Thanks for the question! There’s a lot more about how I arrive at this conception of subjective indistinguishability in the paper itself (section 4.2), but in terms of the analogy with your parody principle, notice that your definition of mathematical indistinguishability just says that there has to be a one-to-one mapping, whereas the proposed account of subjective indistinguishability says that there has to be such a mapping and the mapped pairs must always be pairwise indistinguishable to the subject. If I said that two ranges of numbers are mathematically indistinguishable if there’s a one-to-one mapping among them such that the numbers we map to one another are indistinguishable, that doesn’t sound too implausible and presumably doesn’t generate the counter-example you note? (Though it might turn on what we mean by saying that two numbers are ‘indistinguishable’!) If that’s right, then I don’t think my principle is challenged by the analogy with the parody principle you note.
Thanks for the question! There’s a lot more about how I arrive at this conception of subjective indistinguishability in the paper itself (section 4.2), but in terms of the analogy with your parody principle, notice that your definition of mathematical indistinguishability just says that there has to be a one-to-one mapping, whereas the proposed account of subjective indistinguishability says that there has to be such a mapping and the mapped pairs must always be pairwise indistinguishable to the subject. If I said that two ranges of numbers are mathematically indistinguishable if there’s a one-to-one mapping among them such that the numbers we map to one another are indistinguishable, that doesn’t sound too implausible and presumably doesn’t generate the counter-example you note? (Though it might turn on what we mean by saying that two numbers are ‘indistinguishable’!) If that’s right, then I don’t think my principle is challenged by the analogy with the parody principle you note.