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 title: "Newcomb's Paradox Resolved"
 date: 2020-11-28T00:00:00
 draft: false
-makerefs: false
 ---
 # Background
-I "solved" Newcomb's Paradox[1] about 3 years ago if I remember right. I use solved in quotes because you don't really "solve" a paradox. Paradoxes only seem to be contradictory at first glance. But, upon further inspection, they lead you to a new understanding of the problem where the paradox disappears. In other words, paradoxes arise out of a flawed or incomplete perspective. Newcomb's paradox in particular arises out of a misunderstanding of free will[2].
+I "solved" [Newcomb's Paradox](https://www.wikipedia.org/wiki/Newcomb%27s_paradox) about 3 years ago if I remember right. I use solved in quotes because you don't really "solve" a paradox. Paradoxes only seem to be contradictory at first glance. But, upon further inspection, they lead you to a new understanding of the problem where the paradox disappears. In other words, paradoxes arise out of a flawed or incomplete perspective. Newcomb's paradox in particular arises out of a misunderstanding of [free will](/2020/06/19/free-will-is-incoherent-part-1).
 
 # Telescoping Method
 Before I give away the "solution" to Newcomb's Paradox, I want to talk about my method for solving philosophical problems in general. I call it the telescoping method. When I am confronted with a philosophical problem, the first thing I do is try to understand the essence of the problem. To do that, I look at which abstractions the problem uses. I break them down and down until the problem makes sense. Then, one by one, I build up the abstractions again so I can explain in words what the solution is. I've found it to be very effective for philosophy. I'll use Newcomb's Paradox to show how it works.
 
 # Newcomb's Paradox
 ## The Problem
-Here's the problem from Wikipedia (CC BY-SA 3.0[3]):
+Here's the problem from Wikipedia ([CC BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0/)):
 
 > There is an infallible predictor, a player, and two boxes designated A and B. The player is given a choice between taking only box B, or taking both boxes A and B. The player knows the following:
 > Box A is clear, and always contains a visible $1,000.
@@ -22,11 +21,11 @@ Here's the problem from Wikipedia (CC BY-SA 3.0[3]):
 > The player does not know what the predictor predicted or what box B contains while making the choice.
 
 ## The Paradox
-Let's make it clear why this situation is a paradox before we attempt to resolve it. We are going to assume that the player is trying to maximize their profits. There are 2 strategies from game theory[4] that you can apply to Newcomb's Paradox.
+Let's make it clear why this situation is a paradox before we attempt to resolve it. We are going to assume that the player is trying to maximize their profits. There are 2 strategies from [game theory](https://www.wikipedia.org/wiki/Game_theory) that you can apply to Newcomb's Paradox.
 
-The first is the expected utility hypothesis[5]. It says you should take only box B. Its reasoning goes like this: Imagine you watched 1,000 philosophers play. Philosophers are split 50/50 on the issue, so about 500 would pick only box B, winning $1,000,000 and about 500 would pick both boxes, winning $1000. From a statistical standpoint, it's obvious you should pick box B.
+The first is the [expected utility hypothesis](https://www.wikipedia.org/wiki/Expected_utility_hypothesis). It says you should take only box B. Its reasoning goes like this: Imagine you watched 1,000 philosophers play. Philosophers are split 50/50 on the issue, so about 500 would pick only box B, winning $1,000,000 and about 500 would pick both boxes, winning $1000. From a statistical standpoint, it's obvious you should pick box B.
 
-The second is the strategic dominance principle[6]. It says you should take boxes A and B. Its reasoning goes like this: After the predictor has made its prediction and either put the $1,000,000 in box B or not, it can't change the amounts in the boxes. Therefore, choosing both boxes will always yield $1000 more than choosing only box B. You should take both boxes.
+The second is the [strategic dominance principle](https://www.wikipedia.org/wiki/Strategic_dominance). It says you should take boxes A and B. Its reasoning goes like this: After the predictor has made its prediction and either put the $1,000,000 in box B or not, it can't change the amounts in the boxes. Therefore, choosing both boxes will always yield $1000 more than choosing only box B. You should take both boxes.
 
