The Phenomenology of Search: How Large Language Models Navigate Second-Order Representations

Abstract: Following Sergey Levine’s analogy to Plato’s cave we propose that Large Language Models (LLMs) driven web search works through layers of mediation. First, language encodes how humans think about the world. Second, LLMs learn from this text, creating what we call “shadows of shadows.” LLMs map meaning into geometric spaces where similarity is measured as closeness in vectors. In addition web search is not only about meaning — it is also about authority. Which sources are trusted depends on credibility signals built into the web. This article explains how LLMs combine geometry and authority, and what this means for content optimization.

Series roadmap — Part 1 of 3: This article is Part 1 (Foundations) of a three‑part research guide on LLM‑driven web search. Part 2 (Memory & Agency) turns these foundations into a working LLM Search Optimization Agent with memory management: long‑term memory via RAG over a durable store, and short‑term working memory via distillation/rephrasing; we also explore temporal freshness and causal credit assignment for learning from outcomes. Part 3 (User Behavior & Personas) models web user intent, behavior, and persona segments, showing how an agent stores persona‑level lessons in long‑term memory and uses them to iteratively clarify information needs at inference time.

👉 Practical Note: For readers who want to see how this theory can be tested experimentally, we maintain a companion repository.

I. Double Mediation: Shadows of Shadows

Plato’s Cave gives us shadows of reality. With LLMs, there’s another step: we see shadows of those shadows. Human perception and thought produce language, and LLMs only learn from that language. Yet, through patterns in text, LLMs rebuild something close to our mental structures.

Neuroscience shows that our brains organize meaning geometrically - similar ideas light up overlapping areas. When we process the sentence “The red apple fell from the tree,” specific patterns of neural activation encode spatial relationships, temporal sequences, and categorical knowledge across multiple brain regions. These neural patterns, when externalized through language, create statistical regularities in text that preserve aspects of their underlying geometric structure.

Large Language Models, through next-token prediction over vast corpora, learn to approximate these same geometric relationships in their embedding spaces. Recent research demonstrates that LLM internal states predict human brain activity during natural language processing, suggesting they capture fundamental aspects of how human cognition organizes semantic knowledge.

The Aristotelian Foundation

Aristotle’s De Interpretatione presents the classical triadic structure: spoken words are symbols of affections in the soul, and affections in the soul are likenesses of things. This creates a two-step mediation where language points not directly to reality, but to mental representations that themselves point to reality.

Modern cognitive neuroscience validates this architecture. The brain’s semantic system creates distributed representations that encode perceptual, motor, and conceptual knowledge. These representations exhibit geometric properties: conceptually similar items activate overlapping neural populations, creating measurable similarity structures in neural state space.

Language, as the externalization of these internal geometric relationships, preserves their distributional properties. When we say “dog” and “wolf” in similar contexts, we reflect the fact that their neural representations overlap significantly in human semantic memory. LLMs, learning from millions of such contextual co-occurrences, reconstruct approximations of these original geometric relationships.

II. The Geometry of Meaning

The distributional hypothesis (words appearing in similar contexts have similar meanings) provides the mathematical foundation for understanding how second-order representations can recover first-order structure. This principle, formalized in vector space models, suggests that semantic knowledge can be encoded as geometric relationships in high-dimensional spaces.

Mathematical Framework

World (W): reality itself
Cognition (C): how humans represent the world
Language (L): how cognition gets expressed in words
Human cognition mapping f: W → C
Language mapping g: C → L
Large Language Models learn an approximation h: L → E where E is the Embedding Space.

The composition (h ∘ g ∘ f) maps world states to embedding vectors. The central question is - under what conditions does this composed mapping preserve meaningful geometric relationships?

Theorem (Distributional Preservation): If the linguistic mapping g preserves local neighborhood structure from cognitive space C, and the statistical learning procedure h correctly estimates co-occurrence probabilities, then geometric relationships in E will approximate those in C.

This explains why LLMs trained only on text can exhibit knowledge of spatial relationships, color similarities, and conceptual hierarchies — they recover these through the preserved geometric structure of language use.

While geometric similarity explains relevance, it cannot explain selection under scarcity. When an LLM has to choose among multiple geometrically similar sources, it implements something analogous to what social epistemology defines as “credibility assessment” or which source to trust.

This coresponds to Brandom’s inferentialism: meaning emerges not just from usage patterns, but from the normative structures of who is authorized to make which claims. In digital contexts, this manifests as domain authority, citation networks, and other signals of epistemic credibility.

Knowledge exists within what we call “epistemic communities” — networks of credibility attribution that determine whose claims are trusted. LLMs inherit approximations of these structures through:

Citation patterns: Academic and professional content preserves authority relationships through reference structures
Link topologies: Web link graphs encode implicit credibility assessments
Source hierarchies: News organizations, institutional websites, and expert publications create recognizable authority gradients
Temporal signals: Freshness and update patterns indicate active knowledge maintenance
Authenticity: Is the content innovative, original adds value to the subject knowledge base

The optimization challenge becomes: how do we position content to maximize both geometric similarity (relevance) and authority signals (credibility)?

