Glossary
The book's core vocabulary is drawn from the General Outline and the paper of RC; a few items (the account, and the usage of the boundary of the snapshot, among others) are this book's own transcriptions within the RC framework. Fifteen entries are gathered below as the argument requires; each gives a definition and its source, and by the source the reader can go back to the original text of RC and check.
Ground of Possibility: the totality of all potential existence, holding at every moment and in parallel the states of all potential existence; it is RC's deliberately thin opening move, prior to all determinacy. General Outline 1.1, "Dynamic Existence"; the paper, Section 1.1, definition of the core concepts.
Observation: the act by which a subject at a particular scale of perception performs a directional filtering of a particular interval of the possibility distribution and thereby locks in determinacy; it does not require a human being to execute it in person — instruments may intervene. General Outline 1.1; the paper, Axiom A3 (observational locking).
Convergence: the process by which possibility is locked into determinacy through observation; the observed converges into the object, the observer into the subject, and the two identities exchange with the perspective of observation. General Outline 1.2, "The Emergence of Determinacy"; the paper, Section 1.1.
Secondary construction: relative to the Ground as the base, all determinacy locked by observation is derivative, second-order construction; "secondary" marks the relation of position, "provisional" marks that it carries margin. General Outline 1.1; the paper, Section 1.1.
Consensus reinforcement: observations across subjects and levels that verify one another form a positive reinforcement loop, converging into a stable "objective reality"; "objective" thereby means consistent across subjects, not independent of all observation. The paper, Axiom A6; General Outline 1.2.
Observational consensus: a possible snapshot on which the consciousnesses of all levels are unanimous, letting coherent subjects share a broadly consistent reality, fine-grained observational divergences being ignored. General Outline 1.3, "Space, Time, and Causality".
Snapshot: one frame that observational consensus locks in within the Ground; the snapshot is a selected achievement, not the negative, and behind it lie the parallel states not exhausted. This book's own usage, distilled from the sentence of General Outline 1.3 that all snapshots exist in the Ground of Possibility presently and simultaneously.
Observational divergence: the inconsistency that arises when observational consensus is questioned or negated by different modes of observation; microscopic probability, experimental anomaly, and the failure of predictions are, in this book, its concrete forms. General Outline 1.2, 1.4; the paper, Section 2.2.
Re-convergence: the subjects of a divergence, by re-intervening in the Ground of Possibility, complete an innovation of observational consensus and of the rule framework; the chapters of this book on the geometric revolution and on relativity operationalized it as dated history. General Outline 1.4, "The Unity of Subject and Object"; the paper, Section 2.4.
Available margin: the part of the Ground of Possibility not yet locked; it is where free will and evolution have their space; locking determinacy does not exhaust the Ground (conservation of margin, A7). General Outline 1.4; the paper, Section 1.1 and Axiom A7.
Rule framework: the larger thing into which causal laws are further summarized, which stipulates what counts as normal and as no longer needing to be asked; once the framework is installed it presents itself in reverse as "a priori", but it keeps the interface for re-convergence. General Outline 1.4; the four stages of Chapter Two of this book.
The appearance of apriority: the priority independent of experience that causal laws seem to possess; by RC, this apriority is only the appearance cast by a convergence path sufficiently stable. General Outline 1.3; the paper, Section 2.3.
Theoretical dimensional reduction: every theory is an interpretive system under a finite horizon, a dimension-reducing projection of the real world, constrained by the triple boundary of the level of observation, the imprint of the subject, and the decay of time; the reduction does not negate the value of a theory — it establishes its standing. General Outline 2.3, "Theoretical Dimensional Reduction"; the paper, Section 3.3.
Cognitive relay station: the proper identity of a theory — its value lies not in being forever true, but in converging vast numbers of observations into workable determinacy at the least cost, achieving renewal through being continuously re-observed, and not burning the instruments when the transfer is made. General Outline 2.3; unfolded in Chapters Thirteen and Sixteen of this book.
Account: a bookkeeping metaphor coined by this book, meaning the deposits saved up from countless mutual verifications that stand behind every stable fact; "self-evident" means the account has grown so thick that people have forgotten it was ever opened. Proposed in Chapter One of this book and used throughout thereafter; no correspondence in the original text of RC.
Chapter Guide
Introduction: setting out from Galileo's telescope of 1610 and Wigner's perplexity of 1959, it lays down the three puzzles — the effectiveness of mathematics, the justification of induction, and the Gödel boundary — and points out that the three forms of reason share one garment of "apriority".
Chapter One: opening with Einstein's letter "He does not throw dice", it gives a sketch of the RC framework — the Ground, observation, convergence, consensus reinforcement — and transcribes causal laws as convergence paths trodden solid within the snapshot.
Chapter Two: following the genesis of a child's being scalded, it takes apart the generation of the a priori feel — four stages and two mechanisms of maintenance — and, with Hume and Kant as control groups, gives the third road: apriority has a history of formation.
Chapter Three: taking the three labors of the chess player, the architect, and the navigator as its metaphor, it establishes the book's threefold division — logic, mathematics, and science are three employments of one and the same mechanism of convergence, the difference lying only in the object of convergence and the interlocutor.
Chapter Four: Aristotle's walking path — inference became for the first time an object of observation, form was stripped from content, and the explicitation of pure structures of convergence had its first historical specimen.
Chapter Five: the Begriffsschrift of 1879 in Jena — inference was compressed into mechanically executable transformation rules, the symbolic language became an artificial accelerator of consensus reinforcement, and logicism set out to lock all of mathematics into one explicit path.
