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Gödel proved completeness for first-order logic and incompleteness results for formal arithmetic.
Context and limits
The results concern different notions of completeness. Incompleteness requires hypotheses about the formal theory; it is not a statement that all axiomatic systems fail in the same way.
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Gödel proved completeness for first-order logic and incompleteness results for formal arithmetic.
Assessor finding: supported · historical · Article passage
- Kurt Gödel — Stanford Encyclopedia of Philosophy — Sections 2.1 and 2.2
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- Kurt Gödel — Stanford Encyclopedia of Philosophy — Sections 2.1 and 2.2
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