---
slug: possibility
name: Possibility
one_liner: "The object-level modal structure surrounding an actual state: a space of accessible alternatives paired with an accessibility relation, over which the dual operators NECESSARY (true in all accessible alternatives) and POSSIBLE (true in at least one) — and the derived status CONTINGENT (possible but not necessary) — are defined."
type: prime
schema_version: 2
status: density_v2_draft
categories: [structural, logical, metaphysical]
origin_domain: modal_logic
alternate_origin_domains: [metaphysics, physics, planning_and_ai, everyday_reasoning]
aliases: [alethic_modality, necessity_and_contingency, possible_worlds, modal_status, space_of_alternatives]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-06 modalization, flavor 6a actual→possible) — the STRONGEST op-06 find and a GENUS CONVERGENCE: hundreds of inputs across the corpus mapped to 'the possibility space of P', converging on a single missing genus (the actual/possible/necessary/contingent modal-status structure with its space-of-alternatives + accessibility anatomy). Discovered 2026-07-03. STRONG hold (verified absent as an object-level node; established name — alethic modality, modal logic, Kripke possible-world semantics). This is the modal analog of op-04's `field` (a foundational absent genus surfaced by mass input-convergence). STATUS: HOLD pending owner keep/cut."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "OBJECT-VS-PROCESS SCREEN (dominant question): `modal_reasoning` is PRESENT and is the nearest neighbor (est. similarity ~0.58-0.66, fairly high). The discriminating claim is that `modal_reasoning` is the REASONING PROCESS operating over modal claims, whereas `possibility` is the OBJECT — the modal-status structure (the space of alternatives + accessibility relation + necessary/possible operators) that the process reasons about. The corpus distinguishes object from process elsewhere; owner decides whether that split warrants a distinct node here. Screen prominently."
- "Phase-C action: re-run similarity vs `modal_reasoning` (process-of), `counterfactual_reasoning`, `scenario_planning`, `optionality`, `eventual_realisation_of_possibility`, and `diagonal_impossibility`; confirm it is the genuine object-level modal genus and not a restatement of `modal_reasoning`; decide one head vs a small family (recommend ONE head — the alethic-modality structure — with necessity/contingency as facets, not sibling primes); draw relation edges (process-of → `modal_reasoning`, plus edges to `counterfactual_reasoning`, `optionality`, `eventual_realisation_of_possibility`); write a v1 draft and sync the one_liner across v1/v2 per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 5
  domain_breadth: 5
  structural_abstraction: 5
  transfer_evidence: 5
  reasoning: 'Alethic modality is about as substrate-neutral as a prime can be: the bare structure — a single actual/realized point embedded in a structured field of alternatives, an accessibility relation selecting which alternatives count as reachable from a given standpoint, and the dual operators "true in all accessible alternatives" (necessary) and "true in at least one" (possible) — carries no domain content whatsoever. It recurs, with the SAME anatomy and only the accessibility relation retuned, across logic (logical possibility), metaphysics (metaphysical possibility / possible worlds), physics (physically allowed states, the phase space of a system, physical vs logical possibility), planning and AI (the reachable-state space from an initial configuration), and ordinary reasoning (what could, must, or merely happens to be the case). domain_breadth is 5 because these are maximally-unlike siblings sharing only the abstract modal structure. structural_abstraction is 5 because the core is a pure formal statement — a space, an accessibility relation, two dual quantifiers over it — with no evaluative or substance-bound residue. transfer_evidence is 5: the identical structure is independently formalized (Kripke semantics), named, and used in logic, metaphysics, physics, and planning.'
similarity_to_nearest_existing_prime:
  slug: modal_reasoning
  similarity: 0.62
structural_framed:
  label: structural
  aggregate: 0.30
  criteria: {vocab_travels: 0.9, evaluative_weight: 0.1, institutional_origin: 0.1, human_practice_bound: 0.2, import_vs_recognize: 0.3}
  rationale: 'Reads strongly structural. The core claim — an actual point surrounded by a space of accessible alternatives, with dual necessary/possible operators — is recognized, not imported, and travels cleanly into physics (phase space, physically-allowed states), planning (reachable-state space), and everyday reasoning without carrying any originating vocabulary; "possible world" and "accessibility" are formal scaffolding, not domain content. There is essentially no evaluative weight (modal status is descriptive, not normative), no institutional origin, and only a light human-practice residue (the standpoint-relativity of epistemic possibility). Framing is among the lowest in the candidate set — comparable to op-04''s `field` and to core logical primitives.'
phase_b_passes_completed: []
---
# Possibility

## Core Idea

Possibility is the object-level *modal structure* that surrounds any actual, realized state: the structure distinguishing what IS the case (actual) from what COULD be (possible), what MUST be (necessary), and what merely *happens* to be so (contingent). The realized state is a single point; possibility is the structured field of alternatives around that point. The load-bearing anatomy has three parts. First, a **space of alternatives** — the possible worlds, states, or configurations other than the one that obtains. Second, an **accessibility relation** — which of those alternatives count as reachable or admissible *from a given standpoint*; this is what makes possibility relative and what separates its species, since logical, physical, and epistemic possibility differ precisely in which alternatives their accessibility relation admits. Third, the **dual operators** defined over that space: NECESSARY (true in *all* accessible alternatives) and POSSIBLE (true in *at least one*), with each definable as the negation-dual of the other. From these falls the derived status CONTINGENT — possible but not necessary, i.e. true here yet false somewhere accessible.

