Concretism, ala David Lewis (et al), is the view that all objects in the physical universe stand in relationship to one another in space-time, from beginning to end. The “actual world” we experience is an “indexical” of all other possible worlds. While other (concrete) worlds are possible, the “me” in this world is different from a counterpart in another world. If two worlds were to “collide”—a plotline in some writings—they would constitute one and the same world. In the spirit of Occam’s Razor, this view does not require some other invention to explain the state of affairs in one world versus another.
Abstractionism, ala Christopher Menzel (et al), is the view that possible worlds are not concretely separate and distinct. For example, there is no counterpart to me wearing one outfit in this world and another me in a different world. There is the one me in this world wearing one outfit xor (exclusive or) the one me in this world choosing a different outfit. There are “states of affairs”—my walking across the street versus staying in place or my choosing one outfit over another. Possible worlds are then “maximal alternative states of affairs.”
In this view—all possible worlds are abstract, and the differentiator in this world—the world we experience—is that it “obtains.” Linguistically, abstract worlds describe sets of relationships among objects of experience.
It is posited by Robichaud that concretism does not require the introduction of abstraction to explain the world of experience or worlds of supposition. Conversely, abstractionism does not require the existence of concrete realities we don’t or can’t experience.
I’m inclined to identify as an abstractionist. While skirting ontological questions about the world we experience, abstraction allows us to describe and examine properties and relations among the “objects” of that experience. Moreover, in a Popperean sense, abstractionism is testable whereas concretism is not. Isn’t that the way modern science works? I can falsify a statement about an abstract property or relation. Objects beyond empirical investigation can only be posited.
In other words, there may be concrete multiverses, but they have yet to be identified at a macro (non-quantum) level. Abstraction at least allows us to communicate in the world of our experience without probing the metaphysical substrate.