# Q1012 — Proof

- Q number: Q1012
- Primary URI: https://4p-engine.com/q/Q1012
- Current host route: https://4p-mcb.com/q/Q1012
- Reserved subdomain alias: https://q1012.4p-engine.com/

The first-party semantic item for proof as a reasoned demonstration that points from explicit premises through valid relation toward a conclusion.

> Proof is not an assertion or a credential granted by recognition; it is a structured demonstration whose force depends on premises, valid relation, semantic coherence, evidence class, and declared scope.

Q1012 names proof as the general act of pointing with Reason and reasoning toward Truth and Reality. A proof must expose what it assumes, how its terms relate, why its conclusion follows, and what remains outside its scope.
Formal proof establishes a conclusion from premises by valid derivation. Semantic proof also requires review of the meanings that connect the formal structure to the subject being claimed. Empirical and historical conclusions carry additional evidence obligations; no formal label silently discharges them.
The authored Knowing Logic and Proof record gives proof a reflexive instance: its formal argument is used not only to derive a conclusion, but also to identify the performed reasoning as an instance of knowing Logic and proof. That specific record is Q1014; the broader Logic-proof relation is Q1013.
A proof record is therefore more than a validation score. It is a source-bound object whose premises, derivation, authorial provenance, semantic bridge, truth-table or other checking basis, refutation condition, and limits remain inspectable.

## Two-way derivation from Logic and its use

**Status:** editorial_derivation proof sketch (conditional_concept), distinct from authored source. Logic has its own evidence in reflexive demonstration: any denial, confirmation, observation, or counterexample presupposes identity and valid relation to count as evidence. Logic therefore grounds evidence rather than receiving authority from it. Empirical and documentary evidence can establish contingent instances and test applications, but cannot create, overrule, or exhaust Logic.

### From Logic to this concept

- **Bridge premise:** To count as a proof, a demonstration must expose premises, preserve term identity, apply valid relations, and keep its conclusion within scope; empirical or historical conclusions also need appropriate evidence.
- **Consequence:** Logic plus those proof conditions yields a reasoned path from stated assumptions to a warranted formal conclusion and identifies where semantic or empirical bridges remain open.
- **Proof limit:** A valid proof is conditional on its premises and scope; the label proof does not prove its premises, author, historical context, or empirical interpretation.

### From this concept back to Logic

- **Witness:** Reconstruct a particular demonstration as premise → rule-governed steps → conclusion, then inspect its bridge, refutation condition, source, and evidence class.
- **Disclosure:** The demonstrated chain is intelligible only because each step preserves identity and follows a relation accepted by Logic; a proof's performance therefore reveals the order it uses.
- **Proof limit:** The performance exhibits dependence on Logic, but a separate semantic premise is needed to infer any specific knowledge or ontological claim from the act of proving.

### Intelligence procedure

- **Human:** Translate the argument into numbered premises and steps, check each inference and term, list external evidence required, and state the narrowest supported conclusion.
- **Machine:** Parse a proof graph with premise, rule, bridge, conclusion, and scope nodes; verify valid edges and emit a counterexample or unresolved status instead of an undifferentiated pass.

### Language and vocabulary procedure

- **Contrast:** A proof is the demonstration; proof-shaped rhetoric is only a claim that support exists.
- **Usage rule:** Expand proof vocabulary through premise, inference, entailment, semantic bridge, counterexample, scope, and evidence type.
- **Example:** “The conclusion is formally entailed by these premises; its claim about a historical event is not yet proven until the event evidence and bridge are checked.”

## Semantic meaning frame

- **Role:** reasoned demonstration of conclusion
- **Essence:** A structured act of Reason that points from explicit premises through valid relation toward a conclusion, while keeping formal validity, semantic interpretation, and evidence scope distinct.
- **Logos relation:** Logos requires proof to preserve identity, lawful relation, non-contradiction, and a conclusion that does not exceed what its premises and evidence can carry.
- **Retrieval aliases:** Proof · logical proof · reasoned demonstration · proof by Reason · proof of Truth and Reality · logical proof of knowledge
- **Evidence modes:** explicit premises · formal derivation · truth-functional analysis · semantic bridge review · scope and refutation review

### Distinctions

- proof is not assertion
- formal validity is not empirical confirmation
- a proof record is not every automated check

## Coherence criterion

Proof must preserve identity, explicit premises, valid relation, conclusion fit, semantic interpretation, provenance, evidence class, and scope without claiming more than the argument establishes.

## Evidence boundary

Q1012 is a considered, vetted first-party account of proof as reasoned demonstration, not an unexamined label. A valid formal derivation establishes its conclusion within its premises and scope; the verifier must inspect directly, with semantic, empirical, historical, and ontological conclusions connected through their own bridge premises and evidence.

