We don’t know that it “works equally well”, since we don’t have omniscient knowledge about the existence
of abstract objects. If abstract objects don’t exist, then the quantification criterion is too broad, and therefore
does not work.
This straight-forwardly begs the question. I say “What it means to exist is to be quantified over in our best scientific theories”. Your reply is basically “If you’re wrong about the definition then you’re wrong about the definition.”
We don’t know that it “works equally well”, since we don’t have omniscient knowledge about the existence of abstract objects. If abstract objects don’t exist, then the quantification criterion is too broad, and therefore does not work.
This straight-forwardly begs the question. I say “What it means to exist is to be quantified over in our best scientific theories”. Your reply is basically “If you’re wrong about the definition then you’re wrong about the definition.”
Your claim was “If we are right about the definition, we are right about the definition”.