Logical possibility¶

The status of a proposition that is satisfiable or at least not refutable under the axioms, inference rules, semantics, and consistency policy of a specified logical system.

Version: v1 · 2026-09-28 · History
Domain-specific #: 10487
Domain group: Humanities
Origin domain: Philosophy
Subdomains: Modal Logic, Modal Metaphysics → Philosophy

Core Idea¶

Logical possibility is always relative to a logical framework. A proposition counts as possible when it is compatible with the axioms and rules under consideration—semantically, commonly because at least one admissible model or possible world makes it true; syntactically, because the relevant denial or contradiction is not derivable under a sound/complete account.

The background matters. Euclidean and non-Euclidean theories license different geometrical possibilities; classical, intuitionistic, paraconsistent, and modal logics do not share every consequence principle. In an inconsistent but nonexplosive logic, contradiction does not automatically make every proposition derivable. This also means that a consistency claim proved relative to a stronger metatheory is not an unqualified, framework-free certificate of possibility.

Possibility must not be inferred from ignorance. Undecidability, incomplete proof search, inconsistent axioms, and ambiguous formalization can leave status unresolved. A responsible claim names the language, theory, semantics or proof system, consistency assumptions, and whether a model, relative-consistency proof, decision procedure, or only failed search supports the verdict.

Structural Signature¶

Sig role-phrases:

proposition. Supplies the claim whose status is tested. Constitutive object. If altered: Questions and commands are not propositions without formalization.
logical system. Fixes language, axioms, rules, consequence relation, and treatment of inconsistency. Constitutive frame. If altered: Changing logic can change possibility.
background theory. Adds domain assumptions against which consistency/satisfiability is assessed. Necessary context. If altered: Logical truth alone differs from theory-relative possibility.
admissible interpretation. Provides a model/world/valuation in which the proposition can hold. Identity-bearing witness where semantic. If altered: Syntax-only accounts need a matching proof criterion.
refutation or satisfiability test. Shows contradiction, derivability of negation, model existence, or indeterminacy. Necessary verdict relation. If altered: Failure to find a proof is not always proof of possibility.

What It Is Not¶

Not physical possibility. Natural laws add constraints.
Not probability. Possible can have unspecified likelihood.
Not conceivability. Psychological imagination is not a model proof.
Not absence of refutation search. Computational incompleteness may remain.

Scope of Application¶

Logical possibility is used in modal logic, model theory, proof theory, formal verification, mathematics, philosophy, knowledge representation, counterfactual analysis, and consistency arguments.

Model theory. Finds satisfying structures.
Modal logic. Evaluates accessible worlds.
Proof theory. Tests derivability/consistency.
Verification. Searches reachable satisfying states.
Foundations. States relative consistency.

Clarity¶

Report formal language, proposition translation, logic, axioms/background theory, semantics and admissible models/worlds, accessibility relation if modal, proof calculus, consistency/explosion policy, decidability/completeness, witness model or derivation, tool bounds, and exact contrast with physical/metaphysical/epistemic possibility.

Manages Complexity¶

One ordinary-language ‘could’ can hide multiple modalities. Formalization compresses them into a satisfiability question but introduces dependence on theory, semantics, and metatheory.

Abstract Reasoning¶

Formalize the proposition without changing its modality.
Fix the logic and background theory.
Seek an admissible model or a refutation under sound rules.
Audit consistency, completeness, and computational limits.
State only the system-relative result and its modal boundary.

Knowledge Transfer¶

Satisfiability reasoning transfers among formal domains, but axioms, model classes, and accessibility relations must be remapped. No conclusion about physical realization follows automatically.

Examples¶

Canonical¶

A modal formula ◇P is evaluated on a declared Kripke frame; an accessible world satisfying P witnesses possibility under that model class.

Mapped back: proposition → P; logical system → named modal logic; background theory → frame conditions; admissible interpretation → accessible P-world; refutation or satisfiability test → explicit witness model.

Applied / In Practice¶

A verifier encodes a protocol property and constructs a reachable model state satisfying it, while reporting finite-state abstractions and refusing to call it physically deployable.

Mapped back: proposition → encoded protocol condition; logical system → model-checking logic; background theory → transition-system abstraction; admissible interpretation → reachable state; refutation or satisfiability test → machine-checked witness.

Structural Tensions¶

T1: framework precision vs. ordinary-language breadth. Formal systems decide clear formulas while translation can omit intended constraints. Diagnostic: Which assumptions were formalized?

T2: non-refutation vs. positive witness. Failure to disprove is weak while a model demonstrates satisfiability. Diagnostic: Is there a witness or only incomplete search?

T3: system relativity vs. modal overreach. A result is valid in one logic while rhetoric suggests unrestricted possibility. Diagnostic: Which modal domain is claimed?

Structural–Framed Character¶

Logical possibility is structural. It is a relation among proposition, formal system, theory, and admissible interpretation; philosophical readings frame its application. Its portable skeleton is Constraint Satisfiability, related rather than a strict parent. Evaluative weight is low; proof practice matters; origin lies in logic; vocabulary travels only with semantics. Its character: existence of a permitted interpretation under declared constraints.

Structural Core vs. Domain Accent¶

Skeletal core. Determine whether constraints admit at least one state or interpretation.

Domain-bound accent. Axioms, derivability, models, worlds, and modal distinctions define logical possibility.

Why not prime. Satisfiability travels; this is the logical modality.

This entry is a kind of Modal Status.

Constraint Satisfiability. The portable structural comparison.
Necessity. Necessity requires truth in all relevant interpretations, not one.

Relationships to Other Abstractions¶

Current abstraction Logical possibility Domain-specific

Parents (1) — more general patterns this builds on

Logical possibility is a kind of Modal Status Domain-specific

Logical possibility satisfies the defining boundary of Modal Status: A modal status is the classification of a proposition, state of affairs, event, or world as actual, possible, necessary, contingent, or impossible relative to specified accessibility, logical, metaphysical, temporal, epistemic, or normative semantics.

Hierarchy path (1) — routes to 1 parentless root

Logical possibility → Modal Status

Neighborhood in Abstraction Space¶

Logical possibility sits in a crowded region of the domain-specific corpus (19^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Logical Inference, Modality & Conditional Structures (27 abstractions)

Nearest neighbors

Obligationes — 0.91
Constructional System — 0.91
Modus ponens — 0.90
Alternative facts — 0.90
Cambridge change — 0.90

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Physical possibility. Tell: Are natural laws included?
Metaphysical possibility. Tell: Is formal satisfiability or what could exist intended?
Epistemic possibility. Tell: Is ignorance rather than model existence meant?
Probability. Tell: Possible or likely?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Logical_possibility (revision 1320757113).
Preserved source candidate: http://stanford.library.usyd.edu.au/archives/sum2014/entries/modality-epistemology/
Preserved source candidate: https://books.google.com/books?id=YupiXWV5j6cC

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.