 At first glance, both of these principles seem very compelling. It's paradoxical because they offer conflicting advice. How can we resolve this?
 
@@ -54,7 +53,7 @@ If it's not the infallible predictor causing the paradox, could the essence of t
 Even if your sincere intention is to pick only box B before the predictor makes its prediction, yet you change your mind and choose both boxes in the after prediction stage, the predictor will still correctly predict your choice and you will only win $1000.
 
 ### Choice
-We already examined the infallibility of the predictor and the player intent abstractions. They don't seem to cause the paradox. Perhaps the abstraction of choice is the problem? Newcomb's Paradox assumes it makes sense to talk about the player making a "choice" between 2 boxes and 1 box. But language to describe making a choice between several options is used in plenty of game theory problems. Even though I have shown that free will is incoherent[7], using what I call "the language of free will" doesn't seem to be an issue for other game theory problems. Why then would it be especially problematic in Newcomb's Paradox? Allow me to defer to some dialogue between Neo and The Oracle from The Matrix[8]:
+We already examined the infallibility of the predictor and the player intent abstractions. They don't seem to cause the paradox. Perhaps the abstraction of choice is the problem? Newcomb's Paradox assumes it makes sense to talk about the player making a "choice" between 2 boxes and 1 box. But language to describe making a choice between several options is used in plenty of game theory problems. Even though I have shown that [free will is incoherent](/2020/06/19/free-will-is-incoherent-part-1), using what I call "the language of free will" doesn't seem to be an issue for other game theory problems. Why then would it be especially problematic in Newcomb's Paradox? Allow me to defer to some dialogue between Neo and The Oracle from [The Matrix](https://www.wikipedia.org/wiki/The_Matrix):
 
 > Oracle: Candy?
 > Neo: Do you already know if I'm going to take it?
@@ -69,28 +68,13 @@ TLDR; choose only box B.
 
 Long answer: There is a very subtle contradiction in the definition of Newcomb's Paradox. Can you spot it? It says "The player does not know what the predictor predicted or what box B contains while making the choice". The hidden assumption there is that the "choice point" is after the predictor's prediction. This is impossible. The abstraction of choice collapses after the predictor has made the prediction. If we have to pick a point in time where it still makes any sense to talk about a "choice" being made, it would have to be before the predictor made the prediction. The strategic dominance principle is inherently tied to the idea of the player having a free choice after the predictor made the prediction. Therefore, it can't be the solution.
 
-Meanwhile taking only box B is supported by mathematical expected value, which doesn't rely on free choice being available after the prediction. It just says "If you take only box B, you can expect $1,000,000. If you take both boxes, you can expect $1,000". There's no notion of free will there. It's a purely statistical argument. The strategic dominance principle only seems appealing because of the strong intuition of having a free choice after the predictor has made the prediction. While retrocausality[9] doesn't actually occur in Newcomb's Paradox, it's not a bad mental model for thinking about the problem. Since the predictor is infallible, it has effective retrocausality. What the predictor did in the past is based on the box it already knows you're going to take. There's no real paradox, you just can't outwit the predictor even though your intuitions tell you that you "feel free".
+Meanwhile taking only box B is supported by mathematical expected value, which doesn't rely on free choice being available after the prediction. It just says "If you take only box B, you can expect $1,000,000. If you take both boxes, you can expect $1,000". There's no notion of free will there. It's a purely statistical argument. The strategic dominance principle only seems appealing because of the strong intuition of having a free choice after the predictor has made the prediction. While [retrocausality](https://www.wikipedia.org/wiki/Retrocausality) doesn't actually occur in Newcomb's Paradox, it's not a bad mental model for thinking about the problem. Since the predictor is infallible, it has effective retrocausality. What the predictor did in the past is based on the box it already knows you're going to take. There's no real paradox, you just can't outwit the predictor even though your intuitions tell you that you "feel free".
 
