Identity, Dipert, and LLMs: Structured ComparisoN

dipert_llm.md

Identity, Dipert, and LLMs: Structured Comparison

• Classical Ontological Options

  • Substratum (Substance) Theory: Objects are "bare particulars" which have attributes, but the identity of the object is independent of the attributes.
  • Bundle Theory: Objects are nothing over and above their attributes; what individuates an object is the collection of its properties.
  • Problems: Substrata are metaphysically mysterious; bundles have difficulty with individuation, especially when two objects share all attributes.

• Dipert's Graph-Based Structural Ontology

  • Randall R. Dipert in "The Mathematical Structure of the World: The World as Graph" argues that the world is a single, large graph.
    (https://philpapers.org/rec/DIPTMS?utm_source=chatgpt.com)
  • In this view, nodes (objects, or fundamental particulars) and edges (relations) are not individuated by intrinsic essences, but by their relational position in the overall graph.
    (https://orca.cardiff.ac.uk/id/eprint/20630/1/shacket%20world%20as%20graph%20analysis%20jan%202011%2010-21.pdf?utm_source=chatgpt.com)
  • A key requirement is asymmetry: the graph must distinguish nodes by their relational pattern so that no two nodes are structurally identical. This avoids collapse of identity.
    (https://orca.cardiff.ac.uk/id/eprint/20630/1/shacket%20world%20as%20graph%20analysis%20jan%202011%2010-21.pdf?utm_source=chatgpt.com)
  • Dipert's ontology rejects both primitive substrata (no bare thisness) and primitive attributes outside relations; both objects and properties are grounded in relational structure.
    (https://orca.cardiff.ac.uk/id/eprint/20630/1/shacket%20world%20as%20graph%20analysis%20jan%202011%2010-21.pdf?utm_source=chatgpt.com)

• How LLMs Encode Meaning and Identity

  • Concepts, words, attributes are encoded as vectors in high-dimensional spaces, not as standalone intrinsic essences. Meaning arises from relational positioning (similarity, context) among vectors.
    (https://arxiv.org/html/2508.10003v1?utm_source=chatgpt.com)
  • Empirical studies show categorical and hierarchical relations in LLM embeddings: e.g. "animal -> mammal -> dog -> poodle" are geometrically reflected via simplices, polytopes, orthogonality, etc.
    (https://arxiv.org/abs/2406.01506?utm_source=chatgpt.com)
  • The embeddings naturally break symmetry: two words that might start similar are distinguished via usage, context, co-occurrence etc. This mirrors Dipert's asymmetry condition.
    (https://arxiv.org/html/2508.10003v1?utm_source=chatgpt.com)
  • Limitations in LLMs also appear: meaning can drift over time (e.g. due to changing usage), synonyms may be very close or collapse, and identity over change depends on external/use context. These illustrate the vulnerabilities of purely relational identity.
    (https://arxiv.org/html/2508.10003v1?utm_source=chatgpt.com)

• Why LLMs Support (Validate) Dipert's Thesis

  1. LLMs demonstrate that identity and meaning can emerge purely from relational structure: nodes (concepts), their relations, context all suffice to individuate.
  2. The asymmetry requirement is in practice met in LLMs: usage and context break perfect symmetry among tokens/concepts.
  3. Attributes are not primitives but relational features (directions, clusters, geometric relations). This matches Dipert's view that properties have identity through structure.
  4. The pattern of failure (synonym collapse, drift, etc.) matches exactly the weaknesses Dipert acknowledges, which gives credibility: the theory predicts what LLMs show.

References

• Dipert, Randall R. "The Mathematical Structure of the World: The World as Graph." Journal of Philosophy, Vol. 94, No. 7 (1997), pp. 329-358.
  https://philpapers.org/rec/DIPTMS?utm_source=chatgpt.com

• Shackel, Nicholas. "The World as a Graph: Defending Metaphysical Graphical Structuralism." Analysis, Vol. 71, No. 1 (2011), pp. 10-21.
  https://orca.cardiff.ac.uk/id/eprint/20630/1/shacket%20world%20as%20graph%20analysis%20jan%202011%2010-21.pdf?utm_source=chatgpt.com

• Park, Kiho; Joong Choe, Yo; Yibo Jiang; Victor Veitch, et al. "The Geometry of Categorical and Hierarchical Concepts in Large Language Models." arXiv preprint (2024).
  https://arxiv.org/abs/2406.01506?utm_source=chatgpt.com

• "Semantic Structure in Large Language Model Embeddings." arXiv (2025).
  https://arxiv.org/html/2508.10003v1?utm_source=chatgpt.com