What are the main philosophical theories of identity through change?
I’m trying to understand the philosophical problem of persistence: what makes something count as the same thing over time despite change?
For example, a wave can persist as a recognizable pattern even though the medium’s particles only move locally. A candle flame can continue even though the reacting molecules are constantly replaced. A living organism also exchanges matter over time while still being treated as one continuous being.
What are the major philosophical accounts of this issue?
I’m especially interested in theories that explain whether identity through change is grounded in:
- underlying substance,
- preserved structure,
- causal or process continuity,
- informational continuity,
- psychological/biological continuity,
- or scale/context-dependent criteria.
Also, are there philosophers or traditions that argue identity is not absolute, but depends on the level of description or the kind of continuity being evaluated?
I’m looking for established positions, authors, or readings that deal with this problem.