This work investigates the Logic that permeates our talk exchanges, that normally fall in the realm of Pragmatics. Two linguistic phenomena are specifically investigated in this dissertation: scalar implicatures and donkey anaphora. At first glance, these seem two distant, unrelated phenomena. At a closer look, however, they reveal some similarities that are specifically addressed and highlighted in this dissertation. In particular, the experimental findings discussed here converge on the revelation of a general interpretative strategy, which is captured in the title of this work: in our ordinary conversations, we seem to appeal to Logic consistently. This, in turn, suggests a more systematic way to analyze, even experimentally, the way we deal with the interpretation of pronouns or the computation of pragmatic inferences in our ordinary conversations, revealing Logic underneath Pragmatics.