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Jiro comments on Is Spirituality Irrational? - Less Wrong
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Hmmm. True, but now we're talking about a world specifically designed to produce the appearance of the opposite side of the canyon even when it doesn't exist. I think that we can, at least tentatively, discount active malevolence as an explanation for why I see the opposite side of the canyon.
Mind you, I'm not saying it can't be a mirage. If I'm short-sighted - so that everything beyond a certain distance is blurry and unrecognisable - and there just happens to be a large reflective surface partway across the canyon - then I may see the reflection of this side of the canyon, fail to recognise it due to the blurring, and claim that there is an opposite side to the canyon. (This can be recognised by a simple test, should anyone manage to produce prescription spectacles).
But let us say that my blind peers bring me incredibly convincing evidence for the idea that there is no other side of the canyon. They are very persuasive in that this "sight" business is a brain disease caused by being out and about in the heat of the day, making my brain overheat, and only in the coolness of night, when all is dark, am I sane. (And, sure enough, when it's dark then it's too dark to see the other side of the canyon).
But none of this is evidence that there is no other side. The other side could still be there - even if every argument advanced by my blind peers is true - and while I am sitting here questioning my sanity, the other side continues to sit there, perhaps visible to me alone, but nonetheless visible, and I should not throw that evidence away.
Your blind peers can't bring you convincing evidence that there's no other side to the canyon unless there actually is no other side to the canyon. It's like asking "what if homeopaths provided you with incredibly convincing evidence that homeopathy worked, would you still cling to what science says?" (The answer is that if it was possible to produce incredibly convincing evidence for homeopathy, we would be in a very different world than we are now, and science would be saying different things.)
On the contrary, it is quite possible to come up with some very convincing arguments for something that is false. There are many ways to do this, either by means of flawed argument, logical fallacy, carefully selecting only the evidence that supports a given theory, and so on. If I am sufficiently cautious in examining the arguments, I may identify the flaws and expose them - but it is also possible that I may fail to notice the flaws, because I am not perfect.
A homeopath can provide a convincing argument by providing a very long list of people who were ill, took a homeopathic remedy, and then recovered; and accompanying it with a very long list of people who were ill, took no homeopathic remedy, and got worse.
Anyone who notices the cherry-picking of evidence will see the flaw in that argument, but it will nonetheless convince many people.
I don't consider "evidence which would convince at least some people" to be "incredibly convincing evidence". Even poorly convincing evidence will convince someone--poorly convincing evidence isn't the same as nonconvincing evidence.
Ah, I think we have the point of disconnect here. I consider "incredibly convincing evidence" to be any evidence which would convince me. I am aware that this includes some flawed evidence that would convince me of incorrect things, but I can't provide a good example, because if I knew how it was flawed then it would not convince me (and if it has convinced me, then I don't know that it is flawed). Thus, yes, my examples were only vaguely convincing, in order to make the flaws clearer.