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Kingreaper comments on How to Convince Me That 2 + 2 = 3 - Less Wrong
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It's often poor form to quote oneself, but since this post (deservedly) continues to get visits, it might be good to bring up the line of thought that convinced me that this post made perfect sense:
The space of all possible minds includes some (aliens/mental patients/AIs) which have a notion of number and counting and an intuitive mental arithmetic, but where the last of these is skewed so that 2 and 2 really do seem to make 3 rather than 4. Not just lexically, but actually; the way that our brains can instantly subitize four objects as two distinct groups of two, their minds mistakenly "see" the pattern 0 0 0 as composed of two distinct 0 0 groups. Although such a mind would be unlikely to arise within natural selection, there's nothing impossible about engineering a mind with this error, or rewiring a mind within a simulation to have this error.
These minds, of course, would notice empirical contradictions everywhere: they would put two objects together with two more, count them, and then count four instead of three, when it's obvious by visualizing in their heads that two and two ought to make three instead. They would even encounter proofs that 2 + 2 =4, and be unable to find an error, although it's patently absurd to write SSSS0 = SS0 + SS0. Eventually, a sufficiently reflective and rational mind of this type might entertain the possibility that maybe two and two do actually make four, and that its system of visualization and mental arithmetic are in fact wrong, as obvious as they seem from the inside. We would consider such a mind to be more rational than one that decided that, no matter what it encountered, it could never be convinced that 2 and 2 made 4 rather than 3.
Now, given all that, why exactly should I refuse to ever update my arithmetical beliefs if given the sort of experiences in Eliezer's thought experiment? Wouldn't the hypothesis that I am such an agent get a lot of confirmation? (Of course, I very strongly don't expect to encounter such experiences, because of all the continuing evidence before me that 2 + 2 = 4; but if I did wake up in that situation, I'd have to accept that some part of my mind is probably broken, and the part that tells me 2 + 2 = 4 is as likely a candidate as any.)
Upon suddenly discovering that the whole world looks different this morning than it did last night is the rational belief "I guess I was deluded for my whole life up to this point" or "I guess I'm deluded now"?
Considering the fact that you're not waking up in a mental institution, but the world still seems to contain them (and if you get 2 sets of 2 of them, you have 3); the latter is a much more likely situation
You're neglecting the hypothesis "my memories of the past are being distorted to convince me that 2 and 2 make 4 instead of 3". Given how easily we distort our memories under conditions of sanity, this is as likely as "I'm deluded now".
If you suddenly gain a set of memories indicating that the raptor conspiracy is taking over the world, you would be considered deluded.
If you suddenly gain a set of memories indicating that 2+2 equals something other than what it DOES in fact equal, you are likewise deluded.
So your suggestion is in fact a subset of being deluded*. At which point you should voluntarily seek out psychological/psychiatric help.
If you believe (as you seem to suggest by use of the aactive rather than the passive voice) that this delusion is being deliberately induced, it is important to remember that anyone with the power to induce that delusion could also reduce you to a gibbering wreck; and hence that going to get help is highly unlikely to be "part of their plan".
This is a distraction from the actual point; of course if this happened to me, then my first priority would be getting help (I might be having a stroke, for instance). But once I'm at the hospital and they tell me that I'm all right, but something strange happened to my brain so that it falsely remembers 2 and 2 having made 4, instead of the obviously correct 3...
If you don't agree that some set of circumstances like this should conspire to make me rationally accept 2+2=3, then if the scenario happened to you (with 3 and 4 reversed), you're asserting that you could never rationally recover from that metal event. Since I'd prefer, should I go through a hallucination that 2 and 2 always made 3, to be able to recover given enough evidence, I have to take the "risk" of being convinced of something false, in a world where events conspired against me just so.
Why completely leave out the possibility that you aren't deluded at all? Depending on just what kind of 'different' you wake up in that is a distinct possibility.
I would, by the way, start with a high prior for 'deluded now' which would be altered one way or the other by extensive reality testing. I experience that in dreams all the time. I know from personal experience it is easier for me to be confused about the transient sensory experience of the present than the broad structure of all my memories. Results may vary somewhat.
Good point, in the case of waking up in a logically possible world, remembering a previous logically possible world, there is a non-zero possibility that you've actually gone from one to the other somehow. How low the probability is depends on the nature of the differences
I was too caught up in the case of waking up in a world where the world you remember is logically impossible.
Exactly. And with slightly different wording a world in which it seems like you have changed from one logical world to another is itself a just a logically possible world.
That would be awkward! It would require an awful lot of reality testing on the question of just how logically impossible things were. Even after that your confidence in just about anything would be fubared.