A discussion on materialism and the existence of abstract and non-material entities in comment section here:
“A: Materialism doesn’t deny metaphysics, just superphysics. Abstracts don’t ontologically “exist” per se.
B: Perhaps I need you to clarify, or perhaps my understanding needs to be clarified, but I would say that while your description may be true of atheism, it is not true of materialism. On materialism, only the physical is real.
A: Right, but we can recognize patterns in the physical and call them things by means of abstraction. We can even imagine that they float about in some abstract world. Things like “two,” “justice,” “proposition,” and even “person” qualify. On materialism, only the physical exists, but we can still qualify the physical. That’s metaphysics. “Two” doesn’t actually “exist” in the ontological sense.
We Christians should be united with materialists on this; the philosophically inclined GENERALLY are. Our dispute with the materialists is that we believe there is really existent, ontological “stuff” beyond just the world of matter and energy (and the abstract imaginings of brains).
B: A thoroughgoing materialist would not allow for the existence of a Platonic realm, so you are right to say that they would affirm the number two does not exist in the ontological sense. Abstractions are just useful fictions. All that really exists is the material. But there are many non-material things that are not just fictions, such as propositions, which is why I say it falsifies materialism.
A:You can think that propositions float around in a Platonic realm, but Aristotle’s big “improvement” in metaphysics was that these things aren’t floating around an ideal realm. Rather, they’re vague conceptual tethers or schemas. “Two” and “proposition” are both abstractions, equally non-existent and equally “existent” (with air quotes). A “2”-shaped carving on a slab is “two” only insofar as a person observes it and imputes meaning into it. Same with propositions.
B: Stanrock, personally, I fall into the non-realist camp when it comes to abstract entities. I hold to a fictionalist account of abstract objects. When it comes to the mind, I don’t think mental events are abstractions, though. Mental entities are real spiritual (i.e. non-material) entities, not abstractions like the number two or the equator.”