Fdzfgy

You see a family in the park and you naturally list the members as "Mom, Dad, son, and daughter". But from whose perspective is this?

"Mom" and "Dad" are identifiers as seen from the perspective of the children, while "son" and "daughter" are identifiers as seen from the perspective of the parents. It's as if we shifted perspective midway through the list!

A fixed perspective would be, for example, something like "me, my sister, my mom, and my dad".

Or maybe the perspective is fixed. Not fixed at any particular person, but rather fixed at the center of gravity of the family, floating somewhere between parents and children. Like some sort of averaged perspective.

Then, it gets more complicated when extended family members come along: "Oh, here comes Grandpa and Auntie!"

Now we've got a couple of identifiers from the perspective of the parents, and a bunch of identifiers from the perspective of the children. But why shouldn't it be from the perspective of the mother, since she is now close to the center of gravity of the family? She would describe the whole thing as "me, my husband, my father, my sister, and my children". That gives a completely different sense from "Mom, Dad, son, daughter, Grandpa, and Auntie".

(And don't even think about how Auntie views the whole thing: "me, my father, my sister, my brother-in-law, my niece, and my nephew".)

As our list grows, it becomes more and more a view from nowhere.

Shifting perspective, center of gravity, view from nowhere... What the heck am I talking about?

Kinship terms are a specialized form of social deixis. The things you are pointing out are a consequence of the fact that deictic terms have context-dependent meanings. What you've appropriately called the "center of gravity" is the deictic center - the reference point from which the context is judged.

When you say you see a "Mom, Dad, son, and daughter" you're stating that based on both the social context you find yourself in and the particular people you are referring to. So by "Mom", you're conveying something like "the person who appears to stand in a motherhood role relative to the other people in the group I'm referring to".

This would be how you refer to them to a third party you are talking to. But you wouldn't refer to them that way while addressing them directly. You would never say "*Hello, Mom, Dad, son, and daughter!".

It depends on the skills of the person doing the describing. A could say "My mother is the woman who gave birth to me", B could say "Your mother is the woman who gave birth to you" and C could say "A person's mother is the woman who gave birth to that person". It also depends on the language they are describing, since some languages have separate words for "my-mother" vs. "your-mother" versus "his-mother". It also depends on the facts of the relationship. There is a recurring term "cross-sex sibling" which would be in English the relation between female and male siblings, and "same-sex sibling" (male siblings, female siblings). Or, conventionally translated "mother" could be "woman who gave birth to you and all of her siblings", and "aunt" could be "female siblings of your 'father'," (which is likely to be "biological father plus his male siblings").