Perspective Reasoning and the Sleeping Beauty Problem

bydadadarren7mo22nd Nov 201810 comments

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I want to present a new argument for double-halving position for the sleeping beauty problem. It is my contention that paradoxes related to the anthropic principle such as the Sleeping Beauty Problem and the Doomsday Argument is caused by mixing logics from different perspectives. To solve these paradoxes we only need to reason from a single consistent perspective.

When thinking about anthropic related paradoxes one perspective we can employ is an observer’s first-person perspective. The center of a perspective is primitively unique in logic and reasoning. E.g. I am fundamentally special to myself. I do not need to know any objective differences between me and every other human being to tell “this is me”. Similarly, the present moment is primitively meaningful. I can inherently tell “now” is not any other time. From first-person perceptive it is possible to specify the center, e.g. myself and now, from other people and time without any additional information.

We can also reason as an outside observer, or employ a God’s view, I call it the third-person perspective. The main point is that the center of that perspective is irrelevant to the topic of interest. From this perspective there is no obvious “me”. Every observer in question is ordinary as everybody else. In order to specify someone from a group one have to know the differences between him and the rest. Similarly there is no “now” that inherently stands out from any other moment. From third-person perspective every observer and everyday are treated as equals.

I argue the reasonings from these two perspectives should not be mixed and used together. So I am either inherently special (such that no information is needed to specify me) or just an ordinary person as everybody else is. Similarly “today” is either a meaningful moment uniquely stands out or everyday in the experiment are equals. We should always stick to one perspective and not use both points in the same logic framework. Mix them up and paradoxes would ensue.

From this starting point I derived the answer to the Sleeping Beauty Problem should be double halving. Several point worth mentioning:

  1. No matter which perspective one choose to reason from there is no new information when beauty wakes up.

  2. Questions such as “the probability of today is Monday” is invalid. Such probabilities do not exist since it requires specifying today from first-person perspective and treats both days in the experiment as equals like third-person perspective does.

  3. This means after being told it is Monday beauty could keep her answer unchanged at 1/2.

  4. Repeating the experiment from any single perspective and the relative frequency of heads can be shown to be 1/2.

  5. This provide new arguments for double halfer position when it involves bets and rewards (such as Dutch book arguments)

  6. It provides a perfect explanation for the perspective disagreement troubling halfers as pointed out by Pittard (2015).

  7. It does not result in the embarrassment as other double halfer position do as pointed out by Titelbaum(2012).

  8. It disproves the Doomsday Argument and the Presumptuous Philosopher base on the same principle.

My complete argument in pdf can be found here.

https://www.sleepingbeautyproblem.com/wp-content/uploads/2018/11/Perspective-Reasoning-and-the-Solution-to-the-Sleeping-Beauty-Problem-Xianda-Gao-19-11-2018.pdf

I apologize in advance for my language skills and possible misuse of terminologies. English is not my native language and philosophy is not my field. I desperately need feedbacks especially counter arguments. Thank you.

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