Good question - I doubt there is a complete formal definition of what 'classical' music is. I remember an analogous explanation of the "institutional" theory of art - as being whatever someone of the artworld offers for consideration as art[1]. Same for the subject of (generally regarded) aficionados of the modern "classical music"-world I would guess; or indeed, any genre.

[1] https://en.wikipedia.org/wiki/Theory_of_art