partialness

Partialness, or partiality, is the quality of being partial rather than complete. It describes situations in which a description, assessment, function, or system covers only part of a whole, leaving other parts undefined, unknown, or unspecified. In everyday usage, partial information or a partial answer provides only a subset of what would be known in a full account.

In mathematics and logic, partialness has several precise meanings. A partial function from a set A to a set B is defined only on a subset of A, not for all elements of A. A partial order is a relation that is reflexive, antisymmetric, and transitive but not necessarily total, so some elements are not comparable. In many-valued logics, statements may take more than the binary true/false values, including indeterminate or unknown, reflecting a form of partial truth.

In computer science, partialness appears in programming concepts. Partial application fixes some arguments of a function, producing a new function that awaits the remaining inputs. Partial evaluation specializes a program to known inputs to generate a more efficient version for those cases. Partial functions also arise in programming languages when inputs fall outside the defined domain, potentially requiring error handling or default behavior.

In epistemology and everyday reasoning, partial knowledge and biased perspectives acknowledge limits on what can be known or justified. Partial representations can be useful for managing complexity or acting under uncertainty, but they can also mislead if the missing parts are important. Understanding partialness involves clarifying what is defined, what remains undefined, and how the partial view relates to the whole.