Spirin, Denys (2025) Projection-Based Semantics of Universal Theory of Differentiation. [Preprint]
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Abstract
We introduce a projection-based semantic interpretation of differentiation within the Universal Theory of Differentiation (UTD), reframing acts of distinction as structured projections of relational patterns. Building on UTD’s categorical and topos-theoretic foundations, we extend the formalism with a recursive theory of differentiational convergence. We define Stable Differentiational Identities (SDIs) as the terminal forms of recursive differentiation, prove their uniqueness and hierarchical organization, and derive a transparency theorem showing that systems capable of stable recursion can reflect upon their own structure. These results support an ontological model in which complexity, identity, and semantic expressibility emerge from structured difference. Applications span logic, semantics, quantum mechanics, and machine learning, with experiments validating the structural and computational power of the framework.
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| Item Type: | Preprint | ||||||
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| Keywords: | Theory of Differentiation, differentiation, ontology, identity, categorization, recursion, semantic structure, structural stability, epistemic boundaries, artificial intelligence, self-reference, phase transitions, knowledge representation | ||||||
| Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Artificial Intelligence |
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| Depositing User: | Dr Denys Spirin | ||||||
| Date Deposited: | 16 May 2025 17:43 | ||||||
| Last Modified: | 16 May 2025 17:43 | ||||||
| Item ID: | 25311 | ||||||
| Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Artificial Intelligence |
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| Date: | 15 May 2025 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/25311 |
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