provability

Noun

Meaning

capability of being demonstrated or logically proved

Synonyms

Hypernyms

Examples

Also, it makes the concept of "provability," and thus of "theorem," a clear concept that only depends on the chosen system of axioms of the theory, and not on the choice of a proof system. Source: Internet

Gödel was a platonist and therefore had no problems with asserting the truth and falsehood of statements independent of their provability. Source: Internet

Crucially, because the system can support reasoning about properties of numbers, the results are equivalent to reasoning about provability of their equivalent statements. Source: Internet

Questions about the provability of statements are represented as questions about the properties of numbers, which would be decidable by the theory if it were complete. Source: Internet

Questions about the provability of statements within the system are represented as questions about the arithmetical properties of numbers themselves, which would be decidable by the system if it were complete. Source: Internet

Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified. Source: Internet

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