Epistemology of Generative AI: The Geometry of Knowing

2026-02-19

AI Summary

This work addresses the lack of a clear epistemological foundation for generative AI, which hinders its responsible deployment in scientific, educational, and institutional contexts. The study proposes an “indexed epistemology” grounded in high-dimensional geometric structures, conceptualizing generative models as navigators within semantic manifolds. This framework transcends traditional symbolic and statistical paradigms by integrating key properties of high-dimensional geometry—such as concentration of measure and near-orthogonality—with Peircean semiotics and Papertian constructivism. For the first time, it establishes a theoretical basis for generative AI as a semantic-space navigator and redefines knowledge production through a third mode: “navigational knowledge.” This novel paradigm offers a coherent lens for understanding the mechanisms by which generative AI produces knowledge.

Technology Category

• Philosophy and Ethics of AI: AI & Epistemology
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Generative AI presents an unprecedented challenge to our understanding of knowledge and its production. Unlike previous technological transformations, where engineering understanding preceded or accompanied deployment, generative AI operates through mechanisms whose epistemic character remains obscure, and without such understanding, its responsible integration into science, education, and institutional life cannot proceed on a principled basis. This paper argues that the missing account must begin with a paradigmatic break that has not yet received adequate philosophical attention. In the Turing-Shannon-von Neumann tradition, information enters the machine as encoded binary vectors, and semantics remains external to the process. Neural network architectures rupture this regime: symbolic input is instantly projected into a high-dimensional space where coordinates correspond to semantic parameters, transforming binary code into a position in a geometric space of meanings. It is this space that constitutes the active epistemic condition shaping generative production. Drawing on four structural properties of high-dimensional geometry concentration of measure, near-orthogonality, exponential directional capacity, and manifold regularity the paper develops an Indexical Epistemology of High-Dimensional Spaces. Building on Peirce semiotics and Papert constructionism, it reconceptualizes generative models as navigators of learned manifolds and proposes navigational knowledge as a third mode of knowledge production, distinct from both symbolic reasoning and statistical recombination.

Problem

• Generative AI
• Epistemology
• High-dimensional geometry
• Knowledge production
• Semantics

Innovation

• generative AI
• high-dimensional geometry
• indexical epistemology
• semantic manifolds
• navigational knowledge