From Di-alectics to N-alectics: Indigenous Cultures and Ancestral  Philosophies in Latin America

Florentin Smarandache; Maikel Y. Leyva Vázquez

Authors

Florentin Smarandache Florentin Smarandache, Profesor Emérito de Matemáticas en la Universidad de Nuevo México, Gallup , Nuevo México, EE.UU.;
Maikel Y. Leyva Vázquez Universidad Bolivariana del Ecuador, Durán, Guayas Ecuador; Universidad de Guayaquil, Guayas Ecuador;

Keywords:

n-alectic, neutrosophic logic, indigenous philosophy, ethical decision-making, Andean cosmology, Mesoamerican worldview

Abstract

This paper explores the n-alectic framework, which extends traditional di-alectic and tri-alectic
models by integrating multiple subcomponents through refined neutrosophic logic. Drawing from pre
Columbian philosophies, particularly Mesoamerican, Andean, and Amazonian traditions, the study
demonstrates how indigenous worldviews align with n-alectic structures. The figure of
Quetzalcóatl/Kukulkán illustrates a triadic balance of sky, earth, and underworld, while Andean Yanantin
and Pachakuti reflect complementary duality and transformation. Shuar cosmology further exemplifies a
complex n-alectic system, where multiple spiritual and natural forces interact dynamically. The ethical
decision-making model, applied to resource extraction and Pachamama principles, utilizes weighted
metrics and neutrosophic distance calculations to evaluate sustainable choices. Results highlight n-alectic
reasoning as a powerful tool for balancing economic, environmental, and social factors, promoting
harmonious integration of opposing forces in decision-making.

DOI: 10.5281/zenodo.14795614