The converse inequality argument against tests of statistical significance

Critics have put forth several arguments against the use of tests of statistical significance (TOSSes). Among these, the converse inequality argument stands out but remains sketchy, as does criticism of it. The argument states that we want P(H/D) (where H and D represent hypothesis and data, respectively), we get P(D/H), and the 2 do not equal one another. Each of the terms in 'P(D/H) not equal to P(H/D)' requires clarification. Furthermore, the argument as a whole allows for multiple interpretations. If the argument questions the logic of TOSSes, then defenses of TOSSes fall into 2 distinct types. Clarification and analysis of the argument suggest more moderate conclusions than previously offered by friends and critics of TOSSes. Furthermore, the general method of clarification through formalization may offer a way out of the current impasse.