Chapter Six: the few lines of Russell's letter to Frege in 1902 — once a system has gained a sufficient capacity for self-observation, the observer falls into his own range of observation; total observation was proved an illegal operation, and the community rebuilt its foundations by stratification and authorization.
Chapter Seven: Gödel's quiet announcement at the round table of Königsberg — on RC's reading, the incompleteness theorems are the strictest proof that determinacy equals what is locked; the boundary is not the failure of reason but a definitional component of determinacy.
Chapter Eight: a Elements copied for two thousand years — the axiomatic method is the technique of explicitly publishing the starting point of a convergence path, and two thousand years of re-verification without failure read a one-time choice of starting point into eternal truth.
Chapter Nine: the ghost of the fifth postulate — from the retreat at Saccheri's door to the birth of non-Euclidean geometry; the two-thousand-year failure of the proofs sprang from arguing a one-time choice into the only possibility, and mathematical necessity stood exposed as self-consistency inside the snapshot.
Chapter Ten: the three crises of mathematics and the battle of the foundations — the common form of a crisis is the foundation at some level being pierced by observation into the next level down, the three foundational stances are three snapshots, three strategies of re-convergence — and the building grew wild all the while.
Chapter Eleven: the modern answer to "what is a number" — structuralism and category theory moved the center of study from the objects locked back to the manner of locking itself; mathematics recognized the object of its study as its own method, and Wigner's question was here paid.
Chapter Twelve: a plank with a groove cut in it — experiment is controlled observation; Bacon supplied the program, Galileo the craft, Boyle the charter, Newton the synthesis; results public and method reproducible became the institutionalization of consensus reinforcement.
Chapter Thirteen: the prediction machine — Halley's comet and Neptune proved that locking a path publicly before the observation is the most stringent cross-subject test; theory is a cognitive relay station; and the outstanding debt of 43 arcseconds foretold the rewriting.
Chapter Fourteen: the two eclipse expeditions of May 29, 1919 — from the zero result of Michelson–Morley to general relativity's re-locking of the space-time snapshot, the first rewriting of "necessity" walked the three-act play of divergence, patches, re-convergence, and ritual through to its end.
Chapter Fifteen: the clockwork of a gram of radium and the untimeliness of a single atom — probability is not noise but the honest accounting of what convergence has not yet leveled; the second rewriting of "necessity" fell upon the individual, with Kuhn as the control group lighting up both mechanism and ledger.
Chapter Sixteen: recalling the chess player, the architect, and the navigator to one and the same table — unified formulations and a comparison table redeem all the verdicts, three scales weigh the differences, and theoretical dimensional reduction is applied to the three themselves, establishing their standing as cognitive relay stations.
Chapter Seventeen: with Popper and Lakatos as the examiners — falsifiability is transcribed as keeping an open channel for observational divergence, the protective belt as the continuous adjustment of the deep rules, and the health of reason is measured by the capacity to keep converging, not by the stock of true theorems held.
Chapter Eighteen: following the extended line of observation onto silicon — the machine's pattern recognition is another specialization, its objectivity still depends on cross-subject re-verification, evaluation alienation has already been diagnosed by RC, and the question is delivered to the door of Alternative Observation: The Machine's Gaze.
Epilogue: redeeming the promise and returning to the night of 1610, it answers the introduction's three puzzles one by one, and closes with "the modesty of reason is the strength of reason" — determinacy is the achievement of convergence, not the background color of the world.
Notes on Sources
This book is philosophical argument and narrative intellectual history, not specialized research in the history of science or of mathematics. The historical events the text touches — names, dates, works, formulations of theorems, and results of experiments — are narrated according to the accepted scholarly record, as verified on September 12, 2026; should later research rewrite the accepted record, the later research governs.
The text carries no footnotes, for the reason already given in the introduction's layered statement: this book is written from inside the RC system; its concepts and manner of argument follow the General Outline and the paper of RC, and the text refers to the relevant theses with formulas of the kind "RC, discussing ... in ..., says"; the historical narrative follows the accepted sources, doing its utmost not to let the needs of the story distort the facts. Whatever is interpretation — reading a historical turning point as "re-convergence", reading a school's position as a location on a convergence path — is this book's own construction within the RC framework, and the text marks it as far as possible with "on RC's reading" and "this book's reading is". The reader may accept the facts and refuse the interpretations, or the reverse; the gap between the two threads is precisely the available margin left to the reader.
Two places call for special distinction. First, for the classic cases — Gödel's theorems, non-Euclidean geometry, the eclipse observations of 1919 — the RC-style transcriptions (such as "Gödel = A6's inner limit") are this book's philosophical interpretation, not the settled formulations of the mathematical community or of historians of science; for the content of the theorems and the observations themselves, the primary literature and the standard textbooks govern. Second, for the discussion of thinkers such as Popper, Lakatos, and Kuhn, this book takes each thinker's most influential version of his position as the control group and does not unfold the internal complexity of their several works — for example Kuhn's later revisions to "incommensurability", or Popper's many restatements of the criterion of demarcation; the purpose of the comparison is to light up the theses of RC, not to testify to the full shape of these thinkers.
Theory Version
The version of RC on which this book relies: the RC General Outline ("RC", on the "General Outline" page of this site), whose revision-record table carries the last revision date of December 22, 2025, the author Zhurong, the status "to be continued"; and the companion paper, "Process Realism: Observational Convergence and the Genesis of Determinacy (RC)", first draft dated June 18, 2025. The numbering of the axioms (A1 through A7) and the citations of sections (such as General Outline 2.3 and the paper's 3.3) in this book all follow that version; should the General Outline be revised thereafter at places this book cites, the latest text of the General Outline governs.