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Perspective Reasoning and the Solution to the Sleeping Beauty Problem

Gao, Xianda (2018) Perspective Reasoning and the Solution to the Sleeping Beauty Problem. [Preprint]

Perspective Reasoning and the Solution to the Sleeping Beauty Problem, Xianda Gao, 19-11-2018.pdf

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This paper proposes a new explanation for the paradoxes related to anthropic reasoning. Solutions to the Sleeping Beauty Problem and the Doomsday argument are discussed in detail. The main argument can be summarized as follows:
1. Our thoughts, reasonings and narratives inherently comes from a certain perspective. With each perspective there is a center, or using the term broadly, a self.
2. The natural first-person perspective is most primitive. However we can also think and express from others’ perspectives with a theory of mind.
3. A perspective’s center could be unrelated to the topic of discussion so its de se thoughts need not to be considered, e.g. the perspective of an outside observer. Let’s call these the third- person perspective.
4. First-person reasoning allows primitive self identification as I am inherently unique as the center. Whereas from third-person perspective I am not fundamentally special comparing to others so a reference class of observers including me can be defined.
5. It is my contention that reasonings from different perspectives should not mix. Otherwise it could lead to paradoxes even independent of anthropic reasoning.
6. The paradoxes surrounding anthropic reasoning are caused by the aforementioned perspective mix. Regarding the sleeping beauty problem the correct answer should be double halving. Lewisian halving and thirding uses unique reasonings from both first and third- person perspectives.
7. Indexical probabilities such as “the probability that this is the first awakening” or “the probability of me being one of the first 100 billion human beings” also mixes first- and third- person reasonings. Therefore invalid.
8. Readers against perspectivism may disagree with point 1 and suggest we could reason in objective terms without the limit of perspectives. My argument is compatible with this belief. Objective reasoning would be analytically identical to the third-person perspective. My argument would become that objective reasoning and perspective reasonings should not mix. In the following I would continue to use “third-person perspective” but readers can switch that to “objective reasoning” if they wish so.

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Item Type: Preprint
Gao, Xianda
Keywords: sleeping beauty problem, doomsday argument
Subjects: Specific Sciences > Probability/Statistics
Depositing User: Mr Xianda Gao
Date Deposited: 20 Nov 2018 01:57
Last Modified: 20 Nov 2018 01:57
Item ID: 15355
Subjects: Specific Sciences > Probability/Statistics
Date: 19 November 2018

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