Can LLMs actually represent meaning? / Getting over the impenetrable wall

A discussion of AI and LLM often hits an impenetrable wall: “But it’s just a statistical model, and thus it cannot really …”. The variations of the “stochastic parrot” arguments assert that being trained on a language, LLM can capture only the surface aspects of the language (e.g. that word X often follows a sequence (W1, W2, W3)), but not the underlying meaning.