From 2D Object Space to 3D Perspective Structure

This paper addresses the structural conditions under which objectivity can emerge when 
multiple perspectives are present. Standard approaches typically presuppose a shared object 
space and treat differences between observers as secondary deviations. This working paper 
suspends that assumption and formalizes the transition from a two-dimensional object space 
to a three-dimensional perspective structure. 
The formalization introduces a perspective group that acts on objects, allowing perspective-
invariant comparison through alignment operations. This mathematical framework generates 
operators for reflexivity and contextual coherence without requiring external assumptions. 
The extension from D2 (systematic comparison) to D3 (perspectival alignment) and D4 
(contextual integration) provides a dimensional logic that stabilizes cooperation in rational 
decision-making. 
This compact technical paper demonstrates the core mechanism of dimensional logic through 
a specific application: perspective alignment in cooperation problems. It serves as the formal 
foundation for the framework developed in "Adaptive Rationality through Dimensional 
Logic" (Stegemann, 2025) and illustrates how perspective-invariant metrics can be 
operationalized in decision architectures.