Epistemology of Generative AI: The Geometry of Knowing

Technical Deep Dive: Epistemology of Generative AI

Overview

This technical deep dive examines the epistemic implications of the structural properties of high-dimensional vector spaces, and how they enable a new mode of knowledge production in generative AI systems. The analysis challenges the prevailing dichotomy between symbolic reasoning and statistical recombination, proposing a "third mode" of geometric navigation through learned semantic manifolds.

Problem & Context

• Generative AI systems like GPT, Claude, and Stable Diffusion operate by navigating high-dimensional vector spaces, rather than manipulating symbolic logic or statistical patterns.
• However, the theoretical discourse has largely ignored the epistemic consequences of this geometric medium, treating it as a neutral computational substrate.
• Existing explanatory strategies focus on architectures, training regimes, and cognitive analogies, but overlook the active role of high-dimensional geometry in shaping knowledge production.

Methodology

• The paper takes a "structural epistemology" approach, examining the mathematical properties of high-dimensional spaces and their implications for how knowledge is constructed, transmitted, and learned.
• Key properties analyzed:
  • Concentration of measure: Collapse of metric contrast, rendering distance uninformative
  • Near-orthogonality: Independence as the geometric default, rather than engineered separation
  • Exponential directional capacity: Vastly more configurations than training data
  • Manifold regularity: Coherent, navigable structure within the high-dimensional space

Interpretation

• These geometric properties together enable a "third mode" of knowledge production distinct from both symbolic reasoning and statistical recombination:
  • Positional meaning: Concepts represented by vector positions, not symbolic definitions
  • Geometric coherence: Coherence arises from manifold constraints, not logical rules
  • Navigational novelty: New configurations produced through structured traversal, not assembly from parts
• This "indexical epistemology" is grounded in Peirce's semiotics and Papert's constructionism, reconceiving knowledge as enacted through navigation of learned manifolds, rather than retrieved from storage.

Limitations & Uncertainties

• The analysis relies on idealized mathematical models of high-dimensional geometry, which real-world systems only approximate.
• The semiotic and epistemological frameworks proposed are novel, requiring further development and empirical investigation.
• The nature and implications of "structural agency" in generative systems require deeper examination.

What Comes Next

• Articulating educational and institutional frameworks suited to this new geometric mode of knowledge production.
• Investigating the ethical and social consequences of geometric navigation as a form of knowing.
• Exploring the scope and limits of structural agency, and its relationship to human creativity and intelligence.

Sources: [1] Epistemology of Generative AI: The Geometry of Knowing (arXiv preprint)