There are, apparently, certain Eastern philosophies that permit and even celebrate logical contradiction. To what extent this is metaphorical I couldn't say, but I recently spoke to an adherent who quite firmly believed that a given statement could be both true and false. After some initial bewilderment, I verified that she wasn't talking about statements that contained both true and false claims, or were informal and thus true or false under different interpretations, but actually meant what she'd originally seemed to mean.
I didn't at first know how to argue such a basic axiom -- it seemed like trying to talk a rock into consciousness -- but on reflection, I became increasingly uncertain what her assertion would even mean. Does she, when she thinks "Hmm, this is both true and false" actually take any action different than I would? Does belief in NNC wrongly constrain some sensory anticipation? As Paul notes, need the law of non-contradiction hold when not making any actual assertions?
All this is to say that the matter which at first seemed very simple became confusing along a number of axes, and though Paul might call any one of these complaints "splitting hairs" (as would I), he would probably claim this with far less certainty than his original 100% confidence in NNC's falsehood: That is, he might be more open-minded about a community of mathematicians explaining why actually some particular complaint isn't splitting hairs at all and is highly important for some non-obvious reasons and due to some fundamental assumptions being confused it would be misleading to call NNC 'false'.
But more simply, I think Paul may have failed to imagine how he would actually feel in the actual situation of a community of mathematicians telling him that he was wrong. Even more simply, I think we can extrapolate a broader mistake of people who are presented with the argument against infinite certainty replying with a particular thing they're certain about, and claiming that they're even more certain about their thing than the last person to try a similar argument. Maybe the correct general response to this is to just restate Eliezer's reasoning about any 100% probability simply being in the reference class of other 100% probabilities, less than 100% of which are correct.
It seems to me that you are predicting the path of the pinball, but quickly enough that you don't realize you're doing it. It's such a fundamental axiom that if there is a clear downward path to a given position, this position will be reached, that it's easy to forget that it was originally reasoning about intermediate steps that led to this axiom. At most points the pinball can reach, it is expected to move down. At the next point, it's expected to move down again. You would inductively expect it to reach a point where it cannot move down anymore, and this point is the hole (or sometimes a fault in the machine).
Contrast with the hole being upraised, or blocked by some barrier. All of the paths you envision lead to a point other than the hole, so you conclude that the ball will land instead on some other array of points. There it's easier to see that gravity still requires path-based reasoning.
In case you're still active, I'm curious what your child's reasoning was for placing God in the pretend category. Like, did she know about Occam's Razor, or was she pattern matching God with other fantasies she's heard? I'm mostly curious because I don't think I've ever heard a perspective as undiluted as an Untheist's.
You forgot about MetaOmega, who gives you $10,000 if and only if No-mega wouldn't have given you anything, and O-mega, who kills your family unless you're an Alphabetic Decision Theorist. This comment doesn't seem specifically anti-UDT -- after all, Omega and No-mega are approximately equally likely to exist; a ratio of 1:1 if not an actual p of .5 -- but it still has the ring of Just Cheating. Admittedly, I don't have any formal way of telling the difference between decision problems that feel more or less legitimate, but I think part of the answer might be that the Counterfactual Mugging isn't really about how to act around superintelligences: It illustrates a more general need to condition our decisions based on counterfactuals, and as EY pointed out, UDT still wins the No-mega problem if you know about No-mega, so whether or not we should subscribe to some decision theory isn't all that dependent on which superintelligences we encounter.
I'm necroing pretty hard and might be assuming too much about what Caspian originally meant, so the above is more me working this out for myself than anything else. But if anyone can explain why the No-mega problem feels like cheating to me, that would be appreciated.
Gotcha. So, assuming that the actual Isaac Newton didn't rise to prominence*, are you thinking that human life would usually end before his equivalent came around and the ball got rolling? Most of our existential risks are manmade AFAICT. Or you think that we'd tend to die in between him and when someone in a position to build the LHC had the idea to build the LHC? Granted, him being "in a position to build the LHC" is conditional on things like a supportive surrounding population, an accepting government, etcetera; but these things are ephemeral on the scale of centuries.
To summarize, yes, some chance factor would def prevent us from building the LHC as the exact time we did, but with a lot of time to spare, some other chance factor would prime us to build it somewhen else. Building the LHC just seems to me like the kind of thing we do. (And if we die from some other existential risk before Hadron Colliding (Largely), that's outside the bounds of what I was originally responding to, because no one who died would find himself in a universe at all.)
*Not that I'm condoning this idea that Newton started science.
Are you responding to "Unless human psychology is expected to be that different from world to world?"? Because that's not my position, I'd think that most things recognizable as human will be similar enough to us that they'd build an LHC eventually. I guess I'm not exactly sure what you're getting at.
I'd agree that certain worlds would have the building of the LHC pushed back or moved forward, but I doubt there would be many where the LHC was just never built. Unless human psychology is expected to be that different from world to world?
I am extremely satisfied with this description; I hadn't personally thought of it in such specific terms, and this would be a perfect way to say it. I'll admit I'm a bit confused why you would pay before but not after, considering that either one is done by a person to whom the prophecy is given 50% less often.
The kind of person who pays to fight an infallible prophecy is the same kind of person to whom infallible prophecies are given 50% less often. In this case.
That second paragraph was hard for me. Seeing "a)" and "b)" repeated made me parse it as a jigsaw puzzle where the second "a)" was a subpoint of the first "b)", but then "c)" got back to the main sequence only to jump back to the "b)", the second subpoint of the first "b)". That didn't make any sense, so I tried to read each clause separately, and came up with "1. You are never safe. 2. You must understand. 3. On an emotional basis..." before becoming utterly lost. Only after coming back to it later did I get that repeated letters were references to previous letters.