Ill posed does not necessarily mean impossible. Most of the problems we deal with in real life are ill posed, but we still usually manage to come up with solutions that are good enough for the particular contexts at hand. What it does mean is that we shouldn't expect the problem in question to be definitely solved once and for all. I'm not arguing against attempting to test rationality. I'm arguing against the position some posters have taken that there's no point even trying to make progress on rationality until the problem of testing it has been definitely solved.