Good comment.

However,

arbitrarily decide that everything that predicts observations that would be only 5% likely if it was false is true and everything without such observations is false, regardless of how many observations were actually made

This was hard to parse. I would have named "p-value" directly. My understanding is that a stated "p-value" will indeed depend on the number of observations, and that in practice meta-analyses pool the observations from many experiments. I agree that we should not use a hard p-value cutoff for publishing experimental results.