indefinite extensibility

Compiled with AI assistance and selectively reviewed. Please consult the cited passages; the books remain the authoritative source. About this companion

Editorial synthesis · provisional

Definition

Indefinite extensibility is the generality-relativist position that a proposed domain of absolutely everything can always give way to a wider domain. The author adopts this side of a contested debate about completed totality. Defenders of unrestricted quantification remain explicit opponents: the absence of an all-containing set does not by itself establish that every way of speaking of everything fails.

Explanation

AB names Parsons, Glanzberg and Fine on the side of extensible domains and Richard Cartwright and Williamson on the side of absolute generality. The source does not present set-theoretic paradox as an uncontested proof that unrestricted discourse is impossible. The assessment keeps the disagreement and its attributions intact.

The target is a world conceived as a completed totality-object available for survey. Ordinary ecological, practical and historical uses of world remain unaffected. Gabriel’s fields of sense provide one articulation of the author’s chosen position rather than an independent demonstration compelling every participant in the debate.

The epilogue explicitly recognizes that an absolutist reader will find the conclusion undercut. Incompleteness and cosmology function as analogies and corroboration, not premises establishing the chosen account of generality. The proposed entry therefore preserves philosophical commitment without promoting corroborative examples into a universal logical result.

Scope and attribution

Retain the contested position as adopted philosophy rather than a settled theorem.

AB — The Actual Book

The generality debate is named and the author’s side openly identified.

Occurrence locators: Appendix: 266, 267.

RB3 — The Real Book, Volume III: Murmurations

A completed totality-object is distinguished from ordinary world-talk.

Occurrence locators: Notes: 393, 394; Epilogue: 355.

Background used in the editorial explanation

Named theories and mechanisms are distinguished from neighboring background, homonyms and the author’s own synthesis. Reproduced AI passages retain their separate voice.