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Results for “distinction” 13 papers
Syntactic Token Calculus: Deriving Particle-like Normal Forms from Distinction Operations (Corrected Revision)
High-energy physics explains the observed particle spectrum through continuous quantum fields, spontaneous symmetry breaking, and a growing inventory of unobservable entities, a framework whose theoretical and experimental costs are substantial and whose falsifiability is contested. A gap remains:…
Distinction, Discretisation, and the Cost of Law: A Quantitative Sketch of Approximation Entropy
The deepest question in physics is often posed as "What are the laws?", but a prior question is "What does it cost to state, and to compute with, a law?" Building on the distinction-based formalism of Spencer-Brown's Laws of Form as consolidated in the Quantum Laws of Form (QNFO) programme, and on…
Ontological Re‑Entry: What Can We Say Exists?
The re-entry problem asks which existence claims a finite-resource observer can legitimately make when its internal structure is projected back onto the world. Existing approaches lack a quantitative link between ontological commitments and physical limits. We fill this gap by (i) defining a…
Re-Entry as a Binary Prohibition Law: Enumeration, Impossibility, and the Three-Outcome Completion
Self-referential constraints arise in hardware security, programmable logic, and symbolic execution tools, where a system must forbid a state while generating the very operation that enforces the prohibition. The open question is whether a re-entering form of the calculus of indications — a…
Distinction-Lattice Framework: Eigenforms, Bisimulation, and the Realizability Boundary of Self-Reference
A conservative formal version of the Distinction-Lattice Framework (DLF): stable entities are bisimulation classes of observational behaviour, certified coinductively, with realizability separated from fixed-point existence. This version (v0.2.0, superseding v0.1.1) narrows novelty claims, corrects…
The Void Is Not False: Recovering the Unmarked State in Logic from the Calculus of Indications
Boolean logic treats
falseas a primitive truth value, and classical set theory treats the empty set as a primitive object. This paper argues that both commit a foundational category error: they reify the void — the unmarked state before any distinction — into a member of the system. In the…The Calculus of Re-Entrant Distinctions: A Unified Treatise on the Loop, the Tree, and the Constants of Self-Reference
This treatise develops a single thesis: that the primitive act of distinction — the drawing of a boundary between marked and unmarked — generates, under the discipline of re-entry and linear resource management, the constants $e$ and $\pi$, the landscape of completions of the rational numbers, the…
The Computable Real Boundary: Where Physics Ends and Cognitive Fiction Begins
Every experiment reduces to a finite act of distinction: this reading, not that; this frequency range, not that; this bit string, not its negation. Physics is, at its operational core, a discipline of finite distinguishability. Yet the mathematical architecture physics inherited — the real number…
Automated Formal Verification and Combinatorial Reduction of Distinction-Based Calculus
The foundation of modern formal mathematics has historically rested upon Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC), a container-based ontology that often conflates zero with the empty set and necessitates arbitrary constraints to prevent self-reference. To systematically evaluate…
Formal Ontology of Distinction and Invariance
This document presents the complete, self-compliant synthesis of the Ontic Relational Patternism framework. Starting from a single primitive syntactic token—the mark—and three context-closed reduction rules (Calling, Crossing, Void), we derive a purely relational universe where the cross-ratio is…
Quantum Laws of Form
*Quantum information is not intrinsically fragile; we have been measuring it incorrectly. This monograph presents a radical re‑foundation of physics based on George Spencer‑Brown’s Laws of Form, strictly adhered to and extended into a Syntactic Token Calculus (STC). The framework generates…
Principia Ontologica
Human understanding operates through representational models rather than direct reality apprehension. Alfred Korzybski famously articulated this principle, noting that abstractions derived from perception necessarily differ from their source. Cognitive frameworks function as biological…
Reconstructive Ontology of Brouwerian Intuitionism
This study reconstructs the ontological foundations of Brouwerian intuitionism, arguing that the rejection of the principle of the excluded middle (PEM) is not a technical choice but a necessary consequence of the ur-intuition of time. Drawing on L.E.J. Brouwer’s primary texts from 1905 to 1948, we…
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