# Proposition

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

A proposition is a meaningful statement that can be asserted or denied and discussed as true or false within a specified logical context.

mko-proposition · concept · v0.10.0



## Mathematical statement

This entry uses an introductory classical context: a proposition P may be true or false, but being a proposition does not mean that P has been proved true.





## Representative formula (exact TeX)

P





## Assumptions


- P is a well-formed, meaningful proposition in the specified logical context.
- The true-or-false dichotomy is limited to the introductory classical context used by this entry.





## Symbol scope


- P — proposition variable





## Intuition, definition, and misconceptions

A proposition is a statement that can be asserted or denied. Both true and false propositions remain propositions; truth value is a semantic state, not the sole prerequisite for classifying text as a proposition.

A proof supports a proposition as true, but “P is a proposition” does not mean “P already has a proof.” In Lean one may first have P : Prop and then separately ask whether a proof term of P exists.

An open sentence such as x>0 contains an unspecified free variable. It becomes evaluable in a closed context only after substitution, quantification, or an explicit contextual assignment.

Common mistakes include treating questions, commands, or unclosed open expressions as propositions, or confusing “is a proposition” with “has been proved true.”





## Adopted derivation guide

[Proposition: deciding which candidate sentences are propositions, and separating 'is a proposition' from 'is proved true'](https://ocme.evemisslab.com/en/derivations/derivation-mko-proposition-01/)The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.





## Prerequisites







## Verification boundary

This entry is a conceptual candidate. Its research sources are not OCME Evidence, and no computational check or Lean formal proof has yet been registered.

not_formalized

This does not mean the content is false; it means no replayable computational or formal evidence is registered yet.





## Next obligation

Use P : Prop to establish a minimal Lean bridge between propositions and proof terms, while distinguishing any additional principles needed for classical truth semantics.





## Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.

[Canonical MKO JSON](https://ocme.evemisslab.com/data/mko/proposition.json) · [Plain Markdown](https://ocme.evemisslab.com/en/mko/mko-proposition/index.md)