This example isn’t sitting comfortably in my mind. How I’m thinking is this:
First of all, (boring answer, see the Dreaming Paradox) you should always assume reality is as you directly observe it to be, for safety reasons.
[Objection] “But in this thought experiment, your observations and your inferences based on those observations are likely to be incorrect due to delusion.”
[Response] In that case, there’s no hope for being aligned with reality in the first place and you should abandon the project and continue to assume reality is as you observe it just in case you’re right. I claim that it would be equally delusional for a real psychiatrist to believe themselves to be a patient.
Moving on:
Some people are psychiatrists
Some psychiatrists do work at mental hospitals
[Conclusion] finding yourself in a mental hospital should increase your chances of being a psychiatrist vs. finding yourself in, say, a grocery store or a gym.
I can think of at least a few pieces of evidence that should be very strong evidence that a person has a profession. e.g.:
Being on the payroll (physical evidence: paycheck)
Living somewhere else (physical evidence: driving home)
Generally being able to leave the facility without being strongly challenged, despite obvious contact with security. [If you have to resort to violence to leave, you are escaping and should rethink your employment status.]
Most other employees, particularly high-ranking employees, agreeing that they are your co-workers. Particularly, nobody challenging your profession. [Admittedly, this could still be sketchy in a delusional situation, but still not for nothing.]
It’s not that experiences like these cannot be imagined by a sufficiently deluded mind, but if we’re arguing on those grounds there should be no standard of evidence in general to prove that you are not a mental patient (or a brain in a jar, or simulated for that matter).
[Conclusion] Observing good hard evidence (like being allowed to drive home and cash your paycheck) should increase, not decrease your confidence that you are a psychiatrist and not a patient in a situation where you find yourself at a mental hospital. In the case that you’re still wrong, you’re presumably in the best available place to get the help you obviously need and shouldn’t worry too much about it.
[Objection] “Shut up and actually do the math. You can assume some sufficiently extreme numbers from the scenario to be able to do some calculations. Maybe you’re the only psychiatrist in a ten-thousand patient facility dedicated to delusional disorders.”
[Response] Since the prior probability that you are a psychiatrist and not a patient should actually be quite high in either case, doing a Bayesian update on proportions consistent with the scenario should render only a small decrease in confidence. This is still a step in the wrong direction, though. My intuition is that, like e.g. the 2 envelope paradox, this will actually end up being the wrong math somehow.
[Objection] “You can’t just decide the math is wrong because you don’t like the answer.”
[Response] Agreed, but an actual psychiatrist who does the math without error and updates on the results to become more confident that they are a patient has updated away from being correctly aligned with reality. The math is wrong, just like Newtonian physics is wrong. It works under a wide variety of circumstances, but when you plug in some extreme numbers of the right kind it just fails to make good predictions.
Re: The Psychiatrist Paradox
This example isn’t sitting comfortably in my mind. How I’m thinking is this: First of all, (boring answer, see the Dreaming Paradox) you should always assume reality is as you directly observe it to be, for safety reasons.
[Objection] “But in this thought experiment, your observations and your inferences based on those observations are likely to be incorrect due to delusion.”
[Response] In that case, there’s no hope for being aligned with reality in the first place and you should abandon the project and continue to assume reality is as you observe it just in case you’re right. I claim that it would be equally delusional for a real psychiatrist to believe themselves to be a patient.
Moving on:
Some people are psychiatrists
Some psychiatrists do work at mental hospitals
[Conclusion] finding yourself in a mental hospital should increase your chances of being a psychiatrist vs. finding yourself in, say, a grocery store or a gym.
I can think of at least a few pieces of evidence that should be very strong evidence that a person has a profession. e.g.:
Being on the payroll (physical evidence: paycheck)
Living somewhere else (physical evidence: driving home)
Generally being able to leave the facility without being strongly challenged, despite obvious contact with security. [If you have to resort to violence to leave, you are escaping and should rethink your employment status.]
Most other employees, particularly high-ranking employees, agreeing that they are your co-workers. Particularly, nobody challenging your profession. [Admittedly, this could still be sketchy in a delusional situation, but still not for nothing.]
It’s not that experiences like these cannot be imagined by a sufficiently deluded mind, but if we’re arguing on those grounds there should be no standard of evidence in general to prove that you are not a mental patient (or a brain in a jar, or simulated for that matter).
[Conclusion] Observing good hard evidence (like being allowed to drive home and cash your paycheck) should increase, not decrease your confidence that you are a psychiatrist and not a patient in a situation where you find yourself at a mental hospital. In the case that you’re still wrong, you’re presumably in the best available place to get the help you obviously need and shouldn’t worry too much about it.
[Objection] “Shut up and actually do the math. You can assume some sufficiently extreme numbers from the scenario to be able to do some calculations. Maybe you’re the only psychiatrist in a ten-thousand patient facility dedicated to delusional disorders.”
[Response] Since the prior probability that you are a psychiatrist and not a patient should actually be quite high in either case, doing a Bayesian update on proportions consistent with the scenario should render only a small decrease in confidence. This is still a step in the wrong direction, though. My intuition is that, like e.g. the 2 envelope paradox, this will actually end up being the wrong math somehow.
[Objection] “You can’t just decide the math is wrong because you don’t like the answer.”
[Response] Agreed, but an actual psychiatrist who does the math without error and updates on the results to become more confident that they are a patient has updated away from being correctly aligned with reality. The math is wrong, just like Newtonian physics is wrong. It works under a wide variety of circumstances, but when you plug in some extreme numbers of the right kind it just fails to make good predictions.