---
slug: recursive_theory_of_mind
name: Recursive Theory Of Mind
one_liner: "The nesting of mental-state attribution to arbitrary depth — modeling a mind that is itself modeling minds — so that recursion depth (I believe that she believes that I believe X) becomes a structural variable enabling mutual expectation, strategic regress, and coordination that flat single-level mentalizing cannot represent."
type: prime
schema_version: 2
status: density_v2_draft
categories: [structural, cognitive, social, game_theoretic]
origin_domain: cognitive_science
alternate_origin_domains: [game_theory, developmental_psychology, economics, pragmatics, multi_agent_systems]
aliases: [higher_order_theory_of_mind, recursive_mentalizing, nested_belief_attribution, level_k_reasoning, cognitive_hierarchy, i_know_that_you_know]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-02 self-application, route R / reflexive) — the SECOND-ORDER prime obtained by applying `theory_of_mind` to itself: modeling a mind that is itself modeling minds. First-order theory of mind attributes beliefs/desires to another agent ('she believes X'); recursive theory of mind nests the attribution to arbitrary depth ('I believe that she believes that I believe X'). Discovered in the op-02 self-application sweep 2026-07-03. STRONG hold (verified absent from corpus; established construct spanning developmental psychology, game theory, and pragmatics). STATUS: HOLD pending owner keep/cut."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "SCREEN CAREFULLY vs `keynesian_beauty_contest` (IN CORPUS — the level-k / p-beauty-contest depth structure) and vs `common_knowledge` / mutual knowledge (if present). Discriminating claim: beauty-contest is a specific coordination/market INSTANCE of nested mentalizing; recursive_theory_of_mind is the general cognitive GENUS. common_knowledge is the fixed-point of infinite shared knowledge, distinct from finite nested attribution depth."
- "Phase-C action: re-similarity-check vs `theory_of_mind` (input / parent), `keynesian_beauty_contest`, and `common_knowledge`; confirm it is the genuine second-order lift (recursion DEPTH and nested self-reference are the new structure) and not merely a restatement of first-order theory_of_mind; draw a subsumption edge theory_of_mind → recursive_theory_of_mind and a child/relation edge recursive_theory_of_mind → keynesian_beauty_contest at incorporation; write a v1 draft and sync the one_liner across v1/v2 per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 4
  domain_breadth: 5
  structural_abstraction: 4
  transfer_evidence: 4
  reasoning: 'The bare structure — an attribution operator applied to its own output, so that a mind models a mind that is itself modeling minds, with recursion DEPTH (1st-order, 2nd-order, k-order) as an explicit variable — is a genuinely substrate-neutral second-order form. It recurs wherever agents reason about agents reasoning: 2nd-order false-belief tasks in developmental psychology, level-k / cognitive-hierarchy reasoning in game theory and experimental economics, nested intention recognition in Gricean pragmatics and implicature, and belief-modeling stacks in multi-agent AI. These are structurally-unlike siblings sharing only the abstract nesting operation, so domain_breadth scores 5. Structural abstraction is 4 because the core is a pure statement about applying a mentalizing operator to its own product — the meta-level object is another mind''s theory-of-mind about oneself or a third party — requiring no particular cognitive substance to hold; it stays just short of 5 because "mental-state attribution" carries a residue of agent/intentional vocabulary that a fully content-free recursion (e.g. bare fixed-point nesting) would shed. Transfer evidence is strong (independently named and formalized in developmental psychology, game theory/economics, and pragmatics).'
similarity_to_nearest_existing_prime:
  slug: theory_of_mind
  similarity: 0.58
structural_framed:
  label: structural
  aggregate: 0.37
  criteria: {vocab_travels: 0.7, evaluative_weight: 0.2, institutional_origin: 0.2, human_practice_bound: 0.4, import_vs_recognize: 0.4}
  rationale: 'Reads structural-to-mixed. The core claim — an attribution operator applied recursively to its own output, with nesting depth as a structural variable — is recognized rather than imported, and travels cleanly into game-theoretic level-k reasoning, developmental 2nd-order false-belief, and multi-agent belief stacks without carrying any single field''s vocabulary. The frame residue is moderate: "mental-state attribution," "belief," and "intention" import an agent/intentional cast that keeps human_practice_bound and import_vs_recognize off the floor, but the underlying second-order structure — a distinction between attributing a state and attributing an attribution — is substrate-neutral. Slightly higher framing than its parent `theory_of_mind` only because the recursion is most vividly instantiated in human social cognition, but the nesting operation itself is domain-free.'
phase_b_passes_completed: []
---
# Recursive Theory Of Mind

## Core Idea

Recursive theory of mind is a *second-order* application of mentalizing to its own product: the object being modeled is not another agent's belief about the world, but another agent's *theory of mind* — a mind that is itself modeling minds. Base-level `theory_of_mind` attributes mental states to another agent: "she believes X," "he wants Y." It runs the attribution operator once, over a target whose mental states are about the world. Recursive theory of mind applies that operator to its own output, nesting the attribution to arbitrary depth: "I believe that she believes that I believe X." It is reached from `theory_of_mind` by turning the mentalizing operator on the thing mentalizing produces — a theory of mind about a theory of mind.