 You might think it doesn't make sense to prescribe players the strategy of choosing box B only, since they have "already made the choice" whether or not to take only box B. But, consider that by the same token, we have "already made the choice" whether or not to prescribe the player the strategy to take box B. So, it is equally coherent for us to prescribe the player to take box B as it is for the player to actually take box B. Saying there's no point in prescribing the player a course of action is akin to saying you'll just stay in bed all day since you have no free will. The "choice" to do nothing is also not of your own free will. In other words, you're not escaping your lack of free will by doing nothing. We aren't escaping the lack of the player's free will by not prescribing them a best course of action as we don't have free will either. So, there's no reason not to tell the player to take only box B.
 
 # Closing
-Some of the points I've written down in this post come from my own intuition. I couldn't write a single methodology for how I come up with it all. In philosophy, it's hard to define a single methodology that can solve problems since each problem is unique and touches on many different things. Maybe some day someone will come up with an algorithm for doing philosophy. Although that would be equivalent to finding an algorithm for truth[10], so no one would be able to agree that it actually worked.
+Some of the points I've written down in this post come from my own intuition. I couldn't write a single methodology for how I come up with it all. In philosophy, it's hard to define a single methodology that can solve problems since each problem is unique and touches on many different things. Maybe some day someone will come up with an algorithm for doing philosophy. Although that would be equivalent to finding an [algorithm for truth](https://yewtu.be/embed/leX541Dr2rU?local=true), so no one would be able to agree that it actually worked.
 
 Nonetheless, the telescoping method is good for getting you on the right track. It can also lead you down rabbit holes. I would caution that you don't try to break down abstractions more than necessary. There's a reason we have abstractions. They make it easier to think. Once you start breaking them down, the conceptual complexity increases. For example, if instead of talking about boxes I started talking about the billions of atoms that make up the boxes, that just makes it harder to think about the problem. And it doesn't add clarity. Be careful not to do that unnecessarily.
 
-Finally, in these dense philosophical essays, I welcome criticism[11]. About half of philosophers think you should take both boxes, so don't get the impression that my opinion is the only one. If you think I'm wrong about the paradox, I'd love to get feedback. As always, thanks for reading and feel free to send a donation[12] if you find my posts valuable.
-
-
-Link(s):
-[1: https://www.wikipedia.org/wiki/Newcomb%27s_paradox](https://www.wikipedia.org/wiki/Newcomb%27s_paradox)
-[2: /2020/06/19/free-will-is-incoherent-part-1](/2020/06/19/free-will-is-incoherent-part-1/)
-[3: https://creativecommons.org/licenses/by-sa/3.0/](https://creativecommons.org/licenses/by-sa/3.0/)
-[4: https://www.wikipedia.org/wiki/Game_theory](https://www.wikipedia.org/wiki/Game_theory)
-[5: https://www.wikipedia.org/wiki/Expected_utility_hypothesis](https://www.wikipedia.org/wiki/Expected_utility_hypothesis)
-[6: https://www.wikipedia.org/wiki/Strategic_dominance](https://www.wikipedia.org/wiki/Strategic_dominance)
-[7: /2020/06/19/free-will-is-incoherent-part-1](/2020/06/19/free-will-is-incoherent-part-1/)
-[8: https://www.wikipedia.org/wiki/The_Matrix](https://www.wikipedia.org/wiki/The_Matrix)
-[9: https://www.wikipedia.org/wiki/Retrocausality](https://www.wikipedia.org/wiki/Retrocausality)
-[10: https://yewtu.be/embed/leX541Dr2rU?local=true](https://yewtu.be/embed/leX541Dr2rU?local=true)
-[11: mailto:nick@nicholasjohnson.ch](mailto:nick@nicholasjohnson.ch)
-[12: /about](/about/)
+Finally, in these dense philosophical essays, I welcome [criticism](mailto:nick@nicholasjohnson.ch). About half of philosophers think you should take both boxes, so don't get the impression that my opinion is the only one. If you think I'm wrong about the paradox, I'd love to get feedback. As always, thanks for reading and feel free to [send a donation](/about/) if you find my posts valuable.