Transworld identity without haecceities

Haecceities are individual essences, even of non-existent beings. Necessarily, entity exists iff its haecceity is instantiated. Some folks think we need haecceities to make sense of alien individuals—i.e., individuals that exist in other worlds but not in ours. We don't, as long as we are willing to be Leibnizian in denying the identity of indiscernibles. Here, then, is a simple theory of identity across worlds that entails the essentiality of origins. The theory applies both to substance-like and event-like individuals.

I will give the simplest version of the theory, for beings in an absolute time who do not engage in any time travel and without backwards causation. A general version of the theory requires the replacement of times by "causal (or maybe even explanatory) points"—points in the causal history of an entity. This is a bit tricky, and so I won't bother with it.

Let e be an entity and w a world. Say that H is a qualitative history of e up to t in w provided that e exists at t in w and H is a proposition giving an at least partial description of w such that:

1. H is purely qualitative except respect of e and t: i.e., the only particulars that are de re involved in H are e and t;
2. H states that e exists at t and gives a complete description of the intrinsic properties of e at t, subject to the restriction in (1);
3. For any state of affairs reported in H, any and all the causes in w of that state of affairs are also reported in H;
4. H reports that e exists at t;
5. H is a minimal proposition satisfying (1)-(4).

Now, let w₁ and w₂ be two worlds such that e₁ exists in w₁ and e₂ exists in w₂. Then e₁=e₂ if and only if there are times t₁ and t₂ and histories H₁ of e₁ up to t₁ in w₁ and H₂ of e₂ up to t₂ in w₂, such that H₁'s description of e₁ and t₁ coincides exactly with H₂'s description of e₂ and t₂.

To put it roughly, e₁ and e₂ are identical if and only if there are points in the existence of each one, such that their respective histories up to these points are the same.

This view entails essentiality of origins. It also implies that there cannot be two entities which, along with their causal histories, have been indiscernible up to some time. Thus, there cannot be completely identical twins. This consequence is counterintuitive, but may be but a small price to pay for avoiding haecceities.

Given this view, we can form something like a haecceity from the disjunction of all the histories of an entity in a world.

The view can be varied by relaxing or tightening the conditions (1)-(5) on histories. I do not yet know which is the optimal version.