>> RE Chomsky: You can see it's like epicycles: with enough parameters, an LLM is like a numerical method for curve fitting, that doesn't explain the data (any more than a fourier transform does). Curiously, they do seem to predict very accurately... yet also generalize strangely ("hallucinate"). What to think?
Well, that's the fundamental problem of modelling: that for any set of observations there's an arbitrary number of models that fit the data with great accuracy and even predict future observations well; and we don't know which one is the best in the long term.
The answer is that we should prefer not predictive models, but explanatory theories, that not only predict future observations but also explain why those observations should be expected to be made.
For example, the epicyclical model did not explain anything: it said nothing about why the planets should move on circular orbits with epicycles. Kepler's laws didn't explain anything because they didn't say why the planets should move on ellpitical orbits. Newton's law of universal gravitation explained it all in one stroke: because gravity. And that's why we consider Newton the greatest scientist of his era, not Kepler, not Coppernicus, not Gallileo, but Newton, because he explained the world and didn't just describe it.
Ultimately the advantage is, like you say, that when an explanatory theory fails, we can better know why. When a predictive model fails, we have no clue.
>> BTW Chomsky's point E (which I'd never heard of), the last and most minor, was based on Gold's work.
Gold's negative learnability result was a huge upheaval that led directly to the current paradigm of machine learning. Chomsky used it to support his argument about the poverty of the stimulous but linguistics was only one of the two fields that Gold's result turned upside down.
And it was a negative result. As I say in another comment, science gives you the tools to know when you're wrong and that's how progress is made, when we find out where we were wrong before.
With epicycles, it took almost two thousand years before we figured out where the model was wrong. Let's hope that it doesn't take that long with LLMs and neural nets also, because I doubt we have another couple thousand years to spare on a wild goose chase.
>> (I want to stress that the idea of epicycles, the mechanical craftsmanship, and actual prediction of the planets are all amazing genius.)
The epicyclical model persisted for so long because it was so good, and because there was nothing better. It is common for people who don't understand science to look at scientists of the past with derision and think they weren't even scientists, but for almost two thousand years, astronomers did exactly what a scientist must do: they accepted the best available theory, even if many of them hated it with a burning passion (and they did!). If it wasn't for the ancients stumbling and fumbling in the dark for millennia, we wouldn't today be enlightened and we owe them every respect.