Probability theory is maths, and although I agree that questions like “where is maths?” and “what is maths?” and “does maths exist?” are confusing

See, these questions are not confusing to me at all. Hofstadter's formalism deals with them perfectly. Have you ever read G.E.B.? I assumed so, but I wasn't sure, maybe you haven't.

Yes, I do think that probability theory is a repeatable process of typographical string manipulations. What do you think it is?

Ultimately language should be useful, and I don’t see the point of changing the word “is” to the word “models”. This wouldn’t change my beliefs about probability theory; I’d just be using the word “models” to mean the same thing as the word “is”. And I would then lack a means of saying that the Bayesian interpretation of probability is good, and the frequentist interpretation is stupid and counter-productive – I want to be able to say that probability is X, and probability isn't Y, because this is the most useful way of using language to talk about probability theory – why would I want to put the good interpretation and the dumb interpretation on an equal footing by saying that probability “models” X and also “models” Y?

Here I completely disagree, and almost wonder if you haven't been reading my comments. Bayesianism is stronger, more capable, perfecter, stronger, more rational, more useful than frequentism, first of all, and all of that has nothing to do with the commitment to conceptualism that subjective bayes requires. This is all still true if you are a formalist.

Bayesianism is not righter than frequentism because probabilities are really subjective beliefs, and the frequentists were wrong, it's not frequency. Bayesains are righter than frequentists because bayes-inferences are deductively demonstrable to win more than frequentist-inferences. Again, the argument about what probability really is is just a way to disguise the argument about who's statistical method is more successful, the only way the frequentist even has a shot at such an argument if it is disguised as a question about what probability is instead of a question about who's inferences are theoretically ideal.

So um, platonism? Really? Why? What does it get you that formalism doesn't with less ontological commitment?