposition”. The latter concept is very important and vast (as for its possible applications), both for philosophy and science and it admits since more than two thousand years a standard logical theory, Aristotle’s “opposition theory”, whose culminating formal point is the so called “square of opposition”. In some sense, the whole present enterprise consists in discovering and ordering geometrically an infinite amount of “avatars ” of this traditional square structure (also called “logical square ” or “Aristotle’s square”). The results obtained here go even beyond the most optimistic previous expectations, for it turns out that such a geometry exists indeed and offers to science many new conceptual insights and formal tools.
Keyphrases
following jury logical square latter concept formal possibility called square infinite amount formal point whole geometry n-dimensional geometry modal logic aristotelian q-lattice traditional square structure standard logical theory optimistic previous expectation logical bi-simplexes spatial logic central symmetry present work logical hexagon formal tool conceptual space whole present enterprise aristotelian q-semantics possible application aristotle opposition theory many new conceptual insight logical poly-simplexes
