Scott, Steven (2025) Recursive Ontological Calculus: A Unified Theory of Symbolic Computation. [Preprint]

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Abstract

The Recursive Ontological Calculus (ROC) furnishes a complete, machine-verifiable axiomatisation of symbolic identity, curvature, and semantic recursion. Building directly on C. S. Peirce’s triadic conception of the sign, ROC links category-theoretic morphology with information-geometric entropy bounds. We present formal schemas, a sequent calculus equipped with an infinitary Master Recursion Equation, eleven core theorems (T1–T11), and cross-framework embeddings into ordinary category theory, ZFC, and Homotopy Type Theory. Worked examples demonstrate numeric curvature computation, gauge-orbit quantisation, and prime-gate symbolic statistics.

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Item Type:	Preprint
Creators:	Creators Email ORCID Scott, Steven SigniferNoctis@pm.me 0009-0007-2466-0854
Keywords:	Peircean logic; recursive ontology; self-verifying logic; entropy-based logic; symbolic computation; semantic curvature; triadic logic; Peirce-inspired formalism; reflexive proof systems; homotopy type theory
Subjects:	Specific Sciences > Computation/Information > Classical Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics > Proof General Issues > Scientific Metaphysics Specific Sciences > Artificial Intelligence > Classical AI General Issues > Models and Idealization General Issues > Structure of Theories General Issues > Theory/Observation
Depositing User:	Steven Scott
Date Deposited:	18 Jun 2025 14:20
Last Modified:	18 Jun 2025 14:20
Item ID:	25734
Official URL:	https://zenodo.org/records/15653461
DOI or Unique Handle:	10.5281/zenodo.15653461
Subjects:	Specific Sciences > Computation/Information > Classical Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics > Proof General Issues > Scientific Metaphysics Specific Sciences > Artificial Intelligence > Classical AI General Issues > Models and Idealization General Issues > Structure of Theories General Issues > Theory/Observation
Date:	17 June 2025
URI:	https://philsci-archive.pitt.edu/id/eprint/25734

Available Versions of this Item

• Ontomorphic Peircean Calculus: A Universal Mathematical Framework for Identity, Logic, and Semantic Computation. (deposited 11 Jun 2025 14:30)
  • Recursive Ontological Calculus: A Unified Theory of Symbolic Computation. (deposited 18 Jun 2025 14:20) [Currently Displayed]

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