Lumifer, please update that at this moment you don't grok the difference between "A => B (p=0.05)" and "B => A (p = 0.05)", which is why you don't understand what p-value really means, which is why you don't understand the difference between selection bias and base rate neglect, which is probably why the emphasis on using Bayes theorem in scientific process does not make sense to you. You made a mistake, that happens to all of us. Just stop it already, please.

I feel like this could use a bit longer explanation, especially since I think you're not hearing Lumifer's point, so let me give it a shot. (I'm not sure a see a meaningful difference between base rate neglect and selection bias in this circumstance.)

The word "grok" in Viliam_Bur's comment is really important. This part of the grandparent is true:

Assume that the reported p-values are true (and not the result of selection bias, etc.). Take a hundred papers which claim results at p=0.05. At the asymptote about 95 of them will turn out to be correct and about 5 will turn out to be false.

But it's like saying "well, assume the diagnosis is correct. Then the treatment will make the patient better with high probability." While true, it's totally out of touch with reality- we can't assume the diagnosis is correct, and a huge part of being a doctor is responding correctly to that uncertainty.

Earlier, Lumifer said this, which is an almost correct explanation of using Bayes in this situation:

But that all is fine -- the readers of scientific papers are expected to understand that results significant to p=0.05 will be wrong around 5% of the times, more or less (not exactly because the usual test measures P(D|H), the probability of the observed data given the (null) hypothesis while you really want P(H|D), the probability of the hypothesis given the data).

The part that makes it the "almost" is the "5% of the times, more or less." This implies that it's centered around 5%, with random chance determining what this instance is. But selection bias means it will almost certainly be more, and generally much more. In fields that study phenomena that don't exist, 100% of the papers published will be of false results that were significant by chance. In many real fields, rates of failure to replicate are around 30%. Describing 30% as "5%, more or less" seems odd, to say the least.

But the proposal to reduce the p value doesn't solve the underlying problem (which was Lumifer's response). If we set the p value threshold lower, at .01 or .001 or wherever, we reducing the risk of false positives at the cost of increasing the risk of false negatives. A study design which needs to determine an effect at the .001 level is much more expensive than a study design which needs to determine an effect at the .05 level, and so we will have many less studies attempted, and many many less published studies.

Better to drop p entirely. Notice that stricter p thresholds go in the opposite direction as the publication of negative results, which is the real solution to the problem of selection bias. By calling for stricter p thresholds, you implicitly assume that p is a worthwhile metric, when what we really want is publication of negative results and more replications.