You write
“Suppose, plausibly, that what it is for two experiences to be subjectively indistinguishable is that there exists some one-to-one mapping among the instants that make up those experiences so that you can’t tell apart any instants mapped to one another.”
You note that there is a one-to-one mapping between a continuous one-second-pain and continuous two-second-pain, while the two-second-pain seems obviously worse.
Consider the parody principle “what it is for two ranges of numbers to be mathematically indistinguishable is that there exists some one-to-one mapping among the numbers that make up the two ranges”. This principle is of course false (0 to 1 vs 0 to 2).
Many people might consider the parody principle plausible. Do you have a reason in mind for thinking that the mistaken intuition supporting the parody principle isn’t also the primary intuition supporting your principle?
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.
You write “Suppose, plausibly, that what it is for two experiences to be subjectively indistinguishable is that there exists some one-to-one mapping among the instants that make up those experiences so that you can’t tell apart any instants mapped to one another.” You note that there is a one-to-one mapping between a continuous one-second-pain and continuous two-second-pain, while the two-second-pain seems obviously worse.
Consider the parody principle “what it is for two ranges of numbers to be mathematically indistinguishable is that there exists some one-to-one mapping among the numbers that make up the two ranges”. This principle is of course false (0 to 1 vs 0 to 2).
Many people might consider the parody principle plausible. Do you have a reason in mind for thinking that the mistaken intuition supporting the parody principle isn’t also the primary intuition supporting your principle?
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.