The load-bearing anatomy is a feature present at the meta level but absent at the base: *recursion depth as a structural variable*. First-order mentalizing has a single level — one agent's states about the world — and no vocabulary for "how deep the nesting goes." Lift the operator onto its own output and depth (1st-order, 2nd-order, k-order) becomes an explicit, orderable dimension, and three structures appear that flat single-level mentalizing cannot represent: (1) *nested self-reference*, where the modeled mind's model includes oneself ("she believes that I believe…"), closing a loop the base engine has no way to form; (2) *strategic regress*, the in-principle-unbounded tower "I know that you know that I know…," with the attendant question of where a finite reasoner truncates it; and (3) *coordination via mutual expectation*, where agents converge not on a fact but on a shared point in the depth hierarchy. None of these is a longer or more careful first-order attribution — they are new objects that exist only because the attribution operator is being applied to itself.

Read structurally, the same second-order shape appears wherever agents reason about agents reasoning, and the siblings are genuinely unlike. In *developmental and cognitive psychology*, it is the second-order false-belief competence ("John thinks that Mary thinks the ball is in the basket") that arrives developmentally after first-order theory of mind. In *game theory and experimental economics*, it is level-k / cognitive-hierarchy reasoning (Stahl-Wilson, Camerer) and the epistemic depth of nested best-responses — of which the `keynesian_beauty_contest` is a specific coordination/market instance. In *pragmatics*, Gricean implicature depends on nested intention recognition — a speaker intends that the hearer recognize that the speaker intends… — so meaning itself rides on recursive mentalizing. In *multi-agent AI*, it is the belief-modeling stack an agent maintains over other agents' beliefs. Across these, the shared abstract engine is an attribution operator applied to its own output, with depth as the variable; the human social case is one species of the genus, and the structurally-unlike siblings show the genus is the bare second-order nesting.

## Notes

**Provenance.** Produced by operator 02 (self-application), route R (reflexive), as the second-order prime obtained by applying `theory_of_mind` to itself — modeling a mind that is itself modeling minds, so that mental-state attribution nests to arbitrary depth. Surfaced in the op-02 self-application sweep on 2026-07-03. Established construct with canonical names across fields: recursive / higher-order theory of mind and recursive mentalizing (developmental and cognitive psychology; second-order false-belief tasks); level-k and cognitive-hierarchy reasoning (Stahl & Wilson; Camerer, Ho & Chong) in game theory and experimental economics; nested intention recognition in Gricean pragmatics; the folk formulation "I know that you know that I know." Claimed siblings: second-order false belief in development, level-k depth in game theory, nested implicature in pragmatics, and belief-modeling stacks in multi-agent AI. Verified absent from the corpus. Manifest: STRONG hold.

**For owner evaluation (keep/cut).** The case FOR is strong: recursive theory of mind is a *canonical, named construct* (not a proposer coinage), verified absent, with a clean second-order anatomy — recursion depth over mental-state attribution, distinct from a single flat attribution — and genuinely unlike siblings spanning development, game theory, pragmatics, and multi-agent AI. It is foundational to strategic reasoning, linguistic meaning, and social-cognitive development. The RISKS Kurt should weigh: (1) **overlap with `keynesian_beauty_contest` (IN CORPUS)** — the discriminating claim is that the beauty contest is a specific coordination/market INSTANCE of the level-k depth structure, whereas recursive_theory_of_mind is the general cognitive GENUS of which it is one child; recommend a subsumption/child edge recursive_theory_of_mind → keynesian_beauty_contest rather than merger. (2) **overlap with `theory_of_mind` (the base / input)** — the discriminator is that recursion DEPTH and nested self-reference are the new structure; the base engine names a single-level attribution and has no vocabulary for depth, mutual expectation, or strategic regress, so this is a genuine level-2 lift, not a restatement. (3) **possible overlap with `common_knowledge` / mutual knowledge (if present)** — related but distinct: common knowledge is the *fixed-point of infinite shared knowledge* ("everyone knows that everyone knows… ad infinitum"), whereas recursive theory of mind is *finite nested attribution at a specified depth*, with truncation and depth-limits as first-class features; the fixed-point is a limiting case, not the prime itself. Sharp keep/cut question: *is "modeling a mind that models minds" a distinct prime, or is it just `theory_of_mind` applied more than once?* — the proposer's answer is that applying the attribution operator to its own output introduces depth, nested self-reference, and mutual expectation as level-2 features the base loop lacks.

**At incorporation.** Re-run similarity against `theory_of_mind` (input / parent), `keynesian_beauty_contest` (candidate child — IN CORPUS), and `common_knowledge` / mutual knowledge (screen for confusion) to confirm no collapse. If kept: draw a subsumption edge `theory_of_mind` → `recursive_theory_of_mind` (base → second-order), and a subsumption/child edge `recursive_theory_of_mind` → `keynesian_beauty_contest` (genus → coordination instance). Add a missing-edge note flagging the `keynesian_beauty_contest` child relationship and the `common_knowledge` fixed-point contrast explicitly. Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
