One of the main tenets of Gricean pragmatics is the distinction between what is said and what is implicated; that is, between truth-conditional and non-truth-conditional meaning. The main contribution of post-Gricean pragmatics was a new definition of what is said as a pragmatic and truth-conditional meaning (Carston, 2002; Recanati, 2010; Moeschler, 2018a). However, implicated meaning (mainly conversational implicature) is still defined as non-truth-conditional because it is cancellable without contradiction. The main consequence is that a speaker can deny having intended her implicature, which results in the hearer having no guarantee of the truthfulness of his inference. This paper explores the relationship between truth and pragmatic implicated meaning and posits that the assessment of a truth value of an inference is a crucial step in the comprehension process. To demonstrate this hypothesis, the paper develops a relevance-based approach to inference, which is coupled with Kahneman's dual cognitive system. I argue that the triggering of an inference is an intuitive and automatic process controlled by System 1, whereas its assessment as a true or false assumption is controlled by System 2. In other words, System 2 is responsible for what is defined in relevance theory as epistemic vigilance.