Sean Carroll

To my mind, both mathematical objects are just convenient constructions which allow us to calculate and allocate probabilities to outcomes in a rational way.

A common sense view of what is real might be that the world on a small scale is actually made up of particles or fields or whatever, whose behavior is what we would like to model.

Have I misunderstood what philosophers of science are saying when they use terms like ontology or reality?

So I'm not going to say a lot about reality because that's a contested field.

What counts as something real?

I mean, it's contested in many different ways.

Are mathematical objects real?

Are emergent higher-level structures real?

Is free will real, right?

It really just is both an issue of what is your view of how reality works and your view of what counts as real.

And I have a particular point of view that I put forward in –

the big picture and elsewhere, but people don't agree.

So I think that good philosophers are very careful when they use words like that to explain what sense they're saying that something is real or not.

Ontology is more clearly defined and more sort of uniformly used.

It's the set of ingredients in your most fundamental description of reality.

It's what exists according to that more or less physical version of reality.

Of course, if you're not a physicalist...

then your ontology might include supernatural beings and things like that.

But I don't think that most people include numbers in their ontology, even if they're mathematically realists.

That I'm not sure.