Are there classes of intelligence? Are there things that some classes can and cannot do? Is it a spectrum? Is the set of classes countable? Is it finite? Is there a maximum intelligence? One can dream…
If you just mean what problems can it solve, and how quickly, we already have a well developed theory of that in terms of complexity classes -https://complexityzoo.net/Complexity_Zoo
If you've ever interacted with a very smart animal, it's easy to recognize that their reasoning abilities are on par with a human child in a very subjective and vague way. We can also say with extreme confidence that humans have wildly different levels of intelligence and intellectual ability.
The question is, how do we define what we mean by "Alice is smarter than Bob". Or more pertinently, how do we effectively compare the intelligence and ability of an AI to that of another intelligent entity?
Is ChatGPT on par with a human child? A smart dog? Crows? A college professor? PhD level?
Of course we can test specific skills. Riddles, critical thinking, that sort of thing. Problem is that the results from a PhD will be indistinguishable from the results of a child with the answer key. You can't examine the mental state of others, so there's no way to know if they've synthesized the answer themselves or are simply parroting. (This is also a problem philosophers have been thinking about for millenia)
Personally, I doubt we'll answer these questions any time soon. Unless we do actually develop a science of consciousness, we'll probably still be asking these questions in a century or two.
There's a lot of factors there and more that I haven't specified. But one thing that I believe is essential is the belief that an answer is correct or uncertain.
That presumes a total ordering of intelligence. I think the balance of evidence is that no such total ordering exists.
There are things chatgpt can do that children (or adults) cannot. There are thing that children can do that chatgpt cannot.
At best maybe the Turing test can give us a partial ordering.
I don't think there is much value in viewing "intelligence" as a whole. Its a combination of a multitude of factors, that need to be dealt with independently.
The closest effort I know of as far characterizing intelligence as such is Steven Smale's 18th problem.
The original paper is better, but still seems to be too vauge to be useful. Where it isn't vauge it seems to point pretty strongly to computability/complexity theory.
Intelligence means many different things to different people. If we just gesture vaugely at it we aren't going to get anywhere, everyone will just talk past each other.
Smale is a very smart person but his stuff indeed seems as much a vague gesture as the other efforts. I feel like neural networks have succeeded primarily because of the failure of theorists/developers/etc to create any coherent theory of intelligence aside from formal logic (or Perl, formal probability). Nothing captures the ability of thinking to use very rough approximations. Nothing explains/accounts-of Moravec's Paradox etc.
If there's a nonphysical aspect to human intelligence and it's not computable, then that means computers can never match human intelligence even in theory.
In modern thinking, we do certainly recognize different classes of intelligence. Emotional intelligence, spatial reasoning, math, language, music.
I'd say the classes of intelligence are finite. Primarily because different types of intelligence (generally) rely on distinct parts of our finite brains.
As for maximum intelligence, I like the angle taken by several SciFi authors. Generally, when an AI is elevated to the extremes of intelligence, they detach from reality and devolve into infinite naval gazing. Building simulated realities or forever lost in pondering some cosmic mystery. Humans brought to this state usually just die.
For physical, finite entities, there's almost certainly an upper limit. It's probably a lot higher than we think, though. Biological entities have hard limits on energy, nutrients, and physical size beyond which it's just impossible to maintain any organism. Infinities are rarely compatible with biology, and we will always be limited.
Even an AI is still beholden to the practicalities of moving energy and resources around. Your processor can only get so large and energy/information can only move so fast. Intelligence in AI is probably also bounded by physical constraints, same as biological entities.
My bet is there is some level of “incompleteness” to what an intelligence (ours or a machine’s) can do, and we can’t just assume that making one means it can become a singularity. More likely we’re just going to max out around human levels of intelligence, and we may never find a higher level than that.
I've seen people state this before, but I don't think I've seen anyone make a scientific statement on why this could be the case. The human body has a rather tight power and cooling envelope itself. On top of that we'd have to ask how and why our neural algorithm somehow found the global maxima of intelligence when we can see that other animals can have higher local maxima of sensory processing.
Moreso machine intelligence has more exploration room to search the problem space of survival (aka Mickey7) that the death any attached sensoring/external network isn't the death of the AI itself. How does 'restore from backup' affect the evolution of intelligence?
Granted there are limits somewhere, and maybe those limits are just a few times what a human can do. Traversing the problem space in networks much larger than human sized capabilities might explode in time and memory complexity, or something weird like that.
But a lack of infinities won't prevent the basic scenario of tech improving tech until things are advancing too fast for humans to comprehend.
I think this approximate nature of intelligence is essentially why neural nets have been more successful than earlier Gofai/logic based system. But I don't think that means formal approaches to intelligence are impossible, just they face challenges.