What does undecidable mean?
Undecidable is an adjective for something that cannot be decided, determined, or settled with confidence. It is especially common in law, mathematics, philosophy, and formal systems, where a case or proposition may have no uniquely correct resolution under specified rules. In general discussion, the word can imply that evidence is insufficient, alternatives are genuinely balanced, or a decision would require criteria that have not been established. It is more formal and analytical than simply saying that someone cannot choose. The term should not be used to suggest that every question is permanently beyond thought; usually it identifies a problem as undecidable relative to a particular system, body of evidence, or set of assumptions. That qualification is central in mathematical logic, where Gödel's incompleteness theorems established that some meaningful statements cannot be proved or disproved within sufficiently powerful formal systems. Undecidable is therefore useful whenever precision matters: it distinguishes a difficult choice from one that lacks a determinate answer under stated conditions.
adjectiveUnable to be decided, determined, or settled. It may also mean so difficult to resolve that no clear answer or effective solution is available.
- Unable to be decided, determined, or settled with certainty or by a definite answer.
"The committee confronted an undecidable question that required a choice between two equally defensible principles."
"Whether the proposed rule was consistent became an undecidable issue before the panel."
"The mathematicians showed that the statement was undecidable within the formal system under consideration."
Gödel's incompleteness theorems showed that some statements are undecidable even within sophisticated formal systems.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does undecidable come from?
The English adjective was formed by combining the prefix un- with decidable. Decidable comes from Latin decidere, meaning "to decide," which was formed from de- and cadere, both of which relate to falling or settling. The same Latin root underlies words such as decide, decision, and decisive.
Related word forms
How undecidable is actually used
This is primarily a formal, academic, legal, or mathematical term. In mathematical logic, it usually means that a proposition cannot be proved or disproved within a specified formal system, not that the proposition lacks meaning.
Easily confused with undecidable
Undecidable is the standard modern spelling, while indecidable is a less common variant encountered especially in legal and historical writing.