Resolving Neyman's Paradox

According to Fisher, a hypothesis specifying a density function for X is falsified (at the level of significance α) if the realization of X is in the size‐α region of lowest densities. However, non‐linear transformations of X can map low‐density into high‐density regions. Apparently, then, falsifications can always be turned into corroborations (and vice versa) by looking at suitable transformations of X (Neyman's Paradox). The present paper shows that, contrary to the view taken in the literature, this provides no argument against a theory of statistical falsification.