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Results for “distinction” 19 papers
Laws of Form. Spencer-Brown, re-entry, calculus of indications Tagged papers: 50.
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…
Number Systems as Stratified Distinction Operations: An Enclosure Hierarchy over the Mark
The conventional tower of number systems—$\mathbb{N}\subset\mathbb{Z}\subset\mathbb{Q}\subset\mathbb{R}\subset\mathbb{C}$—augmented by the $p$-adic fields $\mathbb{Q}_{p}$ and the adele ring $\mathbb{A}$ is usually presented as a sequence of completions without a unifying generative principle.…
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 Modes in Solid‑State Quantum Devices: A Calculus of Distinctions with Fully Shown Quantitative Benchmarks
Re‑entry, the self‑referential insertion of a distinction into its own indicational space, is a primitive operation identified in the Laws of Form tradition. Whether this operation can be given operational meaning in solid‑state quantum devices is unknown. Existing solid‑state literature reports…
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…
The Number Builder: Enclosure Sequences in the Laws of Form Calculus as a Constructive Route to Computable Reals
We address the gap that no minimal, mark‑based formalism has been shown to generate all computable reals. We formalize enclosure sequences as finite Laws of Form (LoF) expressions equipped with a computable re‑entry schedule, define an interpretation that maps each unfolding to a rational…
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…
Conditional Truths and the Locale Framework: Map, Territory, and the Rendering Interface
Every physical statement is a conditional truth: it holds only within a locale --- a specified vacuum or symmetry sector, background geometry, medium, energy scale, or observer frame. This paper formalizes the resulting locale framework in four moves. First, a catalog of conditional truths (photon…
The Exchange Phase as a Logical Scalar: R = e^(2 pi i s) from the Re-Entrant Calculus
The boson/fermion dichotomy is conventionally presented as a primitive classification of nature. Recent work established that the underlying invariant is the relation between the exchange phase of identical particles and their topological spin, R = e^{2πis}, with the dichotomy as its shadow in three…
The Idempotent Core: Quantity as Broken Distinction and the Hidden Assumptions of Arithmetic and Algebra
Classical arithmetic treats the statement $1+1=2$ as a primitive truth and quantity as a fundamental concept. This paper examines the hidden premise of that statement: the two instances of the numeral $1$ must denote distinct marks. In the calculus of indications, the law of calling — idempotence…
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…
Pillar 3: PBO/Autaxys — Pattern-Based Ontology as Intrinsic Self-Ordering
PBO/Autaxys (Pattern-Based Ontology) is presented as an intrinsic self-ordering meta-framework grounded in two primitive operations: Distinction (D) and Relation (R). From these D/R primitives, all patterns, structures, and physical laws are shown to emerge without recourse to external agents or…
Syntactic Generation
Traditional models of physical reality rely on the assumption of foundational substances. These base materials are typically conceptualized as particles, fields, or continuous spatial manifolds. Such approaches inevitably generate persistent philosophical dualisms and questions regarding ultimate…
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…
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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