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## Step 1: From Formal Describability to Ontological Identity ## Step 1: From Formal Describability to Ontological Identity
1. A **formal system** is a set of axioms, inference rules, and symbols capable of expressing truths about a domain. 1. A **formal system** is a set of axioms, inference rules, and symbols capable of expressing truths about a domain.
2. If a domain (like reality) can be **fully and self-sufficiently described** by a formal system — such that no semantic interpretation or metaphysical foundation is required beyond that system — then **nothing external** to the system is needed to account for the domain’s structure. 2. If a domain (like reality, from the largest macrostructures to the smallest microstructures) can be **fully and self-sufficiently described** by a formal system — such that no semantic interpretation or metaphysical foundation is required beyond that system — then **nothing external** to the system is needed to account for the domain’s structure.
3. In such a case, the system is not merely a model of the domain; it **is** the domain in structure and function. 3. In such a case, the system is not merely a model of the domain; it **is** the domain in structure and function.
**Conclusion 1**: If something is fully and self-sufficiently describable by a formal system, it **is** that formal system in ontological terms. **Conclusion 1**: If something is fully and self-sufficiently describable by a formal system, it **is** that formal system in ontological terms.