IV. A Kantian Framework for Optimization

Kant’s transcendental idealism provides a useful framework for understanding LLM limitations and optimization opportunities. LLMs access phenomena (textual appearances) but not noumena (things-in-themselves). This creates both constraints and possibilities.

The Phenomenal Domain of Text

Within the phenomenal domain of language, LLMs exhibit remarkable capabilities:

Conceptual manipulation: They can perform valid inferences within consistent conceptual schemes
Analogical reasoning: They recognize structural similarities across domains
Contextual adaptation: They adjust interpretations based on situational cues
Compositional understanding: They combine concepts in novel but meaningful ways

These capabilities suggest that optimization should focus on making content maximally interpretable within the phenomenal domain of language, rather than trying to bridge directly to noumenal reality.

Optimization as Transcendental Logic

Just as Kant’s transcendental logic reveals the necessary conditions for possible experience, optimization reveals the necessary conditions for LLM comprehension:

Conceptual clarity: Content must use concepts in ways consistent with their learned distributional patterns
Inferential validity: Claims must follow patterns of inference recognizable from training data
Contextual coherence: Information must be presented in formats that match learned structural expectations
Authority consistency: Credibility signals must align with learned patterns of trustworthy sources

V. Operational Risks and Limitations

Earlier we saw how LLMs approximate cognitive geometry through symbolic training. Here we turn to the limitations of that approach — the risks when second-order representations fail to connect back to grounded reality.

The Symbol Grounding Problem Revisited

Steven Harnad’s symbol grounding problem identifies a fundamental limitation: symbols can only be meaningful if they connect to non-symbolic representations. LLMs, operating entirely within the symbolic domain of language, risk creating elaborate systems of mutual reference without external grounding.

This limitation manifests in several ways:

Hallucination: LLMs generate plausible-sounding but factually incorrect statements
Contextual brittleness: Performance degrades when queries venture outside training distribution
Causal reasoning deficits: Difficulty with counterfactual reasoning and causal inference
Embodied knowledge gaps: Limited understanding of physical interactions and spatial reasoning

Implications for Optimization

These limitations suggest optimization strategies should:

Emphasize consistency: Ensure content aligns with established patterns, if you bring innovative claims align them logically to the context of the established patterns
Provide multiple convergent signals: Use redundant authority indicators to compensate for limited grounding
Structure information clearly: Employ schemas and formats that minimize ambiguity
Reference established knowledge: Connect to well-grounded, frequently-cited sources

VI. Future Directions: Escaping the Cave

Multimodality and active learning strategies suggest that optimization frameworks will evolve to handle richer grounding and dynamic credibility assessment.

Multimodal Integration

As LLMs incorporate visual, auditory, and other sensory modalities, they begin to escape the pure second-order limitation. Multimodal models can potentially:

Ground abstract concepts: Connect linguistic descriptions to perceptual experiences
Validate textual claims: Check descriptions against visual evidence
Enhance spatial reasoning: Use visual-spatial processing to improve geometric understanding
Reduce hallucination: Cross-modal consistency checking

Active Learning Systems (reinforcement learning)

Future optimization may involve dynamic interaction with LLMs:

Query refinement: Systems that iteratively clarify information needs
Source triangulation: Multi-source verification of factual claims
Uncertainty quantification: Explicit modeling of confidence levels
Real-time updating: Incorporation of new information as it becomes available

VII. Implications for Understanding and Optimization

The Nature of Understanding

Our analysis suggests that LLMs exhibit what Daniel Dennett might call “competence without comprehension” — they demonstrate sophisticated linguistic behavior without necessarily understanding in the way humans do. This raises fundamental questions about:

The sufficiency of behavioral criteria: If an LLM produces appropriate responses to queries, in what sense does it lack understanding?
The role of embodiment: How essential is sensorimotor grounding for genuine comprehension?
The social nature of knowledge: Can understanding exist without participation in communities of practice?

Epistemological Consequences

The success of LLMs in knowledge tasks suggests that:

Formal structure may be sufficient: Much of what we call knowledge might be captured in distributional patterns
Social epistemology is primary: Authority and credibility assessment are central to knowledge systems
Understanding is contextual: The same information can be more or less understood depending on its embedding in conceptual networks

Predictable Second-Order Regularities

Finally, while LLMs are stochastic at the token level, their higher-order preferences and judgments are far more regular and reproducible than the real world. Research on LLM re-ranking, judge prompts, and ensemble self-consistency shows that under fixed protocols, models make stable, protocol-dependent choices. This makes them more predictable than the phenomena they describe, creating a unique opportunity: content can be optimized not only to be legible to human readers, but also to be reliably surfaced by LLM-mediated search. In this sense, the very second-order character of LLM knowledge — its formal, protocol-governed regularity — becomes a positive constraint for practitioners.

VIII. Conclusion: The Geometry of Second-Order Truth

Large Language Models operate in what we might call the “geometric domain of linguistic practice.” Optimization in this domain requires understanding both the mathematical properties of embedding spaces and the sociological properties of authority attribution.

👉 Practical Reminder: The GitHub repo includes ready-to-run code for testing these ideas against your own content and queries.

References

Philosophy:

Cognitive Science:

Neuroscience:

Computational Linguistics:

Robotics: