Scott, Steven (2025) Ontomorphic Peircean Calculus: A Universal Mathematical Framework for Identity, Logic, and Semantic Computation. [Preprint]
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Text (Full preprint draft of a novel formal system modeling identity, logic, and symbolic recursion, grounded in C.S. Peirce's triadic semiotics)
Ontomorphic_Peircean_Calculus - Preprint V1.pdf - Draft Version Available under License Creative Commons Attribution. Download (576kB) |
Abstract
This paper introduces the conceptual foundations of the Ontomorphic Peircean Calculus, a first-order formal system constructed from Charles Sanders Peirce’s triadic logic and recast in categorical, topological, and algebraic terms. Identity, inference, and modality are defined as consequences of recursive morphism closure over a non-metric symbolic manifold. Presence arises from symbolic saturation governed by the compression functional. This system unifies logic, physics, and ontology through symbolic recursion and curvature, replacing metric assumptions with recursive cost topology. All structures—identity, mass, time, causality—emerge from the self-coherence of morphic braids in a purely symbolic substrate, thereby replacing metric foundations with compression-curvature dynamics that computationally bridge the essential logical architecture of the theoretical and practical sciences simultaneously.
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