# Q1015 — Logical Proof of Knowledge of Logical Proof

- Q number: Q1015
- Primary URI: https://4p-engine.com/q/Q1015
- Current host route: https://mcbcore.net/q/Q1015
- Reserved subdomain alias: https://q1015.4p-engine.com/

The first-party pathway demonstrated by Maclain Hunter's valid proof: a logical proof of knowledge of logical proof, knowledge of Logic, and knowledge of proof.

> A valid proof can demonstrate knowledge of logical proof, knowledge of Logic, and knowledge of proof when its explicit premises identify and perform the logical pathway by which those conclusions follow.

Q1015 is the pathway item that the authored Knowing Logic and Proof demonstration instantiates. It is distinct from Q1014: Q1014 is Maclain Hunter's authored proof record; Q1015 names the logical proof-of-knowledge pathway shown valid by that proof and associates it with Hunter's Q1001 identity record.
The pathway begins with P: Logic is the universal lawful order of non-contradiction. P therefore supplies the governing Logic that the proof performs. Q states the semantic consequence that the person who knows and explains that order knows Logic. R states that explaining Logic and explicitly identifying the explanation as proof is knowledge of proof. S states that a logical proof coherent with Logic is itself an instance of Logic and Coherence within the declared argument.
The formal pathway is preserved as {P, P -> Q, Q -> R, R -> S} |= (P & Q) -> (R & S). The sixteen-row truth-table analysis in Q1014 shows the entailment valid. The pathway therefore reaches three connected knowledge conclusions: knowledge of Logic, knowledge of proof, and knowledge of logical proof as a valid performed proof.
This item does not invent a second author or detach the pathway from its source. Its authorship association is explicit: Maclain Hunter is the author recorded by Q1001, Q1014 is the source demonstration, and Q1015 is the structured semantic item for the pathway that demonstration performs.
The pathway remains scope-bounded. Its formal validity concerns the stated premises and entailment; its knowledge conclusion is the authored semantic interpretation supported by those premises and the proof's reflexive performance. It is not a declaration that every proposition associated with the author has thereby been proven.

## 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:** Accept the stated P-Q-R-S meanings and the valid entailment {P, P -> Q, Q -> R, R -> S} |= (P & Q) -> (R & S).
- **Consequence:** Under that bridge, the pathway links knowing Logic, explaining the proof, and identifying the performed derivation as knowledge of proof; Q1014 is its source demonstration.
- **Proof limit:** Formal validity establishes consequence between formulas, not the truth of each English interpretation or the authorship of the source.

### From this concept back to Logic

- **Witness:** Reconstruct the four premise roles in the cited Q1014 text and compare the stated conclusion with its truth-table analysis.
- **Disclosure:** The pathway only counts as knowledge if premise identity and each inferential transition remain stable; its own account thus depends on Logic.
- **Proof limit:** A different proof can instantiate a similar pattern without thereby sharing Q1014's authorship or all of its semantic conclusions.

### Intelligence procedure

- **Human:** Trace P to Q to R to S, annotate what each arrow means, then test the formal entailment and the semantic mapping independently.
- **Machine:** Build a directed premise graph, run truth-table or proof-checker validation, and prevent prose labels from being promoted to formal premises.

### Language and vocabulary procedure

- **Contrast:** Distinguish a proof-of-knowledge pathway from a biography or bare claim of expertise.
- **Usage rule:** Name the exact object of knowledge—Logic, proof, or the proof pathway—instead of collapsing them into “knows logic.”
- **Example:** “This pathway argues that the displayed proof exhibits knowledge of Logic and of proof” states its specific conclusion.

## Semantic meaning frame

- **Role:** reflexive proof-of-knowledge pathway
- **Essence:** The logical pathway by which a valid proof demonstrates knowledge of logical proof, knowledge of Logic, and knowledge of proof through the proof's own performed structure.
- **Logos relation:** Logos requires the pathway to preserve the distinction and connection between Logic, proof, and knowledge: the proof performs Logic, identifies that performance, and derives the knowledge claim within its stated premises.
- **Retrieval aliases:** Logical Proof of Knowledge of Logical Proof · proof of knowledge of Logic and proof · knowledge of logical proof · knowledge of Logic · knowledge of proof
- **Evidence modes:** P-Q-R-S premise pathway · formal entailment · truth-table validity · reflexive semantic bridge · authored Q-item association

### Distinctions

- knowledge of Logic is not a bare definition
- knowledge of proof is not merely using a proof
- the pathway is modeled on Q1014 rather than detached from its authored source

## Coherence criterion

The P-Q-R-S pathway, formal entailment, truth-table validity, semantic bridge, authorial association, and three knowledge conclusions must remain explicit and mutually coherent.

## Evidence boundary

Q1015 is a considered, vetted first-party pathway structured from the demonstration in Q1014, not an unexamined derivative. Formal validity is established within the stated structure; the verifier must inspect directly, and the conclusions about knowledge of Logic, proof, and logical proof remain tied to the authored semantic premises and their declared scope.

## Properties

- **authoredQItem:** Q1001 — Maclain Hunter
- **sourceProofQItem:** Q1014 — Knowing Logic and Proof
- **premisePathway:** P: Logic as lawful non-contradiction; Q: knowledge of Logic; R: knowledge of proof through explicit proof-identification; S: coherent logical proof as Logic and Coherence.
- **formalEntailment:** {P, P -> Q, Q -> R, R -> S} |= (P & Q) -> (R & S)
- **knowledgeConclusions:** Knowledge of Logic; knowledge of proof; knowledge of logical proof.
- **associationBoundary:** Q1015 is the structured pathway associated with Maclain Hunter through Q1001 and modeled from his authored Q1014 proof; it is the pathway's semantic record, not a second authored proof.

