[llasram]

I agree that makes intuitive sense when applied to explicitly constructed experiments we could attempt to exactly repeat, but the intuition begins to break down in more complicated circumstances, such as retrospective or longitutinal studies. Saying something would happen "X% of the time anyway" becomes a philosophical issue.

[omginternets]

Yes, well, we could talk about frequentist vs bayesian statistics, but that's hardly the point of the article.

That is what a p-value means, feasibility aside. There are also more intuitive ways to think about it, "false-positive rate" being one.