Leibniz held that each monad mirrored all the others, namely that by knowing all there is to know about each, you knew all there was to know about all. If essentiality of origins holds, then we get Leibniz-like theses quite easily.
1. If essentiality of origins holds, then each thing mirrors everything in its causal history in the strong sense that the proposition that x exists entails the whole causal history of x's coming into existence.
2. If essentiality of origins and determinism holds, and if we add the further postulate that all of the initial conditions for the whole universe are a part of the causal history of every item in the universe's coming into existence, then for every item x in the universe, the proposition that x exists conjoined with the laws entails the whole past, present and future history of the universe.
3. If to the assumptions in (2) we add the postulate that no item in the universe could have existed with the laws being different, then we get the stronger claim that no item in the universe could have existed in any other world—i.e., that the items in the universe are world-bound individuals.
This might make Leibniz's doctrine of mirroring more plausible to some. But I am not a determinist myself.
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3. If to the assumptions in (2) we add the postulate that no item in the universe could have existed with the laws being different, then we get the stronger claim that no item in the universe could have existed in any other world—i.e., that the items in the universe are world-bound individuals.
I'm missing how you arrive at this. Let w and w' be exactly alike up to time t. You are born at t-5. At t, w' diverges from w, since God performs some miracle in w'. But you have precisely the same origin in w and w' and you exist in w and w'. You are not world-bound. These worlds differ with respect to their futures after t on the basis of a divergence miracle. Certainly the divergence after your birth cannot affect whether you were born. If it did, we'd have one amazing backtracking counterfactual!
Insofar as I've ever understood Leibniz's claim here, I thought it was the relatively trivial (when you think about it) idea that if you knew _all_ the facts about X, you would know all the relational facts about X. Since X stands in some relation to every Y, you would know all the facts about Y.
Heath,
The claim is non-trivial at least in the best of all worlds: on Leibniz's view, the intrinsic properties of each monad encode the rest of the universe in the best world.
I vaguely recall a claim that that in his pre-critical days, Kant tried to explain this by means of gravitation. (If you observe the motions of one of the objects, you can--or so the claim goes--read off the motions of all the other objects.)
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