Search for Causes

[Paleophyte]

If I had an experience which I sincerely believed was God talking directly to me, how would I be able to prove or disprove what I believe?

Your sincerity or God? The former is tricky because people are pretty bad at distinguishing between truth and deception. I honestly wouldn't worry myself much over what other people believe if God was talking to me. The latter might be simpler if you can demonstrate some knowledge that most mortals don't have. Next week's lottery numbers are a favourite. Or ask God to pop in and say "Hi!" if you're on friendly terms with him. If you don't have anything that an average person might have guessed then you should be sceptical of your experience.

If I had advanced stage cancer and it suddenly disappeared or went into remission, how could it be proven to be from natural, rather than supernatural causes?

You might wonder why you got cancer in the first place. Is there a good reason for this supernatural force to give you cancer and then cure it? Was there some point in it not nipping that tumour in the bud when it was a single cell? It could have saved you a lot of grief and anguish but doesn't seem to have. Is there any reason why your cancer was more worthy of curing than the poor bastard in the next bed who's being eaten alive by his own bones? Maybe a trip to the paediatric oncology ward would prove enlightening.

We've gone looking for the supernatural before and every time we do we find either a mundane explanation or a load of bunk. It's either been willow bark or homeopathic preparations of rabid dog drool. Given that track record, and the questions that a "supernatural" cause poses, assuming the supernatural explanation isn't really warranted.

If natural science was unable to determine the cause,  what method could I use to determine if the origin or cause of these was supernatural?

It's rather part of the definition that the supernatural isn't accessible to the natural, so us mere mortals are out of luck unless this supernatural agency wants to pop by for a spot of tea. A good place to start might be to wonder why a supernatural agency would behave in this way. Why you? Why now? Why like this? Why not Bob the janitor, or little Timmy? Why give you cancer, let it progress to the final stages, and then cure it? Why not give that nice lady in the lab coat the proper CRISPR sequence to help you and a lot of other terminal patients?

Should I pursue other avenues or rely on science to eventually come up with an answer?

If you were stuck on Mars would you rather wait for your team to come back and rescue you or rely on a faith-based space program? Granted, the former will involve eating taters grown in your own shit. The latter involves flinging yourself from a cliff whilst chanting "I do believe!" as gravity inexorably does what it does best.

[Rahn127]

Nature is the set of existent things
If supernatural is the set of things that are not natural or non-existent, then what you seem to be asking is ....

"How can I tell if something non-existent has helped me ?"

[The Grand Nudger]

That's the usual crux of these disagreements. Self described supernaturalists need naturalism to mean something more restrictive than it does. Meanwhile, if it turned out that fairies really were painting the morning dew on flower petals, a naturalist would simply include fairies as part of "the world". -Part of nature.

Just as supernaturalists already conceive of them.