Specific Language Impairment (SLI) is understood to be a disorder that predominantly affects phonology, morphosyntax and/or lexical semantics. There is little conclusive evidence on whether children with SLI are challenged with regard to Gricean pragmatic maxims and on whether children with SLI are competent with the logical meaning of quantifying expressions. We use the comprehension of statements quantified with "all", "none", "some", "some...not", "most" and "not all" as a paradigm to study whether Spanish-speaking children with SLI are competent with the pragmatic maxim of informativeness, as well as with the logical meaning of these expressions. Children with SLI performed more poorly than a group of age-matched typically-developing peers, and both groups performed more poorly with pragmatics than with logical meaning. Moreover, children with SLI were disproportionately challenged by pragmatic meaning compared to their age-matched peers. However, the performance of children with SLI was comparable to that of a group of younger language-matched typically-developing children. The findings document that children with SLI do face difficulties with employing the maxim of informativeness, as well as with understanding the logical meaning of quantifiers, but also that these difficulties are in keeping with their overall language difficulties rather than exceeding them. The implications of these findings for SLI, linguistic theory, and clinical practice are discussed. (Contains 12 tables.)