Suppose I eat a chocolate bar and this causes me to have a trope of pleasure. Given assentiality of origins, if I had eaten a numerically different chocolate bar that caused the same pleasure, I would have had had a numerically different trope of pleasure.
Now, imagine that I eat a chocolate bar in my right hand and it causes me to have a trope of pleasure R, and immediately as I have finished eating that one chocolate bar, I switch to eating the chocolate bar in my left hand, which gives me an exactly similar trope of pleasure, L, with no temporal gap. Nonetheless, by essentiality of origins, trope L is numerically distinct from trope R.
To some (perhaps Armstrong) this will seem absurd. But I think it’s exactly right. In fact, I think it may even an argument for trope theory. For it seems pretty plausible that as I switch chocolate bars, something changes in me: I go from one pleasure to another exactly like it. But on heavy-weight Platonism, there is no change: I instantiated pleasure and now I instantiate pleasure. On non-trope nominalism, likewise there is no change. It’s trope theory that gives us the change here.
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