The paper discusses some ways in which vagueness and its phenomena may be thought to impose certain limits on our knowledge and, more specifically, may be thought to bear on the traditional philosophical idea that certain domains of facts are luminous, i.e., roughly, fully open to our view. The discussion focuses on a very influential argument to the effect that almost no such interesting domains exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts (...) that are best candidates for being luminous plays an illicit role in such argument. The paper centres around the idea that vagueness brings with itself the prima facie plausibility of soritical principles. Using the diagnostics of sharpenings, it is first pointed out that, despite certain considerations to the contrary, the margin‐for‐error principle required by the anti‐luminosity argument may well derive all of its plausibility from an underlying soritical principle. The notion of confidence that is relevant to the argument is then isolated and sharply distinguished from the notion of subjective probability. Against this background, it is argued that the reasoning about confidence involved in the argument in favour of the problematic margin‐for‐error principle is fallacious in the same way in which sorites reasoning is. This reveals the possibility of having reliable knowledge even at the penumbral limit with falsity, a possibility for which a concrete formal model is constructed. The model in turn permits a deeper appreciation of the role played in the dialectic by the distinction between confidence and subjective probability as well as by confidence requirements on knowledge. It is concluded that careful heeding of vagueness and its phenomena, far from forcing new and surprising limits on our knowledge, actually removes one of the main barriers – unreliability – often thought to stand in its way. (shrink)

I argue that no successful version of Williamson's anti‐luminosity‐argument has yet been presented, even if Srinivasan's further elaboration and defence is taken into account. There is a version invoking a coarse‐grained safety condition and one invoking a fine‐grained safety condition. A crucial step in the former version implicitly relies on the false premise that sufficient similarity is transitive. I show that some natural attempts to resolve this issue fail. Similar problems arise for the fine‐grained version. Moreover, I argue that Srinivasan's (...) defence of the more contentious fine‐grained safety condition is also unsuccessful, again for similar reasons. (shrink)

Whether some condition is equivalent to a conjunction of some conditions has been a major issue in analytic philosophy. Examples include: knowledge, acting freely, causation, and justice. Philosophers have striven to offer analyses of these, and other concepts, by showing them equivalent to such a conjunction. Timothy Williamson offers a number of arguments for the idea that knowledge is ‘prime’, hence not equivalent to or composed by some such conjunction. I focus on one of his arguments: the requirement that such (...) conjuncts must be freely recombinable. Although there has been a great deal of discussion of Williamson's arguments, the flaw I describe has gone unnoticed. Williamson's argument is expressed in terms of conditions, and cases of the condition. Does the condition include specific information, or is the specific information only part of the case? His argument equivocates between more and less general specifications of the conditions. Once this distinction is clarified, his argument can be seen to be vitiated by this conflation. Neither option yields a sound argument for Williamson's desired conclusion. (shrink)