strong compossibility

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

Strong compossibility is the manuscript’s formal requirement that a composed world both avoid collapse and preserve participants’ admissible revisions. Each revision must lift to a corresponding world revision through a commuting relation, remaining non-isomorphic when the participant’s revision is non-isomorphic. This adds effective room for correction to distinct embedding; it is a chosen definition of non-foreclosure, not a theorem guaranteeing institutional goodness.

Explanation

Weak compossibility preserves the participants through monic coprojections. The stronger requirement responds to an inert form of preservation: a component may remain distinct while its outgoing revisions cease to make any difference. The model introduces a wide category of admissible revisions, with identities and composition, to distinguish corrigibility from revision-rigidity.

For each participant revision the construction demands a compatible revision of the composed world and commuting embedding maps. Non-isomorphic participant change must not become merely an isomorphism of the world. This is the precise exit-preservation condition, not a generic claim that relations or the existence of choices alone make a regime ethical.

The text explicitly calls these definitions, acknowledges the revision structure as an unverified sketch and warns that local strong compositions may still fail at their seam. RB3 supplies the ethical context of viable agency, repair and revisability. The proposal preserves the additional normative premise rather than claiming the mathematics derives why these goods ought to be sustained.

Scope and attribution

Retain the revision-lifting definition and its explicit model and compositional limits.

PB — The Possible Book

Strong compossibility adds revision lifting to weak non-collapse and remains a chosen formal model.

Occurrence locators: 155, 178, 179, 180, 181.

Background used in the editorial explanation

PB p.176 defines weak compossibility. RB3 p.229 supplies ethical motivation about agency, repair and revisability. Neither establishes the specific formal revision-lifting construction; both remain background.