Thanks for this comment. I was attempting to abstract away from the specific details of NHST and talk about the general idea since in many particulars there is much to criticize, but it appears that I abstracted too much - the ordering of the hypothesis space (i.e. a monotone likelihood ratio as in Neyman-Pearson) is definitely necessary.

In a closely analogous fashion, a hypothesis test is a probe for a certain kind of inadequacy in the statistical model. The statistic is the equivalent of the grade, and the threshold of statistical significance is equivalent of the standard of bare adequacy.

This seems to back up my claim that we can still view NHST as a sort of induction without a detailed theory of induction (though the reasons for and nature of this "thin" induction must be different from what I was thinking about). Do you agree?