Combining Philosophers
Ideas for Melissus, Alexander and Kurt Gdel
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11 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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17885
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Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]
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10614
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The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]
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10072
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First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P]
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9590
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Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman]
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3198
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Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey]
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11069
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Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna]
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10118
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First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman]
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10122
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Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman]
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10611
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There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P]
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10867
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'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg]
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10039
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Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
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