Yoneda, Realism and Antirealism.

First posted on October 7, 2018

The empiricists are right; no direct access to the world as it is exists. All information about the world is gleaned from interaction with it and its inhabitants. This however, poses no problems. As the Yoneda lemma illustrates, all of an entity’s properties are encapsulated by its interactions with other entities. There is no way, not even in principle, to distinguish between two objects, except by interacting with them. Hence if two objects interface with the world identically, then they are indistinguishable, and in particular, there is no means by which to show that they are not equal. Liebniz equality for real physical objects.

I would go further. Since the only way of gathering information about the world is through interaction, it is incoherent to suppose that one can refer to an “object” underlying a collection of interactions, which exists as something more than the collection of those interactions. Nothing beyond those interactions is even available for reference.