incompletion

Incompletion is the state or condition of not being complete or finished. As a general term, it denotes lacking one or more essential elements, details, or stages necessary to reach a finished or fully specified form.

In linguistics and discourse analysis, incomplete utterances, or sentence fragments, occur when a speaker leaves a thought unfinished or relies on context to fill in gaps. Such incompletions can be intentional (ellipsis) or due to interruption, difficulty, or recording issues. They are often resolved by the listener’s or reader’s inference, and their acceptability depends on context, genre, and communicative goals.

In mathematics and logic, incompleteness is a central concept. In topology or analysis, a space is incomplete if not every Cauchy sequence converges within the space; for example, the rational numbers with the standard metric form an incomplete metric space because a Cauchy sequence may converge to an irrational number outside the rationals. In mathematical logic, Gödel's incompleteness theorems show that any sufficiently strong formal system cannot prove all arithmetic truths, reflecting a related notion of inherent incompleteness.

In data processing and computing, incomplete data or records have missing values that complicate analysis and modeling. Techniques such as imputation, deletion, or the use of models that accommodate missing data are applied to mitigate the effects of incompleteness.

Other uses include descriptions of partial performance in contracts, drafts in writing, or any situation where a process or product is not yet finished.