Proposition pour un archétype urbain logico-géographique : l’association « logique trichotomique -logique ternaire antagoniste » et son intérêt géographique

Abstract

Our previous papers showed the interest of using both structural binary logic and, particularly, processual ternary logic to apprehend resilience in urban geography. This paper is an in depth exploration of the association of S. Lupasco’s antagonistic ternary logic and the logic proposed by J.-Y. Béziau, in his work on the power of the hexagon. The heuristic improvements that these logics – amply explicated here – can bring to city systems issues are further examined. First by drawing from the results of the previous papers which defined the city as a type of geo-anthroposystem; then, by using current studies in mathematics, logic and geography which evolved a ternary thinking, integrating or exceeding the traditional binary-based thinking.The initial postulate behind this work was what can be called the “hexagonal” logic of R. Blanche and J.-Y. Beziau. Comparing a geographic hexagon, developed with well-known or easily understood urban concepts, to the trichotomic hexagon proposed by these authors produced a real but partial correspondence between the two forms, limited to the structure. This made it necessary to associate it with S. Lupasco’s antagonistic ternary logic to achieve a logico-geographical structure-processual construction of an urban geo-anthroposystem. Conceived on this basis, the resulting diagram goes beyond the initial requirement and establishes itself as an axiomatic construction conducive to verification and refutation: it can then be proposed as the archetype for any urban area, whether finished or in progress.

Keywords

• complexity
• logic
• resilience
• geo-anthroposystem
• hexagon
• contradictory ternary logic