I guess it's very important to note that I very well understand that empiricism/quasi-empirical character of mathematics are not somehow "better" explanations than just presenting the given particular physics explanation. This is just a variation of Deutsch's idea that presenting arguments that empiricism is all the knowledge there is seem to rule themselves out....there's ultimately nothing holy or self-justifying about empiricism!
However, the point to me is that when we use some kind of umbrella term for the type of knowledge we're pursuing (whether that type is moral or physical), it seems to me if there's any sense in using these words, there should be something distinguishing these kinds of knowledge. Popper was happy to describe a criterion of testability for science, for instance -- this is one principle repeatedly invoked to claim the hard-to-vary property holds in scientific explanations.
Otherwise, we could dispense with the term "moral" and simply present examples of good explanations directly -- not distinguishing moral from physical ones. It's not that this would be wrong,it's just we seem to clearly think there's types of statements, so it can be helpful to qualify what kinds of principles are commonly invoked to justify the hard-to-vary-ness in the different bodies of knowledge.
I think at the core of it, when we pursue rational discussion/ask questions, we obviously can't have ZERO idea what we're talking about, else criticism doesn't make any sense -- we need to have some idea. And it seems to me that, even if we may not fully know the objects in question (whether moral objects or physical ones), the bottom line is the more precise a statement we make+the more canonical a source of turning our ideas about something into precise statements there is, the more definitively we can criticize it or affirm. I think the quasi-empirical character of math/the physical-math map is mainly a source of making our ideas about the physical world into precise claims, even if there remains much mysterious about what exactly the physical world is.
That is why I think it can help result in hard-to-vary explanations -- it's hard to feel it is up to chance whether a certain mathematical description of the physical world is true or not.
I am personally on a quest to find similar such principles (not empirical, though) which apply in the moral sphere. No, this isn't necessary -- we could jump straight to examples without characterizing what is common to the examples, but since we bother to categorize "moral" explanations at all, as I said above, I think it's at least nice to have some reason why we'd expect there's objective knowledge we can refer to by an umbrella term called "moral". I agree there's no reason to inherently dismiss moral knowledge as illusory just because it is not necessarily empirical.
It isn't vital to discussing (as opposed to concluding about!) morality that we have complete knowledge of what "morality" is, but if we hope to arrive at truly hard-to-vary explanations, at some point we have to have good reason to believe there are some things we can say about it with relatively high definiteness, else we'll forever be stuck in arguing over what morality even means as a term -- and if there's nothing whatever we can say about it with precision and certainty, I think our criticisms and affirmations can only be so certain.
Notice that we may change our interpretation of empirical facts (E.g. no longer believe in determinism after quantum physics), but that the equations of classical physics work hasn't changed, and this ensures there is something we definitely can precisely say about the physical world--even if we don't know what it really is.
I realize I'm pushing hard to acknowledge there's something that's worked in physics, and that isn't because I think physics has a monopoly on objectivity so much as we should take seriously why it's worked so well as a clue (this doesn't mean blindly apply empiricism everywhere).
However, the point to me is that when we use some kind of umbrella term for the type of knowledge we're pursuing (whether that type is moral or physical), it seems to me if there's any sense in using these words, there should be something distinguishing these kinds of knowledge. Popper was happy to describe a criterion of testability for science, for instance -- this is one principle repeatedly invoked to claim the hard-to-vary property holds in scientific explanations.
Otherwise, we could dispense with the term "moral" and simply present examples of good explanations directly -- not distinguishing moral from physical ones. It's not that this would be wrong,it's just we seem to clearly think there's types of statements, so it can be helpful to qualify what kinds of principles are commonly invoked to justify the hard-to-vary-ness in the different bodies of knowledge.
I think at the core of it, when we pursue rational discussion/ask questions, we obviously can't have ZERO idea what we're talking about, else criticism doesn't make any sense -- we need to have some idea. And it seems to me that, even if we may not fully know the objects in question (whether moral objects or physical ones), the bottom line is the more precise a statement we make+the more canonical a source of turning our ideas about something into precise statements there is, the more definitively we can criticize it or affirm. I think the quasi-empirical character of math/the physical-math map is mainly a source of making our ideas about the physical world into precise claims, even if there remains much mysterious about what exactly the physical world is.
That is why I think it can help result in hard-to-vary explanations -- it's hard to feel it is up to chance whether a certain mathematical description of the physical world is true or not.
I am personally on a quest to find similar such principles (not empirical, though) which apply in the moral sphere. No, this isn't necessary -- we could jump straight to examples without characterizing what is common to the examples, but since we bother to categorize "moral" explanations at all, as I said above, I think it's at least nice to have some reason why we'd expect there's objective knowledge we can refer to by an umbrella term called "moral". I agree there's no reason to inherently dismiss moral knowledge as illusory just because it is not necessarily empirical.
It isn't vital to discussing (as opposed to concluding about!) morality that we have complete knowledge of what "morality" is, but if we hope to arrive at truly hard-to-vary explanations, at some point we have to have good reason to believe there are some things we can say about it with relatively high definiteness, else we'll forever be stuck in arguing over what morality even means as a term -- and if there's nothing whatever we can say about it with precision and certainty, I think our criticisms and affirmations can only be so certain.
Notice that we may change our interpretation of empirical facts (E.g. no longer believe in determinism after quantum physics), but that the equations of classical physics work hasn't changed, and this ensures there is something we definitely can precisely say about the physical world--even if we don't know what it really is.
I realize I'm pushing hard to acknowledge there's something that's worked in physics, and that isn't because I think physics has a monopoly on objectivity so much as we should take seriously why it's worked so well as a clue (this doesn't mean blindly apply empiricism everywhere).
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and again, let's be very clear, this isn't an assertion that it isn't ultimately reason that produces hard to vary explanations. It's simply an ingredient of the claim of goodness often in science .... i.e. the simple old-fashioned "hey, your theory can't be as good as mine, cuz it just doesn't pass muster with the data!"