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, ...


4

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 (hard AI). So far there have been some successes with soft AI, as computers can perform tasks that required some "intelligence", though the degree of this ...


3

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 technical concept of formal systems that means the system cannot prove every formula. It is commonly framed as a system not being able to prove both a formula and ...


3

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 over a standard theorem proving algorithm: the mathematician can "step out of the system" (as Douglas Hofstadter called in Gödel, Escher, Bach), and start ...


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 ...


2

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

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 first machine cannot produce as being true, concede that that machine is indeed inadequate, but thereupon seek to construct a second, more adequate, machine, in ...


2

Artificial intelligence cannot be boiled down to designing algorithms, binary or otherwise, simply because the exhibition of intelligence in biological systems predated the invention of algorithmic computing. From this, we can further draw the conclusion that algorithms are not a necessary component of systems that exhibit behavior we deem intelligent. A ...


1

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 try to define AI (whose definition changed since the previous century). You could look at the table of contents of the Artificial Intelligence journal and ...


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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