We investigate the effects of alternative utterances on pragmatic interpretation of language. We focus on two specific cases: specificity implicatures (less specific utterances imply the negation of more specific utterances) and Horn implicatures (more complex utterances are assigned to less likely meanings). We present models of these phenomena in terms of recursive social reasoning. Our most sophisticated model is not only able to handle specificity implicature but is also the first formal account of Horn implicatures that correctly predicts human behavior in signaling games with no prior conventions, without appeal to specialized equilibrium selection criteria. Two experiments provide evidence that these implicatures are generated in the absence of prior linguistic conventions or language evolution. Taken together, our modeling and experimental results suggest that the pragmatic effects of alternative utterances can be driven by cooperative social reasoning.