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### Incompleteness theorems

The two incompleteness theorems of Gödel claim that statements can be formally undecidable.

##### Explanation

The first incompleteness theorem states that any formal system that is internally consistent, contains statements for which cannot be proved that they are true or false.

The second incompleteness theorem says that from within a formal system you cannot prove that it is internally consistent.

##### Artificial intelligence

The incompleteness theorems come down to the fact that artificial intelligence is not possible because computers always are formal finite systems. Most probably, human intellect is also restricted by those limitations.