> If all the training data contains semantically-meaningful sentences it should be possible to build a network optimized for generating semantically-meaningful sentence primarily/only.
Not necessarily. You can check this yourself by building a very simple Markov Chain. You can then use the weights generated by feeding it Moby Dick or whatever, and this gap will be way more obvious. Generated sentences will be "grammatically" correct, but semantically often very wrong. Clearly LLMs are way more sophisticated than a home-made Markov Chain, but I think it's helpful to see the probabilities kind of "leak through."
But there is a very good chance that is what intelligence is.
Nobody knows what they are saying either, the brain is just (some form) of a neural net that produces output which we claim as our own. In fact most people go their entire life without noticing this. The words I am typing right now are just as mysterious to me as the words that pop on screen when an LLM is outputting.
I feel confident enough to disregard duelists (people who believe in brain magic), that it only leaves a neural net architecture as the explanation for intelligence, and the only two tools that that neural net can have is deterministic and random processes. The same ingredients that all software/hardware has to work with.