Given that they are Turing complete when you put a loop around them, that claim is objectively false.
The last time I had this discussion with people I pointed out how LLMs consistently and completely fail at applying grammar production rules (obviously you tell them to apply to words and not single letters so you don't fight with the embedding.)
LLMs do some amazing stuff but at the end of the day:
1) They're just language models, while many things can be described with languages there are some things that idea doesn't capture. Namely languages that aren't modeled, which is the whole point of a Turing machine.
2) They're not human, and the value is always going to come from human socialization.
They absolutely are. It's trivial to test and verify that you can tell one to act as a suitably small Turing machine and give it instructions to use to manipulate the conversation as "the tape".
Anything else would be absolutely astounding given how simple it is to implement a minimal 2-state 3-symbol Turing machine.
> Assuming the model can even follow your instructions the output is probabilistic so in the limit you can guarantee failure.
The output is deterministic if you set the temperature to zero, at which point it is absolutely trivial to verify the correct output for each of the possible states of a minimal Turing machine.
It's pretty hard to make any kind of complex system that can't be coerced into being Turing complete once you add iteration.
But these endless claims that the fact they're "just" predicting tokens means something about their computational power are based on flawed assumptions.