6

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 AI tool. Basic equivalence of two first-order logic statements is undecidable, which has implications for knowledge-based systems and databases. For example, ...


3

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 undecidable questions. It's really not clear that this is so. Consider what Godel's theorems say, in essence: "powerful" formal systems cannot prove, using ...


2

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 certain "truths" about mathematics, but unless I am mistaken, the PSSH doesn't imply that the symbol system of the mind needs to decide truths. Though implicitly ...


1

A system is Turing complete if it can be used to simulate any Turing machine. Given the Church-Turing thesis (which has not yet been proven), a human brain can compute any function that a Turing machine can (given enough time and space), but the reverse is not necessarily true, given that the human brain might be able to compute more functions than a ...


1

My answer is yes, but in a trivial way. The least you would expect from an intelligent agent is that it is able to execute a given Turing machine on a given input. This requires actually no intelligence, just following rules. If however, you are referring to the capability of predicting if the Turing machine will terminate on the given input, that is another ...


1

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 in full on my personal website, but here's the conclusion: In the above it was shown that there are infinitely many proof constructions to Gödel’s theorem ...


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