Huh? The identity of an object allows for mutable state, it doesn't change with its state. I am the same person I was yesterday even if I'm in a different place or I cut my hair. State is predicated on identity, not the other way around (and given identity, you can have any kind of mutable state even in a language that doesn't support mutation, since an identity can be used as a key in an immutable map, changing the map changes the state where identity provides for a constant frame of reference).
True, but that doesn't change what identity is. It is only a key into a table, it is up to the table to contain values indexed by time if that is what is required.
I agree with you there. Nowadays the identity points to a single thing without any notion of time, in the perfect world it would point to a set of things with their respective dates (and the database would have operations to deal with that).
If you want to get philosophical you can argue that in the real world everything mutates, even the identities. Heck, you can even say that the identity comes out of the value (the river is just on your mind, there's only water flowing). But in our digital/fuzzyless/mechanic computing models those abstractions are just unrealistic.
Identity, or objectness, is a distinct concept from being a value that is defined purely by its form. So in that sense, identity is immutable because it is defined that way, it isn't a property that falls out of the universe. At least, its been that way since the Greek philosophy days.
A ball is an object, it has state, if its state changes, we can recognize it as being the same ball. A point/position is a value. It doesn't make sense for it to have state, a position with a different value is simply a different position. Getting around the arrow of time is something else entirely.
That still isn't right. Identity is immutable, state is something that is...identified by identity. The key of a map entry is different from the value of the entry, and in general the key can access the value, but not vice versa.
