That's not even a bayesian point of view, even in a frequentist setting the p-value is a conditional probability, conditioned on the dataset.

What he says is (I gather) worse: those events are only separated be 1.1std deviations, which is little.

I think that's what he's saying too, but what is that supposed to show? Is he arguing against some claim that every interval of 1 standard deviation is equally significant? Did anybody make this claim? So far as I know, nobody considers (say) a 6-sigma effect to be 6 times stronger than a 1-sigma effect...

I don’t get it either. It’s a trivial consequence of having a threshold: if we say two cities are “far” when they are at least 1000 miles away then Washington D.C. is not far from Jacksonville while Boston is far from Jacksonville, even though Boston is not far from Washington.

That's not quite the problem.

Let's assume you've already decided in advance what "far" means.

Without moving either city from its current location, the same experiment can give you "very far" and "very close" in identical replications.

I’m commenting on pfortuny’s (correct) interpretation “those events are only separated be 1.1std deviations, which is little” of the original post by Gelman (the difference between a significant result and a non-significant result may not be significant = a city which is far from Jacksonville and a city which is not far from Jacksonville may not be far from each other).

I still don't get it. What p-value observations would not be "reasonable" here? It seems to me he's saying that anything between 0 and 1 is completely reasonable, which is a completely pointless statement as I see it.

His point is that the whole point of the field of statistics is that cherry picking results or getting lucky once is not proof of anything, unlike nonstatistical mathematics where one example is enough to justify a claim.

> He is seeing the p-value as a random variable that can take values from 0 to 1 and follows some distribution.

That is the frequentist point of view!