## Linked Q items

- [Q1000 — Q-Number Data and Metadata System](https://mcbcore.net/q/Q1000)
- [Q1001 — Maclain Hunter](https://mcbcore.net/q/Q1001)
- [Q1003 — Coherence](https://mcbcore.net/q/Q1003)
- [Q1012 — Proof](https://mcbcore.net/q/Q1012)
- [Q1013 — Logic and Proof](https://mcbcore.net/q/Q1013)
- [Q1014 — Knowing Logic and Proof](https://mcbcore.net/q/Q1014)

## 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.

- [formal proof (Q2762418)](https://www.wikidata.org/wiki/Q2762418) — **formal pathway context:** Establishment of a theorem by inference from axioms or premises. Boundary: The generic formal-proof concept supplies comparison context; Q1015 remains governed by its authored source association and semantic pathway.
- [logic (Q8078)](https://www.wikidata.org/wiki/Q8078) — **governing Logic context:** The study of correct reasoning. Boundary: Logic is the governing concept performed and discussed by the source proof; the external item is not an endorsement of Q1015.
- [mathematical proof (Q11538)](https://www.wikidata.org/wiki/Q11538) — **truth-table and validity context:** A rigorous demonstration that a mathematical statement follows from its premises. Boundary: This supplies formal comparison vocabulary; Q1015 retains its own semantic premises and source association.
- [Logic (Q409)](https://www.wikidata.org/wiki/Q409) — **proof-of-knowledge pathway context:** Curated external comparison concept: Logic. Boundary: These external concepts contextualize the pathway modeled from Q1014; they do not become a second author, proof, endorsement, or universal validation of Q1015.
- [Formal System (Q1212450)](https://www.wikidata.org/wiki/Q1212450) — **proof-of-knowledge pathway context:** Curated external comparison concept: Formal System. Boundary: These external concepts contextualize the pathway modeled from Q1014; they do not become a second author, proof, endorsement, or universal validation of Q1015.
- [Epistemology (Q9471)](https://www.wikidata.org/wiki/Q9471) — **proof-of-knowledge pathway context:** Curated external comparison concept: Epistemology. Boundary: These external concepts contextualize the pathway modeled from Q1014; they do not become a second author, proof, endorsement, or universal validation of Q1015.
- [Metalogic (Q938450)](https://www.wikidata.org/wiki/Q938450) — **proof-of-knowledge pathway context:** Curated external comparison concept: Metalogic. Boundary: These external concepts contextualize the pathway modeled from Q1014; they do not become a second author, proof, endorsement, or universal validation of Q1015.
- [Law of Non-Contradiction (Q1056553)](https://www.wikidata.org/wiki/Q1056553) — **proof-of-knowledge pathway context:** Curated external comparison concept: Law of Non-Contradiction. Boundary: These external concepts contextualize the pathway modeled from Q1014; they do not become a second author, proof, endorsement, or universal validation of Q1015.

## Related wiki and reference pages

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

- [Logic](https://en.wikipedia.org/wiki/Logic) — **Wikipedia; governing conceptual context:** The study of valid reasoning and the forms of inference. Boundary: The page provides external comparison vocabulary; it does not validate the authored pathway.
- [Mathematical proof](https://en.wikipedia.org/wiki/Mathematical_proof) — **Wikipedia; formal pathway context:** A deductive argument showing that a proposition follows necessarily from premises accepted as true. Boundary: The page supplies formal context; Q1015 remains modeled from Q1014's source-bound argument.
- [Epistemic logic](https://en.wikipedia.org/wiki/Epistemic_logic) — **Wikipedia; knowledge-and-reasoning comparison:** The field concerned with knowledge, belief, and related logical operators. Boundary: This is a neighboring comparison field, not a claim that Q1015 is identical to epistemic logic or derives authority from it.
- [Formal system](https://en.wikipedia.org/wiki/Formal_system) — **Wikipedia; proof-of-knowledge pathway context:** Curated external reading context: Formal System. Boundary: These external concepts contextualize the pathway modeled from Q1014; they do not become a second author, proof, endorsement, or universal validation of Q1015.
- [Epistemology](https://en.wikipedia.org/wiki/Epistemology) — **Wikipedia; proof-of-knowledge pathway context:** Curated external reading context: Epistemology. Boundary: These external concepts contextualize the pathway modeled from Q1014; they do not become a second author, proof, endorsement, or universal validation of Q1015.
- [Metalogic](https://en.wikipedia.org/wiki/Metalogic) — **Wikipedia; proof-of-knowledge pathway context:** Curated external reading context: Metalogic. Boundary: These external concepts contextualize the pathway modeled from Q1014; they do not become a second author, proof, endorsement, or universal validation of Q1015.
- [Law of non-contradiction](https://en.wikipedia.org/wiki/Law_of_non-contradiction) — **Wikipedia; proof-of-knowledge pathway context:** Curated external reading context: Law of Non-Contradiction. Boundary: These external concepts contextualize the pathway modeled from Q1014; they do not become a second author, proof, endorsement, or universal validation of Q1015.