Looking back at my core argument I find it dry and abstract. More clarification might be helpful. The principle difference is that my approach regards (postulates) perspective reasoning as fundamental and objective reasoning as derived. While traditional arguments recognize (postulate) objective reasoning (i.e. perspective-independent reasoning) as fundamental and perspectives as additional information.
An Analogy
My core position is that our reasonings are perspectival, and a valid argument shall be formulated from one consistent perspective. This reminds me of different axiomatic systems in geometry.
Euclidean geometry is based on five postulates. If we change one of them, e.g. the parallel postulate, then we get something entirely different, e.g. elliptic geometry. It is pretty obvious we cannot use propositions derived from one system and use them in another. (unless of course, the same proposition can be independently derived from the other system) For example, one cannot derive the triangle internal angle sum as 180° in Euclidean geometry and then use it in an elliptic analysis.
The perspective center is primitive, much like an axiom, it is not logically reducible or derivable. Changing the perspective is like changing a postulate in geometry. The result is a completely different axiomatic system. Reasoning from different perspectives should not mix, analogous to propositions from different geometry should not be used together.
“Objectively Speaking”
In fact, reasoning from different perspectives does not mix is quite intuitive. For example, from my perspective I might say “I am a male”, while from my wife’s perspective she might say “I am not a male”. Obviously, these two conflicting statements cannot be directly used together without causing paradoxes. So the real question is, can we mix objective reasoning with perspective reasoning?
“Objective” is one of those terms that everyone has a pretty good idea of yet hard to define. We all agree it should be free of bias, subjectivity, and personal beliefs. Most notably, being objective means getting rid of any self-importance in the logic. “I” shouldn’t be inherently significant in objective thinking. However, even with these generally accepted features, “objective thinking” is still an elusive concept. In fact, I think it could mean two distinctive ways of reason.
“Objective” as an Imaginary Impartial Perspective
Objective reasoning could mean thinking from the perspective of an imaginary impartial observer. From this perspective, no actual person would be inherently logically special. Indexicals such as “I” or “now” would be useless in analyses since they would only point to the imaginary perspective center. Thinking as an outsider, or metaphorically speaking, thinking with a God’s eye view, are objective reasoning per the Imaginary Impartial Perspective (IIP) interpretation. I also think this is what we typically mean by “thinking objectively”.
By this interpretation, objective reasoning is just another axiomatic system. As such, it cannot be mixed with reasoning from another perspective. Therefore, we can either take the first-person perspective and recognizes “I” and “now” as inherently significant OR take the imaginary impartial perspective and treat all observers/moments indifferently. But not both in the same analysis.
“Objective” as Metaperspective Reasoning
Another perhaps less common way to get rid of self-importance is to collectively consider reasonings from multiple perspectives. Then common logics from all of these perspectives, propositions remaining true with perspective changes, can be regarded as objective. In another word, it is the reasoning of a higher hierarchy, the reasoning about perspective reasonings. Let’s call it metaperspective objectivity.
Metaperspective objectivity is impartial in the sense that it treats each observer’s reasoning indifferently. There is no preferred perspective. However, it does not deny the indexicals’ uniqueness within each perspective. It merely recognizes them as perspective specific, therefore bears no objective significance. So being objective does not mean one must treat all observers indifferently in his first-person reasoning. Rather, it means one shall recognize reasonings from other perspectives are just as valid as his.
The Difference
Based on the above, the uniqueness of “I” and “now” and the indifference towards all observers/moments would never be simultaneously valid in the same analysis. This holds for objective reasoning regardless of interpretation. For IIP objectivity, the uniqueness and indifference are bounded by two distinct perspectives. While metaperspective’s impartialness does not apply directly to the observers/moments themselves, but the reasonings from their respective perspectives.
Almost all other anthropic camps (I have yet to find an exception) treats “objective reasoning” as something fundamental and absolute. They treat perspective reasoning as objective reasoning with additional details. Therefore the objective impartialness applies indiscriminately. So even from a first-person perspective, where the perspective center (like “I”) inherently plays critical roles, all observers are still somehow indifferent. Because “objectively speaking” nobody is special.