Higher order ignorance inside the margins

According to the KK-principle, knowledge iterates freely. It has been argued, notably in Greco (J Philos 111:169–197, 2014a), that accounts of knowledge which involve essential appeal to normality are particularly conducive to defence of the KK-principle. The present article evaluates the prospects for employing normality in this role. First, it is argued that the defence of the KK-principle depends upon an implausible assumption about the logical principles governing iterated normality claims. Once this assumption is dropped, counter-instances to the principle can be expected to arise. Second, it is argued that even if the assumption is maintained, there are other logical properties of normality which can be expected to lead to failures of KK. Such failures are noteworthy, since they do not depend on either a margins-for-error principle or safety condition of the kinds Williamson (Mind 101:217–242, 1992; Knowledge and its limits, OUP, Oxford, 2000) appeals to in motivating rejection KK. “Introduction: KK and Being in a Position to Know” Section formulates two versions of the KK-Principle; “Inexact Knowledge and Margins for Error” Section presents a version of Williamson’s margins-for-error argument against it; “Knowledge and Normality” and “Iterated Normality” Sections discuss the defence of the KK-Principle due to Greco (J Philos 111:169–197, 2014a) and show that it is dependent upon the implausible assumption that the logic of normality ascriptions is at least as strong as K4; finally, “Knowledge in Abnormal Conditions” and “Higher-Order Ignorance Inside the Margins” Sections argue that a weakened version of Greco’s constraint on knowledge is plausible and demonstrate that this weakened constraint will, given uncontentious assumptions, systematically generate counter-instances to the KK-principle of a novel kind.