Finite Relativist Geometry Grounded in Perceptual Operations

Formal geometry is a fundamental tool for showing how relevant metric qualities, such as depths, lengths, and volumes, as well as location concepts, such as points, can be constructed from experience. The ontological challenge of information grounding lies in the choice of concepts to consider as primitive, vs. those to be constructed. It also lies in accounting for the relativity and finiteness of experiential space. The grounding approach proposed here constructs geometrical concepts from primitives of the human attentional apparatus for guiding attention and performing perceptual operations. This apparatus enables humans to take attentional steps in their perceived vista environment and to perform geometric comparisons. We account for the relativity of experienced space by constructing locations relative to a reference frame of perceived point-like features. The paper discusses perceptual operations and the idea of point-like features, and introduces a constructive calculus that reflects the generation of domains of geometric comparison from the perspective of an observer. The calculus is then used to construct a model and to motivate an axiomatization of absolute geometry in a finite relativist flavour.