Different people might justify vegetarianism by citing the suffering of animals, health benefits, environmental impacts, or purely spiritual concerns. As long as there isn't a camp of vegetarians that claim it does not have e.g. redeeming health benefits, we can more or less add all those opinions together.
I think that this is actually very close to the bible/koran example. If people reach similar conclusions from different reasons, they're probably just rationalizing. It would be very surprising if truly independent aspects of vegetarianism all happen to point the same way.
I guess this means that you and I reach the same conclusion about the bible/koran example, but for different reasons ;-)
ETA: I am more negative about vegetarian evidence than James, but I am also more positive about the theists (cf Unknowns, Michael Vassar). In both cases, I say that they are mistaken about why they hold the beliefs they do, but that doesn't necessarily mean the reason is bad. So maybe my position does not apply to my agreement with James.
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I dispute none of this, but so far as I can tell or guess, the main thing powering the superior statistical strength of PatientsLikeMe is the fact that medical researchers have learned to game the system and use complicated ad-hoc frequentist statistics to get whatever answer they want or think they ought to get, and PatientsLikeMe has some standard statistical techniques that they use every time.
Also, I presume, PatientsLikeMe is Bayesian or Bayes-like in that they take all available evidence into account and update incrementally, while every medical experiment is a whole new tiny little frequentist universe.
This is not really an article about PatientsLikeMe being strong, it is an article about the standard statistical methods of academic science being weak and stupid.
1) I'd like to see independent evidence of their "superior statistical strength".
2) On the face of it, the main difference between these guys and a proper clinical trial is an assumption that you can trust self-reports. Placebo effect be damned.
In particular, I'd really, really like to see the results for some homeopathic "remedy" (a real one, not one of those that silently include real active compounds).