La Profilée — Identity Without Invariance Assumptions

The problem of personal identity over time has resisted resolution for three centuries. Every proposed solution either presupposes an invariance condition — something that must remain the same across time and change — or collapses into reductionism, denying that identity is anything over and above the continuity of psychological or physical relations. Neither position is satisfactory: invariance assumptions beg the question of what justifies selecting one invariant over another, while reductionism cannot account for the normative and practical weight identity carries. This paper argues that both positions are unnecessary. La Profilée (LP) derives, from two minimal structural conditions — determinability and real transformation — that identity exists as the maximal transformation-invariant equivalence relation on any system satisfying these conditions, and that this identity relation is structurally non-eliminable without collapse of determinability: its collapse entails the collapse of determinability itself. No invariance assumption is required. Invariance is not assumed but derived — it is the structural consequence of the existence of identity, not its precondition. The result is stronger than any position in the current persistence debate. It does not propose a new criterion of identity. It derives the structural necessity of identity from conditions weaker than any existing account presupposes, and shows that the identity relation so derived cannot collapse without destroying the minimal conditions under which any system can be described at all. This is not a contribution to the debate about which invariance condition is correct. It is a demonstration that the debate has been asking the wrong question.