Summary: I argue perspectives are axiomatic and fundamental in reasoning. Perspectives cannot be derived. What we typically regard as objective reasoning are special forms of perspective thinking. Anthropic paradoxes are caused by defining the indexicals using imaginary sampling processes, E.g. treating I as a typical observer, or now as a randomly selected moment.
Primitive Perspective Centers
Let us assume the perspective of, say, this mug beside my laptop. Here we can make some perspective specific statements, such as “there is coffee within” or “there is a table immediately below”. We can also make statements not so restrictive to this particular perspective. Imagine observing the world as the mug to come up with physical laws. It would produce the same result as we have now. E.g. conservation of momentum still holds true from the mug’s perspective. However, from this perspective, one thing is logically unexplainable: “why is the perspective centered on this mug?”. Because we cannot reason from the mug’s perspective without first accepting it as the center. To put it more generally, recognizing the perspective center is the starting point of further reasonings. It has to be taken as given. Like an axiom, perspective centers are not derived. Its identification is primitive, which cannot be reduced by logic, only inferred by intuition or by postulation.
It may seem there is an obvious explanation as to why the perspective center is the mug. “Because I specified it so at the beginning of the last paragraph”. But that answer only applies to our (as the writer and readers’) perspectives, not the mug’s. It is more obvious in cases involving a natural person. Imagine we are discussing Julius Caesar’s life. Each of us is talking about what we would do if we were him. If one of us asks “why are we talking about Caesar anyway?”. A valid answer could be “because I brought him up in the conversation”. However, from Caesar’s perspective, if he ponders on the perspective center and asks “why am I Caesar?”. The answer cannot be because someone mentioned him in a random conversation two thousand years later. I argue there is no logical explanation for that question, only an appeal to intuition: because, for him, it just feels to be so. This particular human named Caesar is simply most immediate to the subjective experience, period. It cannot be reduced further.
Unique Status of Indexicals
Words such as “I”, “now” and “here” are called indexicals. Philosophers study them extensively and there are contending theories about them. However, for the scope of anthropic reasoning, I argue a simple and intuitive definition suffices. The indexicals are references to different aspects of the perspective center. E.g. “I” refers to the agent at the perspective center, “now” refers to the time of the perspective center, and “here” the location. Because the perspective center is primitive, indexicals have a unique logical status. This is, again, best illustrated with a natural person’s perspective.
For every single person, who “I” refers to is inherently clear. But to specify someone or something else would require a feature-description, e.g. “the tallest man alive”, and/or a relational property, e.g. “the mug to my left”. In contrast, the identification of “I” is purely primitive. It is not to be confused with the task of providing a description so that others, from their respective perspectives, could specify me. We can imagine cases where the latter is hard or impossible. For example, assume there is a parallel world whose contents are exactly like ours. Here it would be impossible to come up with a description so someone outside of both worlds could identify us. Yet each of us would still intuitively know which person is “me”, just point the finger at oneself.
Similarly “now” and “here” are primitively understood. I do not need a calendar and a clock to know what which moment is “now”, nor is a map of the universe required for me to know where “here” is supposed to mean. Each and everyone from their first-person perspective inherently understands them.
It should be noted the unique method of identification is only one manifestation of their specialness. Indexicals’ central status is reflected in many fundamental ways in our reasoning. For example, from a first-person perspective, our reasoning naturally focuses on “me” and “now”. In decision-making problems, self-interest is regarded as a basic objective. This logical significance of the present and self-focus is impossible to justify without employing a particular perspective.
Indifference and Sampling
Because the indexicals refer to the perspective center, their uses are restricted within each perspective. That is, they are incommunicable. If you knock on someone’s door and they ask “who is it?”. The sentence “It’s me” would be a pointless answer. Even though it is perfectly clear to you, “me” or “I” used here could not point to a specific potential visitor from their perspective. Of course, in real-life scenarios, you could utter that sentence and be identified by some extralinguistic features, such as your voice. Nonetheless, indexicals do not convey any information. They have a better chance of identifying you if you randomly decided to recite the alphabet. Simply put, “I” is unique from each one’s first-person perspective.
However, we often do not take the first-person perspective when reasoning about serious problems. We typically try to think objectively. Regardless of how one chooses to interpret it, objective thinking (e.g. taking a god’s eye perspective) is principally impartial. So objectively speaking, nobody is inherently special. That is, it is naturally indifferent to any particular agent/time or location. Due to this indifference, an explanation is needed when attention is given to a particular person/time. That explanation is, conceptually speaking, a sampling process. The sampling can be explicit, e.g. “a randomly selected entity among all potentially existing observers”. It can also be implicit by description, e.g. “the tallest person in all of the human history”. Either way, indexicals such as “I” cannot be used because we are no longer taking a particular observer’s first-person perspective.
Source of the Paradoxes
Many anthropic arguments end up as paradoxes because they do not reason from a consistent perspective. These arguments claim to reason objectively by treating all observers/moments (in their proposed reference class) indifferently. Yet they would ultimately focus on “I” or “now” without any logical explanation.
As discussed, the indifference is valid if we reason objectively or take a god’s eye perspective. As such, some form of sampling is needed to pick out a particular observer/moment. This sampling process is missing in these anthropic arguments because they also take the first-person perspective of an observer. From the first-person perspective, attention is naturally given to indexicals such as “I” and “now” as they are logically unique. Yet, the indifference to all and the uniqueness of one cannot coexist because they come from two different perspectives. Because of this mixed reasoning, each part of the argument appears to be sensible. However, the combined argument is invalid.
This also explains the root cause of the reference class debate between SSA and SIA. If we consistently reason objectively, then the sampling process would define the reference class of the particular observer/moment. If we consistently reason from the first-person perspective, then with their unique status, indexicals like “I” or “now” would have no reference class (i.e. it is the only member of its class). The need to find a reference class for the indexicals is due to the mix of the two. They have to interpret the primitively identified indexicals as the outcome of some imagined sampling process. Because it is required to reconcile the conflict of the special attention given to the first-person center and the indifference towards it.
Since the reference classes are not the cause but a result of the false arguments, there can be no “correct” reference class. SSA, SIA, and other proposed reference classes would inevitably give some paradoxical results. Subsequently, the notion of probability distributions of indexicals among such reference classes is also invalid. In literature, such probabilities are often called “self-locating probabilities”. In Part 3, using a simple thought experiment, I will explain in detail what they are and why they are invalid.
See Part 3. for the thought experiment.
Edit 2020/06/19: I think this extension might help to illustrate the main difference between my approach and other anthropic camps.