The feature this prime names, and that a bare description of the actual state lacks, is the *modal status* itself. To say a proposition is actual is to locate it at the realized point; to say it is possible, necessary, or contingent is to say something about the whole field of alternatives and the actual point's place within it. This is why the same actual fact can carry different modal statuses under different accessibility relations: a state that is physically necessary (forced by the laws in every physically-accessible world) may be merely contingent logically (false in some logically-accessible world), and a proposition unknown to an agent may be epistemically possible while being metaphysically impossible. Possibility is thus not a property of the actual state in isolation but a relation between that state and a structured space of alternatives.

Read structurally, the identical anatomy — space of alternatives, accessibility relation, dual necessary/possible operators — recurs across maximally-unlike domains with only the accessibility relation retuned. In **modal logic and metaphysics** it is Kripke possible-world semantics and the metaphysics of modality (logical vs. metaphysical possibility, essence as necessity). In **physics** it is the distinction between physically-allowed and merely-logically-conceivable states — the phase space of admissible configurations, physical possibility as law-constrained accessibility. In **planning and AI** it is the reachable-state space: which configurations are attainable from an initial state under the available operators. In **everyday reasoning** it is the ordinary sorting of claims into what could be, what must be, and what merely happens to be. Across all of these the substance is different but the modal skeleton is the same, which is what makes possibility a foundational structural primitive rather than a domain fact.

## Notes

**Provenance.** Produced by operator 06 (modalization), flavor 6a (actual→possible), as the modal structure that is absent when a prime is described only at its actual/realized state. It was the STRONGEST op-06 find and a **genus convergence**: hundreds of inputs across the corpus, when modalized, mapped onto the same target — "the possibility space of P" — pointing not at hundreds of bespoke coinages but at a single missing genus, the actual/possible/necessary/contingent modal-status structure with its space-of-alternatives + accessibility anatomy. Surfaced 2026-07-03. This is the modal analog of op-04's `field` (a foundational absent genus that mass input-convergence surfaces). Established name and formalization: **alethic modality** (possibility / necessity / contingency) in modal logic, Kripke possible-world semantics, and the metaphysics of modality. Verified absent from the corpus as an *object-level* node. Manifest: STRONG hold.

**For owner evaluation (keep/cut).** The case FOR is strong: possibility is a foundational, maximally-general structural primitive — the actual/possible/necessary/contingent distinction plus the possible-world/accessibility structure — that *dozens* of primes presuppose (any prime about options, reachability, laws, counterfactuals, or scenarios quietly stands on it) but for which the corpus has no object-level node. The genus-convergence signal (hundreds of inputs collapsing to one target) is the strongest evidence the search can produce, and the SI/SF profile is near the substrate-neutral ceiling — the modal analog of `field`. The RISKS Kurt should weigh: (1) **the dominant question — does `modal_reasoning` already cover it?** `modal_reasoning` is present and is the nearest neighbor (est. similarity ~0.58–0.66, fairly high). The proposer's answer is that `modal_reasoning` is the *reasoning PROCESS* that operates over modal claims, whereas `possibility` is the *OBJECT* — the modal-status structure it reasons about; the corpus distinguishes object from process elsewhere, so this is a genuine object-level lift, not a restatement. Owner decides whether that split warrants a distinct node. (2) **Generality** — is it *too* foundational to be a useful prime, or is that exactly what makes it a keystone the DAG has been leaning on implicitly? (3) **One prime or a family?** — whether possibility / necessity / contingency should be one head or a small cluster; recommend ONE head (the alethic-modality structure) with necessity and contingency as facets of it, not separate sibling primes. Sharp keep/cut question: *is the modal-status structure a distinct object-level prime, or is it inseparable from the `modal_reasoning` process that manipulates it?*

**At incorporation.** Re-run similarity against `modal_reasoning` (the process-of neighbor — the key screen), `counterfactual_reasoning` (a specific possibility-manipulation), `scenario_planning` (an instance/practice), `optionality` (the possibilities one can act on), `eventual_realisation_of_possibility` (present — the *dynamics* of a possibility becoming actual, i.e. the process this structure feeds), and `diagonal_impossibility` (a specific impossibility result) to confirm no collapse and to fix the object/process boundary. If kept: draw a "process-of" relation edge `modal_reasoning` → `possibility` (process over object), plus edges to `counterfactual_reasoning`, `optionality`, and `eventual_realisation_of_possibility`; add a missing-edge note flagging that `eventual_realisation_of_possibility` presupposes this modal space as its domain. Decide the one-head-vs-family question (recommend one head). Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
