Diagrams, conceptual space and time, and latent geometry. Toward the Development of Euclidean Axiomatics

The ``origins'' of (geometric) space is examined from the perspective of the so-called ``conceptual space'' or ``semantic space''. Semantic space is characterized by its fundamental ``locality'' that generates an ``implicit'' mode of geometrizing. This view is examined from within three perspectives. First, the role that various diagrammatic entities play in the everyday life and pragmatic activities of selected ethnic groups is illustrated. Secondly, it is shown how conceptual spaces are fundamentally linked to the meaning effects of particular natural languages and these are very different from the global and universal aspects of Euclidean spaces. Thirdly, it is contended that these modes of creating body and culture-based spatial frameworks and related cosmogonies and cosmologies can be described as forms of ``latent geometry'' that initially appear unexplainable in any rational way. Nonetheless, and thanks to the deep mathematical reflections provided by Ren'{e} Thom, it is illustrated how the various ways of generating space can be further analyzed as distortions of mainstream spatialization furnished by Euclidean geometry that established the dominant universality of the ideas of space (and time).