[jasperry]

I think your definition still leaves the essence of the discussion in the same place: do topological properties "exist"? That's how I tend to blanket-interpret this debate; it's whether one is wiling to define existence to include things that aren't material.

[BriggyDwiggs42]

Yeah but then neither does the cheese right? There’s no actual unity to objects, even solid objects, just parts interacting circumstantially, and any part can be subdivided into more parts interacting circumstantially.

[jasperry]

The unity of the block of cheese is circumstantial, but nonetheless we define a piece of cheese defined on the presence of actual matter. The article goes to some trouble to devise a definition of holes that's also based on matter rather than its absence. But only a strict materialist would feel the need to do that, assuming they didn't want to outright deny existence to holes.

[eesmith]

Topological properties exist to the same degree that the number 2 exists, which Argle and Blargle blithely accept.

I still object to how the exchange mixes two different concepts of "hole".