Most linguists and philosophers agree that the language system includes a syntax and a compositional semantics. Recently, several influential semanticists have argued that the language system also includes an automatic inferential system---sometimes called a `natural logic'---that can determine when expressions are informationally useless, and mark them as unacceptable. Building on this work, I have advanced three claims. First, I argue that the natural logic used by the language system is largely classical. This suggests that we need not posit a logic that is idiosyncratic and domain specific for language, as various extant accounts have done. Second, I argue that the logical forms of natural language expressions are representations which can support general reasoning. This contrasts with several recent accounts which postulate various levels of representation between linguistic logical form and the representations which support general cognition and inference. Third, I argue that this view works best when combined with the hypothesis that the lexicon encodes, and the language system has access to, rich sets of encyclopedic and other information. Taken together, these claims support a view of the language system as, ultimately, a very powerful inferential device, i.e., a system that does a lot of useful yet unconscious/automatic thinking for us.