So I think here you're mainly talking about the process by which artificial intelligence can be achieved. I don't disagree that, in principle, it should be possible to do this by some kind of brute-force, big-data optimisation programme. There is such a thing as evolutionary computation and genetic algorithms, after all. I think it's probably unrealistic to do that in practice, at least in other than evolutionary time scales, but that's just a hunch and not something I can really support with data, like.

But what I'm talking about is testing the intelligence of such a system, once we have it. By "testing" I mean to things: a) detecting that such a system is intelligent in the first place, and, b) measuring its intelligence. Now ARC-AGI muddles the waters a bit because it doesn't make it clear what kind of test of intelligence it is, a detecting kind of test or a measuring kind of test; and Chollet's white paper that introduced ARC is titled "On the measure of intelligence" which further confuses the issue: does he assume that there already exist artificially intelligent systems, so we don't have to bother with a detection kind of test? Having read his paper, I retain an impression that the answer is: no. So it's a bit of a muddle, like I say.

In any case, to come back to the brute force issue: I assume that, by brute force approaches we can solve any problem that humans solve, presumably using our intelligence, but without requiring intelligence. And that makes it very hard to know whether a system is intelligent or not just by looking at how well it does in a test, e.g. an IQ test for humans, or ARC, etc.

Seen another way: the ability to solve problems by brute force is a big confounding factor when trying to detect the presence of intelligence in an artificial system. My point above is that we have no good way to control for this confounder.

The question that remains is, I think, what counts as "brute force". As you say, I also don't think of neural net inference as brute force. I think of neural net training as brute force, so I'm muddling the issue a bit myself, since I said I'm talking about testing the already-trained system. Let's say that by "brute force" I mean a search of a large combinatorial space carried out at inference time, with or without heuristics to guide it. For example, minimax (as in Deep Blue) is brute force, minimax with a neural-net learned evaluation function (as in AlphaGo and friends) is brute force, AlphaCode, AlphaProof and similar approaches (generating millions of candiates and filtering/ ranking) is brute force, SAT-Solving is brute force, searching for optimal plans is brute force. What is not brute force? Well, for example, SLD-Resolution is not brute force because it's a proof procedure, arithmetic is not brute force because there's algorithms, boolean logic is not brute force, etc. I think I'm arguing that anything for which we have an algorithm that does not require a huge amount of computational power is not brute force, and I think that may even be an intuitive definition. Or not?