A profound question

A well-known distinction that has been with us from the beginning of discourse is that between concrete and abstract objects. Now, are there any abstract objects? That is to say, is ‘the abstract’ an instantiated category of being? Or should we hold that only concrete objects exist? Are there no abstract objects?

Famously Plato provided a negative answer to this latter question. He reified or hypostatized the abstract. Whereas medieval nominalists later on famously argued that abstract objects do not exist. I believe we have no choice but to accept the existence of abstract objects.

For there being such objects is an immediate entailment from the conclusion of the semantic argument I developed some time ago (short version here and long version here). The conclusion of my semantic argument has it that there are no universal properties. So the property of being concrete is not universal. But then not all objects are concrete. There are abstract objects. Abstract objects exist and thus the abstract is indeed instantiated. Plato was surely right to hypostatize it.

The question of how concrete and abstract objects interact becomes therefore quite relevant. If there are abstract objects, if they are part of reality or being, how then are they ontologically related to concrete ones? Is there any metaphysical relation at all between them? This is a profound and important philosophical question indeed. A question perhaps even part of philosophia perennis.