[Philo]

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It also looks as though you aren't just making a claim about the persistence of objects, but also about the existence of objects. Is your view that the only objects that really exist are the fundamental particles (assuming they can be 'separated'), or the universe as a whole (if it's all just a big vibrating field, and the fundamental particles cannot be separated)?

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That's basically my position. We can ascribe "existence" to them, and it's perfectly valid in a contingent sense, but the only basis for this conception of existence is the set of criteria applied to determine that quality.

There are many ways to cut a cake. I can cut a cake into 8 pieces, and then there are indeed 8 pieces in the cake. Those pieces matter, because they'll determine who gets what part of the cake (and where crumbs will be left behind). But there is nothing special or fundamental that separates piece 1 from piece 2 - I just happened to divide the cake at a certain location. I could have divided the cake at another location, and it would have been equally valid. The individual pieces of cake are a function of my slicing, not a property of the cake itself.

When the cake hasn't yet been sliced, asking about where slice 1 and slice 2 are seems arbitrary and nonsensical. That all depends on where you slice it. In the same sense, a person or object's identity depends on how we choose to assign the property of identity - that property doesn't exist in the universe itself, it's a function of how we choose to divide the universe. I view animalism as a way of assigning idenity - it's just a method of slicing the cake, it's no more "true" or "false" than any other method. The dilemma presented in the OP strikes me as a different method of slicing - or maybe a question of "what should we do with the crumbs?" I don't think there's a right answer.

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This is the view that Michael Dummett describes as "the picture of reality as an amorphous lump." Dummett is sympathetic to the view, and I am as well.

If you are not familiar with four-dimensionalism it is the view that objects have temporal parts as well as spatial parts, and was motivated in large part by the change in our conception of space and time due to relativity theory.

It is complementary to the "cookie cutter" metaphor (that we carve up reality ourselves), since four-dimensionalists usually believe that every matter-filled region of space-time contains an object, and in that sense the world does not come ready-made but is carved up ontologically by us relative to our own interests. (This was W.V.O. Quine's view, a staunch empiricist with a very parsimonious ontology-see Quine's "Ontological Relativity," "On What There Is," and "Identity, Ostension and Hypostasis." To see how four-dimensionalism is applied to the problem of personal identity see David Lewis' "Survival and Identity.")

It is certainly a philosophically convenient view since it deflates most philosophical problems (though it brings new ones in its wake). I would not go so far as to say that "nobody in their right mind" accepts the alternative view that the natural sciences study genuine natural kinds/objects though.