I feel like some of the thought experiments are impossible in ways that are essential and not merely the result of informal formulation of something that could be pinned down.
On counterfactuals and causality, the universe doesn’t work in a way that allows you to only change the aim of a rock so it doesn’t hit a window. If you hold all else including the past constant then the change in the rock’s position or momentum is discontinuous. Our world conserves momentum and doesn’t allow rocks to teleport.
Back in the 1990s a meteorologist told me about a problem with weather models. Scientists would feed observations into the computer and say “go”. The model would forecast waves rippling out from observation points. Discrete, imprecise observations represent an impossible state. The waves were a result of the model relaxing from a physically impossible configuration to a physically possible configuration.
If you start teleporting rocks or winking the window out of existence for a moment you have broken the world like the bad observations broke the weather model.
If you define the laws of nature as “the entire future state of the universe” you run into a cousin of the the halting problem and Gödel’s incompleteness theorem. An arbitrarily complex system can not contain a complete model of itself. If there is not a simpler representation than “the entire future state is this”, laws of nature do not exist.
]]>1. Stochastic processes definitely are epistemic, are they also real? that’s a question beyond our capacity to figure out, in my humble opinion. To me, a stochastic process is one that under exactly the same state may evolve to more than one other possible subsequent state, so it depends on what we define the state to be. If we are presentists and the state is “The Present”, then it may be that it’s stochastic, but if we are eternalists then it’s impossible: the state is all spacetime (including past, present, and future) and this state uniquely identifies the position of each point. Now is that distinction useful? probably not, :D.
2. Definitely a one-boxer. the two boxers ignore the information that we know that the genie knows my decision in advance. If we accept this premise then the implication goes from my action to the genie’s decision, and not temporarily (remember, he knows the future).
I have to select the action that maximizes the money the genie will give me.
This problem reminds me A LOT of medieval scholastic philosophers talking about predestination, god’s omniscience (the genie), and free will. I hope I’m not breaking the rules, but for anyone interested, I would very highly recommend Peter Adamson’s podcast, History of Philosophy without any gaps. episode 276: “Back to the Future: Foreknowledge and Predestination.” You’ll be surprised at how modern scholastic philosophers sound, and how their concepts are almost on a one-to-one mapping with the modern terminology.
]]>Then, the puzzle is that the Principle of max. utility (based just on “evidence”) says to pick the one box: assuming your utility goes up in a typical way with money, you maximize your expected utility by going for one box.
However, the principle of dominance says to pick both boxes. Dominance seems to apply because the money is already in the opaque box (or not) and so you’ll pick up the extra 1K either way. So two boxing seems to dominate one boxing in the decision theoretic sense.
Here’s a variation. Suppose the back of the opaque box is transparent. I’m Sean Carroll’s friend. I can see whether the million is in the opaque box or not, just before Sean chooses. Either way, I’m going to tell him to take both boxes! Otherwise, he’s turning down an extra 1K.
So, it looks like one should use the Principle of Maximizing “Causal” expected utilities – in that case, you can reconcile dominance with rational way to make decisions.
So, I’m with Katie. In this case, the puzzle is set up to reward irrationality. But the rational thing to do is to take both boxes.
]]>‘Newcomb’s paradox| Famous Math Problems| NJ Wildberger’ (2013)
]]>I guess this observation must have been made a million times in this debate! Sorry, but I haven’t read the literature.
]]>How delightful! You should have Michael Strevens on your podcast. I wonder whether he is a 2-boxer?
]]>I really don’t understand the box problem. It was implied (at least I think it was) that picking both boxes is the “better” algorithm. Ok, perhaps there’s math that proves this? But to me it seems more important to describe exactly *how* the magical being makes his prediction. Is he looking into my brain and seeing what I personally am going to do in this situation? Or is he assuming that I’m a rational being and because I listen to podcasts like this one I will choose both boxes? Because I can’t think of a good reason why I would not choose the opaque box that will have $1 Million dollars in it. I’m very motivated to receive $1 Million dollars, no matter how “irrational” my choice might be (according to the math that I assume says “rationally I’m supposed to pick both boxes”.) – The MB seems to never be wrong, so it should know I will pick the opaque box and therefore get my $1 Million dollars. What would make the MB predict incorrectly for me – that I would *not* choose the single opaque box? Why is this choice not the right one?
For the one-boxers, I wonder how your choice and this experiment would change if the MB were penalized a significant amount of money for predicting incorrectly. Would that alter the outcome for you?
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