The same kind of proof we accept for any scientific claim: converging, reproducible evidence that rules out competing explanations.

Concretely, that means: We already have indirect evidence: conscious states vary predictably with brain states. Damage specific regions, lose specific functions. Alter chemistry, alter experience. This is not proof, but it’s systematic dependence, which is exactly what emergence predicts. Stronger evidence would look like precise, bidirectional mappings between neural activity and reported experience: to the point where you could reliably read subjective states from brain data, or induce specific experiences through targeted stimulation. We’re already moving in that direction.

The hardest bar would be building a system from physical components, having it report coherent subjective experience, and being able to explain why that configuration produces experience while others don’t. That’s the hard problem: and no, we’re not there yet. And it’s worth being honest: we’ve been assuming physicalism will eventually solve it, but there’s no guarantee that’s true rather than hopeful. The fact that brain states correlate with conscious states doesn’t explain why there is something it is like to have those states. Correlation is not mechanism.

But here’s the key point: you’re implicitly holding emergence to a standard of certainty that no scientific theory meets. We don’t have that standard of proof for evolution, gravity, or quantum mechanics either. We have overwhelming evidence that makes alternatives implausible.

So the question isn’t “can you prove it beyond all doubt?” It’s “does the evidence favor it over alternatives?” Right now, it does — but that’s a pragmatic verdict, not a metaphysical one. Idealist frameworks like Kastrup’s or Faggin’s remain serious contenders. The debate is more open than mainstream science often admits.