Epistemology of Generative AI: The Geometry of Knowing

TL;DR

This paper explores how high-dimensional geometric spaces in neural networks fundamentally alter our understanding of knowledge and meaning in generative AI, proposing a new epistemological framework.

Contribution

It introduces an Indexical Epistemology based on high-dimensional geometry, reconceptualizing generative models as navigators of learned manifolds and a new mode of knowledge production.

Findings

High-dimensional geometry underpins generative AI's epistemic processes.

Generative models operate as navigators of learned semantic manifolds.

Proposes navigational knowledge as a distinct mode of knowledge production.

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.