This pandemic has allowed me some time to finish up my anthropic arguments. The complete argument is now accessible on my website, https://www.sleepingbeautyproblem.com
My approach is a Perspective-Based Argument (PBA). I think anthropic problems often end up paradoxical because a critical aspect of reasoning has been consistently overlooked. I propose perspectives are integral parts of reasoning. If an argument seems to be purely objective and does not appear to originate from any particular agent, that typically means it is formulated from a god's eye perspective, i.e. a view from nowhere.
PBA can be expressed as follows:
Perspective and its center are primitively identified. It cannot be derived. Nor is it the outcome of any event. E.g. If Caesar ponders upon his perspective center and asks "Why am I Caesar?" Then there is no logical explanation to that question other than "it just feels so". The perspective center is a reasoning starting point. Very much like an axiom or a postulate.
Indexicals, such as "I", "now", and "here", are references to the perspective center. Each of them points to a different aspect of it. "I" refers to the agent at the perspective center; "now" the time; and "here" the location.
Due to their relationship with the perspective center, indexicals are logically unique. E.g. the concept of "I" and the concepts of other physical persons are incomparable. In plain language, it just means "to me, I am inherently special."
Indexicals' uniqueness is perspective-bounded. So the person referred to as "I" from my perspective is not inherently unique from your viewpoint. If we reason as an impartial outsider, i.e. with a god's eye view, then no particular person/time would be unique. Due to this indifference, an explanation is needed when attention is given to a particular person/time. That explanation would be, conceptually speaking, a sampling process.
Because perspectives are reasoning starting points, logics from different perspectives must not be mixed. It's like propositions from different axiomatic systems cannot be used together. A valid argument must be formulated from one consistent perspective.
Anthropic paradoxes treat all observers/moments with indifference, yet their arguments focus on "I" or "now" without any justification. The indifference is valid from a god's eye view while the special focus is valid from the first-person view. They are conflicting since they are based on different perspectives.
It might be tempting to try to validate this conflict. The easiest way would be to regard indexical such as "I" and "now" as the outcome of some fictional sampling process. That would lead to common approaches such as SSA and SIA (and FNC in a less obvious manner). However, that is unjustified as perspective centers are primitively identified. It is not the outcome of some event.
There is no valid reference class for indexicals. Subsequently, self-locating probabilities (the probabilities of indexicals being a particular member of some proposed reference class) are also invalid concepts. Examples include "the probability that "today" is Monday/Tuesday" in the sleeping beauty problem; "the prior probability distribution of "my" birth rank among all humans " in the doomsday argument, etc.
Perspective disagreement over probability while sharing all information can exist in anthropic problems. It happens when the probability's underlying meaning depends on the answerer's perspective. Just like the question of "Am I a man?". Its answer depends on who the responder is.
Base on the above, PBA leads to the following conclusions:
- Double-halving in the Sleeping Beauty Problem without being unBayesian
- The Doomsday Argument is false.
- The presumptuous philosopher is wrong
- In the Simulation Argument, the probability of me being simulated is an invalid notion
- The idea of the fine-tuned universe is invalid.
Obviously I am biased. However, I genuinely believe PBA starts with plausible postulates then explains all paradoxes in this field without ever being ad hoc. If anything, I hope people would pay more attention to other anthropic arguments besides common approaches as SSA, SIA, and FNC.