Why I am a Platonist

I know that Platonism is out of fashion these days. People who study philosophy like to look at Plato's theory of Forms and say, "How quaint!" and admire how much knowledge has advanced since then. Abstractions and idealizations are not real, we think now. They are "just" ideas. We just make them up -- and cannot even come to agreement about them, anyway.

But I've noticed that there are some living, breathing Platonists still among us. They are usually not philosophers, but mathematicians or musicians.

Some mathematicians are Platonists because they think that there is something more real about mathematical entities and their properties than just being abstract ideas we make up.

But the case of music may be easier for people to understand: what exactly is a piece of music? In what way is it real?

It does have physical manifestations: it can take the form of air vibrations that people can hear, when it is performed. It can be recorded. It can be written as a musical score. Yet, even while it is not being played at the moment, we regard it as still existing in some way. So, what is this existence? It is existence like a Platonic Form!

Or, to put this somewhat differently: the way that we take a piece of music to exist even while it is not being played is the nature of "being" that is indicated by Plato's theory of Forms.

Plato's theory is meant to show that something like that (e.g., a piece of music) does have a kind of enduring existence and perfection above and beyond the transitory and often imperfect instantiations (e.g., performances) of it.

I'm not sure that I can come up with a better theory to explain the nature of reality of triangles or numbers or pieces of music than that. Can you?