Nobody has to believe that ordinary non mathematical langage contains a single well defined meaning of “exists”. And if “exists” is polysemous , then one of its meanings could be the meaning of mathematically-exists … it doesn’t have to have a unique meaning. Fictivism is an example: the theory that mathematically-exists means fictionally-exists, since ordinary language allows truth and existence to be used in reference to fictional worlds.
Nobody has to believe that ordinary non mathematical langage contains a single well defined meaning of “exists”. And if “exists” is polysemous , then one of its meanings could be the meaning of mathematically-exists … it doesn’t have to have a unique meaning. Fictivism is an example: the theory that mathematically-exists means fictionally-exists, since ordinary language allows truth and existence to be used in reference to fictional worlds.