Not really. It distinguishes LLM output from human output even though they look the same sometimes. The process by which something comes into existence is a valid distinction to make, even if the two processes happen to produce the same thing sometimes.
It makes sense to do so in the same way that it’s useful to distinguish quantum mechanics from classical mechanics, even if they make the same predictions sometimes.
A proposition of any kind of mechanics is what can be true or false. The calculations are not what makes up the truth of a proposition, as you’ve pointed out.
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