Online research in philosophy

This paper evaluates a number of closure principles (for both knowledge and justification) that have appeared in the literature. Counterexamples are presented to all but one of these principles, which is conceded to be true but trivially so. It is argued that a consequence of the failure of these closure principles is that certain projects of doxastic logic are doomed, and that doxastic logic is of dubious merit for epistemologists interested in actual knowers in the actual world.

This paper looks at an argument strategy for assessing the epistemic closure principle. This is the principle that says knowledge is closed under known entailment; or (roughly) if S knows p and S knows that p entails q, then S knows that q. The strategy in question looks to the individual conditions on knowledge to see if they are closed. According to one conjecture, if all the individual conditions are closed, then so too is knowledge. I give a deductive argument for this conjecture. According to a second conjecture, if one (or more) condition is not closed, then neither is knowledge. I give an inductive argument for this conjecture. In sum, I defend the strategy by defending the claim that knowledge is closed if, and only if, all the conditions on knowledge are closed. After making my case, I look at what this means for the debate over whether knowledge is closed.

It is nowadays taken for granted that the core radical sceptical arguments all pivot upon the principle that the epistemic operator in question is 'closed' under known entailments. Accordingly, the standard anti-sceptical project now involves either denying closure or retaining closure by amending how one understands other elements of the sceptical argument. However, there are epistemic principles available to the sceptic which are logically weaker than closure but achieve the same result. Accordingly the contemporary debate fails to engage with the sceptical problem in its strongest form.

It is nowadays taken for granted that the core radical sceptical arguments all pivot upon the principle that the epistemic operator in question is 'closed' under known entailments. Accordingly, the standard anti-sceptical project now involves either denying closure or retaining closure by amending how one understands other elements of the sceptical argument. However, there are epistemic principles available to the sceptic which are logically weaker than closure but achieve the same result. Accordingly the contemporary debate fails to engage with the sceptical problem in its strongest form.

It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or epistemic rationality ) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.

It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or “epistemic rationality”) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.

It is nowadays taken for granted that the core radical sceptical arguments all pivot upon the principle that the epistemic operator in question is ‘closed’ under known entailments. Accordingly, the standard anti-sceptical project now involves either denying closure or retaining closure by amending how one understands other elements of the sceptical argument. However, there are epistemic principles avail- able to the sceptic which are logically weaker than closure but achieve the same result. Accordingly the contemporary debate fails to engage with the sceptical problem in its strongest form.

The Knower Paradox has had a brief but eventful history, and principles of epistemic closure (which say that a subject automatically knows any proposition she knows to be materially implied, or logically entailed, by a proposition she already knows) have been the subject of tremendous debate in epistemic logic and epistemology more generally, especially because the fate of standard arguments for and against skepticism seems to turn on the fate of closure. As far as I can tell, however, no one working in either area has emphasized the result I emphasize in this paper: the Knower Paradox just falsifies even the most widely accepted general principles of epistemic closure. After establishing that result, I discuss five of its more important consequences.

Epistemic closure, the idea that knowledge is closed under known implication, plays a central role in current discussions of skepticism and the semantics of knowledge reports. Contextualists in particular rely heavily on the truth of epistemic closure in staking out their distinctive response to the so-called "skeptical paradox." I argue that contextualists should re-think their commitment to closure. Closure principles strong enough to force the skeptical paradox on us are too strong, and closure principles weak enough to express unobjectionable epistemic principles are too weak to generate the skeptical paradox. I briefly consider how the contextualist might live without (strong) closure.