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I don't think the assumption that LLM training data is random with respect to truth value is reasonable - people don't write random text for no reason at all. Even if the current training corpus was too noisy for the "truth surface" to become clear - e.g. because it's full of shitposting and people exchanging their misconceptions about things - a better-curated corpus should do the trick.
Also, I don't see how this idea would invalidate the last couple centuries of Western philosophy. The "truth surface", should it exist, would not be following some innate truth property of statements - it would only be reflecting the fact that the statements used in training were positively correlated with truth.
EDIT: And yes, this would be a huge thing - but not because of some fundamental philosophical reasons, but rather because it would be an effective way to pull truths and correlations from aggregated beliefs of large number of people. It's what humans do when they synthesize information, but at a much larger scale, one we can't match mostly because we don't live long enough.