Questions tagged [incompleteness-theorems]

Gödels Incompleteness Theorem is a theorem that gives a limit on what can be mathematically derived. It is possible for a formal system to have statements that are true in the system, whose truth cannot be derived in a finite number of steps. Use this tag for questions about how the incompleteness theorem affects artificially intelligent systems.

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How does Lucas's argument work?

In Minds, Machines and Gödel (1959), J. R. Lucas shows that any human mathematician can not be represented by an algorithmic automaton (a Turing Machine, but any computer is equivalent to it by the ...