from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • noun The condition of being unprovable


from Wiktionary, Creative Commons Attribution/Share-Alike License

un- +‎ provability or unprovable +‎ -ity


  • We need to look at this so-called unprovability a little more closely to gain a better understanding of it and its context.

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  • He hinted that he had made great progress in the theory of provability and unprovability by exploring the connections between logic and topology.

    Nobody Knows Nothing

  • He did, however, conjecture in correspondence with Gödel the unprovability of the consistency of arithmetic and therefore of mathematics as a whole, in some absolute sense.


  • The unprovability construct is represented explicitly in the language, by means of a modal operator

    Logic and Artificial Intelligence

  • The TMS also provided specific intuitions: the idea that the key to nonmonotonicity has to do with inferences based on unprovability was important for the modal approaches to nonmonotonic logic and for default logic.

    Logic and Artificial Intelligence

  • The Second Incompleteness Theorem establishes the unprovability, in number theory, of the consistency of number theory.

    Kurt Gödel

  • Several commentators on the surprise test paradox object that interpreting surprise as unprovability changes the topic.

    Epistemic Paradoxes

  • Because on the science-test-ology, let's push the boundaries of known unprovability side, you have people that will sometimes build new stuff without much thought for the art-and-social welfare.

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  • Gödel's first incompleteness theorem states that, for a sufficiently strong formal theory like Peano Arithmetic, any sentence asserting its own unprovability is in fact unprovable.

    Provability Logic

  • The significance of this is that all questions of provability (or unprovability) of mathematical statements can be in principle reduced to formal questions of formal derivability from the generally accepted axioms of Set Theory.

    Set Theory


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