Williamson’s anti-luminosity argument forms the backbone of Knowledge and Its Limits: not only does he take it to show that no non-trivial condition is luminous, but he also uses the argument (or variants of it) to reply to an important objection to his claim that knowledge is a mental state (ch. 4); to contest Dummett’s argument for an anti-realist theory of meaning (ch. 4); to argue against a version of the KK-principle according to which one is always in a position to know when one knows a given proposition (ch. 5); to provide a solution to the surprise-examination paradox (ch. 6); to rebut any argument for skepticism about the external world that assumes that we and the envatted versions of ourselves possess the same evidence (ch. 8); and to buttress his claim that our evidence is all and only what we know (ch. 9). Moreover, similar uses of a safety requirement on knowledge to derive margin-for-error principles play a crucial role in Williamson’s theory of vagueness. And more generally, Williamson’s anti-luminosity argument constitutes a novel way of criticizing a venerable philosophical tradition — a way which Williamson uses to lay the foundation for a radical new theory of (as he puts it) knowledge and its limits.
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