Knowledge and deductive closure

Abstract

The question whether epistemological concepts are closed under deduction is an important one since many skeptical arguments depend on closure. Such skepticism can be avoided if closure is not true of knowledge (or justification). This response to skepticism is rejected by Peter Klein and others. Klein argues that closure is true, and that far from providing the skeptic with a powerful weapon for undermining our knowledge, it provides a tool for attacking the skeptic directly. This paper examines various arguments in favor of closure and Klein's attempted use of closure to refute skepticism. Such a refutation of skepticism is mistaken. But the closure principle is in any case false, so the skepticism that depends on it is undermined. The appeal of the closure principle derives from a failure to recognize an important feature of our epistemological concepts, namely, their context relativity.