Epistemologists have profited from studies of the ways in which ‘know’ is ambiguous. We can also profit by studying the ways in which ‘know’ is vague. After classifying sources of vagueness for ‘know,’ I spend the second section examining theories of vagueness. With the exception of the theory that vague predicates are incoherent, which I try to refute, we need not take a stand on a particular theory to show that the vagueness of knowledge has substantive epistemological implications. The third (...) section supports the thesis through a survey of ways in which appeals to vagueness can be applied to the field's issues. First, I show how higher order vagueness is evidence against the KK thesis, the incorrigibility of sense data, and the completability of epistemology. An interesting resemblance between infinity and vagueness provides the point of departure for the next type of application. For this resemblance suggests a new way of handling apparently infinite belief structures. The approach is illustrated with an analysis of common knowledge. The third type of application concerns the ways in which disguised sorites creep into our thinking about knowledge. In addition to brief illustrations concerning naive holism, question begging, and an objection to incorrigibilism, I provide more detailed illustrations involving Jonathan Adler's sceptical appeal to epistemic universalizability, the prediction paradox, and William Lycan's objection to Gilbert Harman's social knowledge cases. I conclude with some general remarks on the lessons to be learned from the vagueness of knowledge. (shrink)

Arithmetical self-reference through diagonalization is compared with self-recognition in a mirror, in a series of diagrams that show the structure and main stages of construction of self-referential sentences. A Gödel code is compared with a mirror, Gödel numbers with mirror images, numerical reference to arithmetical formulas with using a mirror to see things indirectly, self-reference with looking at one’s own image, and arithmetical provability of self-reference with recognition of the mirror image. The comparison turns arithmetical self-reference into an idealized model (...) of self-recognition and the conception(s) of self based on that capacity. (shrink)