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### 1. Conceptual Assumptions: The Substantivalist Binary
* **The Preserved Identity Assumption:** The argument assumes a binary choice for the metaphysical definition of an "object": an entity must either possess a primitive classical identity (*haecceity* or self-subsisting substance) or be completely eliminated in favor of pure structure.
* **Contestability:** High. This framework ignores alternative metaphysical models, such as bundle theories built on tropes (particularized qualities) or dynamic process ontologies (e.g., Alfred North Whitehead’s process philosophy).
* **Impact of Challenge:** If an object can be conceptualized as a localized, persistent bundle of relational properties without requiring an underlying "substratum" or *haecceity*, the dilemma collapses. Quantum entities can remain "objects" in a non-classical, non-substantival sense, rendering radical elimination unnecessary.
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### 2. Logical Assumptions: The Concrete Realization of Relations
* **The Invariance-to-Ontology Leap:** The argument assumes that because a mathematical structure remains invariant across theoretical transformations (such as permutation symmetries in statistical mechanics), that structure directly mirrors the fundamental *ontological state* of the physical world.
* **Contestability:** Moderate to High. This logical step confuses an *epistemic condition for physical law* (invariance under transformation) with an *ontological claim about existence*.
* **Impact of Challenge:** If mathematical invariance is merely a formal requirement for formulating coherent, observer-independent physical laws, then structural symmetry reflects our mode of modeling reality rather than proof that reality itself consists solely of abstract, relataless equations.
```
Logical Premise: Mathematical relations are invariant across quantum symmetries.
Assumed Inferential Leap: Therefore, physical reality consists exclusively of structural relations.
Alternative Logic: Symmetries are formal constraints on theory-building, not direct ontologies.
```
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### 3. Factual/Empirical Assumptions: Realist Interpretation of Quantum Formalism
* **The Literal Hilbert Space Assumption:** The argument takes the formal, non-relativistic mathematical apparatus of quantum mechanics—specifically permutation symmetry in tensor-product Hilbert spaces and state-vector entanglement—as a direct, unmediated representation of fundamental reality.
* **Contestability:** High. It assumes the correctness of realist, anti-hermeneutic interpretations of the wave function (like Everettian or Ghirardi-Rimini-Weber models) while assuming the failure or irrelevance of non-eliminative alternatives.
* **Impact of Challenge:** Under pilot-wave interpretations (De Broglie-Bohm theory), particles remain fundamental, point-like classical entities with precise trajectories, where non-locality and entanglement are mediated by a physical quantum potential rather than the dissolution of objecthood. If De Broglie-Bohm or QBism (Quantum Bayesianism) holds, the empirical motivation for eliminating objects vanishes entirely.
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### 4. Methodological Assumptions: The Rejection of "Relations Require Relata"
* **The Intelligibility of Pure Topology:** The thesis assumes that a relation without distinct terms (*relata*) to instantiate it is a logically coherent concept, rather than a category mistake or semantic contradiction.
* **Contestability:** Extremely High. Prominent metaphysicians (e.g., E.J. Lowe, David Lewis) argue that the concept of a "relation" is inherently second-order; it is defined as a mapping between domain entities. A "pure relation" without entities is as conceptually vacuous as a "velocity" without a moving object.
* **Impact of Challenge:** If "relations without relata" is ruled logically incoherent, eliminative OSR collapses into either:
1. *Moderate OSR* (where objects and structures are mutually ontological co-dependents), or
2. *Epistemic Structural Realism* (where objects exist fundamentally, but remain veiled beyond our structural equations).
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### Summary Matrix of Scaffolding
| Assumption Type | Core Implicit Premise | Vulnerability Level | Consequences if Invalidated |
| :--- | :--- | :--- | :--- |
| **Conceptual** | "Object" requires classical *haecceity* or substance. | High | Allows objecthood to be redefined structurally without eliminating objects. |
| **Logical** | Symmetry invariance entails ontological primacy. | Moderate-High | Reduces OSR from a physical necessity to a preference in mathematical modeling. |
| **Factual** | Standard Hilbert space realism is uniquely correct. | High | Alternative interpretations (e.g., Bohmian mechanics) fully restore individual objects. |
| **Methodological**| Relations without relata are syntactically and semantically coherent. | Very High | Renders radical eliminative OSR a logical category error. |