## Properties

- **proofStructure:** Explicit premises; valid derivation; semantic bridge where required; conclusion; scope; refutation condition.
- **evidenceClassBoundary:** Formal, semantic, empirical, historical, and system-generated evidence remain distinct rather than being collapsed into one proof label.
- **sourceRelation:** Q1012 defines the proof concept and links it to the authored Q1013 Logic and Proof relation and Q1014 Knowing Logic and Proof demonstration.

## Linked Q items

- [Q1000 — Q-Number Data and Metadata System](https://4p-mcb.com/q/Q1000)
- [Q1003 — Coherence](https://4p-mcb.com/q/Q1003)
- [Q1006 — 4P Proof](https://4p-mcb.com/q/Q1006)
- [Q1013 — Logic and Proof](https://4p-mcb.com/q/Q1013)
- [Q1014 — Knowing Logic and Proof](https://4p-mcb.com/q/Q1014)
- [Q1015 — Logical Proof of Knowledge of Logical Proof](https://4p-mcb.com/q/Q1015)

## Related Wikidata concept items

These are typed external concept links for discovery and comparison. They are not sameAs assertions, endorsements, or substitutes for the first-party source and evidence.

- [mathematical proof (Q11538)](https://www.wikidata.org/wiki/Q11538) — **formal-evidence context:** A rigorous demonstration that a mathematical statement follows from its premises. Boundary: The generic concept supplies formal comparison vocabulary; it does not validate or author any first-party proof record.
- [formal proof (Q2762418)](https://www.wikidata.org/wiki/Q2762418) — **derivation context:** Establishment of a theorem by inference from axioms or premises. Boundary: This identifies a neighboring formal concept; each first-party proof retains its own premises, derivation, provenance, and scope.
- [logic (Q8078)](https://www.wikidata.org/wiki/Q8078) — **governing reasoning context:** The study of correct reasoning. Boundary: Logic is the governing reasoning context, not an external endorsement of a particular proof or conclusion.
- [Logic (Q409)](https://www.wikidata.org/wiki/Q409) — **proof and formal-reasoning context:** Curated external comparison concept: Logic. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.
- [Formal System (Q1212450)](https://www.wikidata.org/wiki/Q1212450) — **proof and formal-reasoning context:** Curated external comparison concept: Formal System. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.
- [Tautology (Q237375)](https://www.wikidata.org/wiki/Q237375) — **proof and formal-reasoning context:** Curated external comparison concept: Tautology. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.
- [Reductio ad Absurdum (Q188506)](https://www.wikidata.org/wiki/Q188506) — **proof and formal-reasoning context:** Curated external comparison concept: Reductio ad Absurdum. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.
- [Metalogic (Q938450)](https://www.wikidata.org/wiki/Q938450) — **proof and formal-reasoning context:** Curated external comparison concept: Metalogic. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.
- [Axiom (Q17736)](https://www.wikidata.org/wiki/Q17736) — **proof and formal-reasoning context:** Curated external comparison concept: Axiom. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.

## Related wiki and reference pages

These pages provide historical, conceptual, or primary-text context. They are not identity, authorship, endorsement, or sameAs assertions.

- [Mathematical proof](https://en.wikipedia.org/wiki/Mathematical_proof) — **Wikipedia; formal-evidence context:** A deductive argument showing that a proposition follows necessarily from premises accepted as true. Boundary: The page supplies comparison vocabulary; it does not validate or author a first-party proof.
- [Proof (truth)](https://en.wikipedia.org/wiki/Proof_(truth)) — **Wikipedia; general proof context:** The establishment of the truth of a proposition by argument. Boundary: This is an external conceptual reference, not a substitute for the item's own premises, derivation, or evidence.
- [Logic](https://en.wikipedia.org/wiki/Logic) — **Wikipedia; reasoning context:** The study of valid reasoning and the forms of inference. Boundary: The page provides external context for reasoning; Q1012 remains governed by its own premises, derivation, and evidence boundary.
- [Formal system](https://en.wikipedia.org/wiki/Formal_system) — **Wikipedia; proof and formal-reasoning context:** Curated external reading context: Formal System. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.
- [Tautology (logic)](https://en.wikipedia.org/wiki/Tautology_%28logic%29) — **Wikipedia; proof and formal-reasoning context:** Curated external reading context: Tautology. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.
- [Reductio ad absurdum](https://en.wikipedia.org/wiki/Reductio_Ad_Absurdum) — **Wikipedia; proof and formal-reasoning context:** Curated external reading context: Reductio ad Absurdum. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.
- [Metalogic](https://en.wikipedia.org/wiki/Metalogic) — **Wikipedia; proof and formal-reasoning context:** Curated external reading context: Metalogic. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.
- [Axiom](https://en.wikipedia.org/wiki/Axiom) — **Wikipedia; proof and formal-reasoning context:** Curated external reading context: Axiom. Boundary: These external concepts provide comparison context for Proof; formal validity, semantic interpretation, and evidence scope remain distinct in the first-party record.