Levin, Ilya (2026) Epistemology of Generative AI: The Geometry of Knowing. [Preprint]
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Abstract
Generative AI presents an unprecedented challenge to our understanding ofknowledge 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. Draw ingonfourstructuralpropertiesofhigh dimensionalgeometry—concentration of measure, near-orthogonality, exponential directional capacity, and manifold regularity—the paper develops an Indexical Epistemology of High-Dimensional Spaces. Building on Peirce’s semiotics and Papert’s constructionism, it reconceptualizes generative models as navigators of learned manifolds and proposes navigational knowledge—a third mode of knowledge production, distinct from both symbolic reasoning and statistical recombination.
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