What does definability mean?
Definability is the property of being able to be defined: the quality that allows a word, concept, object, or set to have its meaning or extent pinned down with precision. In ordinary language it signals that something admits a clear, exact description rather than remaining vague or ineffable. Its most rigorous life, however, is in logic and mathematics, where definability is a precisely studied notion: an object is definable in a structure if some formula of the language singles it out uniquely. Landmark results such as Beth's definability theorem explore when concepts can be characterized explicitly versus only implicitly, and Gödelian phenomena show that certain truths resist definition altogether. The word carries a formal, analytical connotation and appears chiefly in philosophy, linguistics, theoretical computer science, and mathematics, making it valuable wherever precision about precision itself matters.
nounThe quality or state of being definable; the property of a concept, term, or object that its meaning or extension can be precisely specified, especially within a formal system.
- The general quality of being able to be defined or described precisely (everyday and general academic use).
- A technical property in logic and mathematics: the existence of a formula in a given language that uniquely specifies an object, relation, or set within a structure.
"Mathematicians debated the definability of the set within Zermelo–Fraenkel set theory."
"The charm of the place lies partly in its indefinability — though critics insisted on its definability through careful description."
"Beth's definability theorem shows that implicit definability entails explicit definability in first-order logic."
Rarely pluralized; the plural appears occasionally in technical discussions comparing different notions of definability across systems, but the singular with modifiers is strongly preferred.
"The survey compares several distinct definabilities arising in model theory."
In mathematical logic, some things can be proven to exist yet provably cannot be defined — definability has hard limits, and proving them won Gödel-level fame.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of definability
Definability is built from the verb "define," which English borrowed in the late Middle Ages from Latin "definire," meaning to mark out the limits or boundaries of something — literally de- (completely) + finire (to limit, from finis, "boundary"). The suffix "-ability" attaches to the participle stem "definable" to form an abstract noun denoting capacity. Its cognates therefore include the whole Latin-derived family around finis: finite, finish, final, and infinitive. The word gained particular prominence in nineteenth- and twentieth-century mathematical logic, where it became a term of art.
Related word forms
How definability is actually used
Predominantly formal and academic register, appearing most often in philosophy, linguistics, logic, and computer science. In everyday prose it is rare, where phrases like 'hard to define' are preferred. In technical contexts it is frequently qualified by the system involved, e.g. 'first-order definability' or 'definability in ZFC'.
Easily confused with definability
A definition is the statement that specifies meaning, whereas definability is the abstract property of being able to be so specified.
"Definite" describes something clear and unambiguous; "definability" names the capacity of something to have a precise definition assigned to it.