7 votes
Accepted

What are some implications of Gödel's theorems on AI research?

Definitely there are a lot of implications for AI, including: Inference with first-order-logic is semi-decidable. This is a big disappointment for all the folks that wanted to use logic as a primary ...
4 votes
Accepted

How does Lucas's argument work?

Yes, it applies. If a statement cannot be derived in a finite number of steps, then it doesn't matter if the person trying to prove it is a human or a computer. The mathematician has one advantage ...
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4 votes

Do Gödel's theorems imply that intelligence systems may end up in some undecidable situation (that may make them take a wrong decision)?

Your initial statement on the core of AI is rather limited. In general, AI is concerned with modeling human behaviour either by imitation (soft AI) or by replicating the way human cognition works (...
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3 votes

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

I think the colloquial understanding of Gödel's incompleteness theorems allows them to be too broadly applied. Gödel's second incompleteness regards the consistency of a formal system, which is a ...
3 votes
Accepted

Shouldn't Gödel's incompleteness theorems disprove the physical symbol system hypothesis?

The PSSH is often attacked via either Godel's theorems or Turing's incomputability theorem. However, both attacks have an implicit assumption: that to be intelligent is to be able to decide ...
2 votes

How does Lucas's argument work?

After he lays out his argument, he deals with some counterarguments. The following looks like the weakest one to me: We can use the same analogy also against those who, finding a formula their ...
2 votes

Shouldn't Gödel's incompleteness theorems disprove the physical symbol system hypothesis?

Although there seems to be an apt analogy between Gödel's theorems and the PSHH, there is nothing formal linking the two together. More concretely, Gödel's theorems are about systems that decide ...
1 vote
Accepted

Do Gödel's theorems imply that intelligence systems may end up in some undecidable situation (that may make them take a wrong decision)?

Your question is mostly philosophical, not technical or scientific. So I am giving opinions and references here. the core of AI boils down to design algorithms I am noticing that you are not even ...
1 vote

What are some implications of Gödel's theorems on AI research?

I've written an extensive article on this some twenty years ago, which was published in Engineering Applications of Artificial Intelligence 12 (1999) 655-659. It's fairly technical and you can read it ...
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1 vote

What are some implications of Gödel's theorems on AI research?

I found this paper by mathematician and philosopher Solomon Feferman on Gödel's 1951 Gibbs lecture on certain philosophical consequences of the incompleteness theorems, while reading the following ...
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