Research Group
in Analytic Philosophy

Abstract

The paper presents an overarching argument to the effect that, given a certain attractive picture according to which—in certain situations, for certain obviously true propositions—(being in a position to have) knowledge iterates, single-premise closure principles are bound to fail in certain situations. The situations in question involve inexact knowledge, originating with one’s less than perfect powers of discrimination. Along the way to the main conclusion, it is first argued that the justification of margin-for-error principles as principles governing inexact knowledge is based on two flawed assumptions and that the principles themselves fail to provide a necessary condition for inexact knowledge. That crucially disposes of an influential argument against the KK-principle, whose validity—at least with respect to the highly controlled situation of inexact knowledge that will be taken as example—is then positively supported with two arguments concerning respectively the elevation of evidence for epistemically higher-order propositions and the norms of assertion and belief. A new and more powerful argument from inexact knowledge is then proposed against the KK-principle. However, it is observed that the argument crucially relies on certain closure principles that, under the extremely plausible assumption that knowledge iterates for certain obviously true propositions, can be shown to be unacceptable since they in effect license soritical principles. Finally, the model theory and proof theory of a non-regular modal logic for the knowledge modality are developed, and a consistency proof is given of the conjunction of the KK principle (a fortiori, of the assumption that knowledge iterates for certain obviously true propositions) with certain principles reflecting the inexactness of much of our knowledge.