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What does undecidability mean?

Looking for the meaning or definition of the word undecidability? Here's what it means.

Noun
  1. the state of being undecidable.
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We realize that some undecidability hangs permanently on her shoulders, when Majaj depicts an irremovable rift in her identity.
This work was largely on recursion theory and undecidability.
Perhaps it was part of a more general interest in undecidability, and ambiguity.
Such concepts point to the undecidability of affect, its existence in the self and the other, the film and the theorist.
Such an attempt quickly presents the problem of undecidability, an interesting principle with wide-ranging implications.
But, in the haze and visual undecidability of Lyons' St Albans facades, perhaps some remnants of both these lost ideals also hover.

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