[abrezas]

You think that they are confusing the term exists but the reality is that what "exists" means is very hard to define.

Where is the line between abstract objects and the real world you mentioned? Can you give a rule that separates the two?

Do black holes exist? Electrons? Magnetic fields? Is one of these a model but doesn't really exist?

[Houshalter]

Arguing about the definition of a word is a huge red flag that a discussion is going nowhere. Sadly a lot of philosophy seems to be basically arguing about words.

>Do black holes exist? Electrons? Magnetic fields?

Yes. I mean we might not know what they are exactly or how they work, but they are clearly real phenomena that we can observe. In the same sense, "twoness" is a real property that a set of objects can have.