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I'm not sure particularists actually do need to offer verdicts on the full array of cases - part of the attraction of their moral epistemology is that it seems to allow gappiness. But even if we reject that, they don't have to offer theoretically consistent verdicts on all cases (if their verdicts were theoretically consistent, they would implicitly have a general moral theory!). On the spectrum argument and the mere addition paradox, I think the particularist can and should do what Scott Alexander does (https://astralcodexten.substack.com/p/book-review-what-we-owe-the-future) and simply reject the train of logic at the price of ethical inconsistency.

More formally, particularists can - and I think should - use a deontic logic weaker than K+D. As such, they can allow a certain kind of ethical inconsistency without it infecting their overall belief system with logical inconsistency. You might say that this logic is too weak, but the particularist can supplement universal rules of logic with context-specific ethical judgments to get an *overall* ethical epistemology that is sufficiently strong. I read Bernard Williams (a particularist, although he didn't use the label) as arguing exactly this point in 'Ethical Consistency' and in parts of Shame and Necessity, although obviously he doesn't use the language of deontic logic.

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