Knowledge is closed under analytic content

Samuel Z Elgin

doi:10.1007/s11229-021-03027-5

Abstract

I am concerned with epistemic closure—the phenomenon in which some knowledge requires other knowledge. In particular, I defend a version of the closure principle in terms of analyticity; if an agent S knows that p is true and that q is an analytic part of p, then S knows that q. After targeting the relevant notion of analyticity, I argue that this principle accommodates intuitive cases and possesses the theoretical resources to avoid the preface paradox.

Highlights

Knowledge of some truths requires knowledge of others
Under what conditions does knowledge of one proposition require knowledge of others? Is it a feature of conjunction and negation in particular, or are they instances of a more general pattern? What is it in virtue of that this epistemic restriction occurs?. This is the interpretive question of the closure principle, the most basic formulation of which is the following: Naïve Closure: If an agent S knows that p, and p entails q, S knows that q
If an agent disbelieves that something is true, they do not know that it is true. In light of these considerations, some may be tempted by the following modification: Not-Quite-So-Naïve Closure: If an agent S knows that p, and S knows that p entails q, S knows that q

Summary

Introduction

Knowledge of some truths requires knowledge of others. All those who know that p ∧ q know that p—as do all those who know that ¬¬ p. We might further amend this principle by requiring agent S to believe that q in order to count as knowing that q, but this does not accommodate cases in which S believes that q for spurious reasons, rather than because it is entailed by p. This, I claim, is the notion of entailment under which knowledge is closed: the type between a sentence and its analytic parts.

Results

Conclusion