What do you imagine a statistical output is ? and why do you imagine you can't be certain about it ? LLM are not picking words out of a bag at random and neither are they just blindly picking the most frequent words in the training set. What do you imagine all that computation is doing?
>given that it has no model of the meaning of any of the words in its output to compute certainty in the form of correspondence with reality?
Says who ? I mean basically all the research (quite a few) on the topic points to LLMs having a pretty good idea of the certainty and truth of their outputs internally. Some pretrained models even have the logit probabilities directly correspond to the probability of being right (https://imgur.com/a/3gYel9r).
Statistics is not magic. LLMs clearly have a model of the meaning of the words they use amongst many other things.
But in this case, it means that the underlying point in embedding space doesn't map clearly to only one specific token. That's not too different from when you have an idea in your head but can't think of the word.
Humans are similar. A human's reality is built on the experiences (senses) it's been feed. There definitely are several major differences, the obvious one being that we have a different sensory input than an LLM, but there are others, like human's having a instinctual base model of reality, shaped by the effects of natural selection over our ancestors.
Just like an LLM can't tell if the reality it's been fed actually corresponds to the "truer" outside reality (you could feed an LLM lies like the sky is plaid in such a way that it would report that it's true), a human can't tell if the reality it's been fed actually corresponds to a "truer" outside reality (humans could be feed lies like we are in true reality, when we're actually all NPCs in a video game for a higher level).
The LLM can't tell if it's internal reality matches an outside reality, and humans can't tell if their internal reality matches an outside reality, because both only have the input they've received to go on, and can't tell if it's problematic or it's incomplete.
You're basically saying that no computer program can work, because if you randomly generate a computer program then most of them don't work.