The Generalized Coordinate System for Rhetorical Modes

This paper introduces the Generalized Coordinate System (GCS) as a framework for analyzing and generating rhetorical modes---the conventional patterns of discourse. The GCS is composed of low-dimensional, mediating and high-dimensional axes. The low-dimensional axes are Thing, Feature, Quantitative Attribute, Qualitative Attribute, Formal Attribute axes and form the objects or foundational elements for rhetorical modes. The mediating axes are Basic Expressive-Representational Elements and Rhetorical Mode axes and transform the raw material into communicable languages. The high-dimensional axes include Cognitive Function axis, Epistemic Purpose axis and the Five-Level Expression Staircase axis (Depth axis). The high-dimensional axes determine the cognitive depth and ultimate purpose, and capture the developmental progression of language competence- from raw perception to paradigm-shattering insight. Three types of semantic or modal mapping are defined: low-dimensional mapping (from low-dimensional axes to the mediating axes), high-dimensional mapping (from the mediating axes to high-dimensional axes), and full-dimensional mapping. These mappings form a pyramidal hierarchy, progressing from foundational elements (things, features, and attributes) to higher-order cognitive functions and epistemic purposes. By employing three core logical structures---combinatory, parallel, and embedded---the GCS consolidates infinite expressive possibilities within the finite intersections of its axes. The system's generative capacity, quantifiable by the number of axis intersections (generalized mode number), enables the navigation of nearly infinite expressive variations while steering practical applications toward finite, purpose-driven goals. The GCS transitions rhetorical modes from a static taxonomy to a dynamic analytical system for discourse construction and analysis, offering possibly insights for the development of large language models through the integration of a programmable rhetorical mode system.