Questions tagged [incompleteness-theorems]

For questions related to Gödel's incompleteness theorems, which are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modeling basic arithmetic.

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Does Gödel's second incompleteness theorem put a limitation on artificial intelligence systems?

According to Brian Cantwell Smith no calculation without representation Therefore, computers depend on models. So, we can say that AI is limited internally by the model and external by the ...
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Do Gödel's theorems imply that intelligence systems may end up in some undecidable situation (that may make them take a wrong decision)? [closed]

So far I understand - I know very little on the topic - the core of AI boils down to design algorithms that shall provide a TRUE/FALSE answer to a given statement. Nevertheless, I am aware of the ...
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Shouldn't Gödel's incompleteness theorems disprove the physical symbol system hypothesis?

According to the Wikipedia page of the physical symbol system hypothesis (PSSH), this hypothesis seems to be a vividly debated topic in philosophy of AI. But, since it's about formal systems, shouldn'...
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What are some implications of Gödel's theorems on AI research?

Note: My experience with Gödel's theorem is quite limited: I have read Gödel Escher Bach; skimmed the 1st half of Introduction to Godel's Theorem (by Peter Smith); and some random stuff here and there ...
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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 ...