There are many different answers to this question. One common answer is that we should believe an object exists if a theory we accept quantifies over that object. If quantum field theory requires quantification over the integers then 2 (and other integers) exist. Since contemporary physics doesn’t quantify over a domain containing phlogiston, phlogiston does not exist.
There’s something wrong when smart people argue and disagree over a question when there are many different ideas as to what the words in the question actually mean...
Then what does it mean for an abstract object like 2 to “exist”?
There are many different answers to this question. One common answer is that we should believe an object exists if a theory we accept quantifies over that object. If quantum field theory requires quantification over the integers then 2 (and other integers) exist. Since contemporary physics doesn’t quantify over a domain containing phlogiston, phlogiston does not exist.
There’s something wrong when smart people argue and disagree over a question when there are many different ideas as to what the words in the question actually mean...