undecidable

adjective

un·de·cid·able ˌən-di-ˈsī-də-bəl

: not capable of being decided : not decidable

… a huge popular audience, most of whom must have been baffled and exasperated by its elaborate and undecidable mystifications.—

David Lodge

… deconstruction, which teaches that literature is essentially "undecidable," beyond interpretation …—

James Atlas

To be complete such a system must be able to prove that any formula expressible in its language (a mathematical equation, for example, or a statement in symbolic logic) is either true or false; nothing can be undecidable.—

George Johnson

undecidability

ˌən-di-ˌsī-də-ˈbi-lə-tē

noun

Examples of undecidable in a Sentence

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Only a few years after Kurt Gödel had proved that mathematics was incomplete, Church and Turing showed with this work that some problems in mathematics are undecidable — no algorithm, however sophisticated, can tell us whether the answer is yes or no. —

Sheon Han, Quanta Magazine, 3 May 2023 But these, too, can turn out to be undecidable, since one set of interpreters can ascertain an implicit right to privacy, which is invisible to another—or even an explicit right to private ownership of guns, which has been invisible to every preceding set of interpreters. —

Adam Gopnik, The New Yorker, 26 Nov. 2021 Could a statement about a single tile also be undecidable? —

Jordana Cepelewicz, Quanta Magazine, 15 Dec. 2022