Intuitions about contextualist cases such as Cohen’s airport case pose a problem for classical anti-skeptical versions of invariantism. Recently, Tim Black (2005), Jessica Brown (2006), and Patrick Rysiew (2001, 2005, 2007) have argued that the classical invariantist can respond by arguing that pragmatic aspects of epistemic discourse are responsible for the relevant problematic intuitions. This paper identifies the mechanisms of conversational implicature and impliciture as the basic sources of hope for this explanatory strategy. It then argues that neither of these sources provides the classical invariantist with a convincing response to the airport case and its analogs.