A patient believes she will recover against the odds. Is that irrational?
Its coordinates: 2.6 Rationality · 2.8 Formal Epistemology
A situation I meet in different forms every month, described here as a composite. A woman with a serious illness has, by the best evidence we have, about a one in three chance of recovering. She tells her doctor, and me, calmly and repeatedly, that she will recover. Not that she hopes to. That she will.
Is this irrational?
By one standard, obviously yes. Rational belief should be proportioned to the evidence, and the evidence says one in three. Believing it is certain is a mistake, the way believing a coin will land heads is a mistake.
By another standard, possibly not. If the belief helps her eat, sleep, keep appointments and endure treatment, then holding it may improve her odds a little. The research on whether optimism itself changes outcomes is, I think, weaker and more mixed than popular books suggest. But suppose it helps somewhat. Then the belief serves her ends, and believing what serves your ends is also a kind of rationality.
These two standards give opposite verdicts, and I don't think one is a trick. "Rational" seems to be doing two jobs: tracking truth and serving goals. Usually they coincide. At the bedside they sometimes don't.
My practical question: her doctor's duty is to tell her the truth about her prognosis. Is it also a duty to correct her belief? Or is her belief something other than a probability estimate, so that there is nothing to correct?