Nonhuman great apes inform one another in ways that can seem very humanlike. Especially in the gestural domain, their behavior exhibits many similarities with human communication, meeting widely used empirical criteria for intentionality. At the same time, there remain some manifest differences, most obviously the enormous range and scope of human expression. How to account for these similarities and differences in a unified way remains a major challenge. Here, we make a key distinction between the expression of intentions (Ladyginian) and the expression of specifically informative intentions (Gricean), and we situate this distinction within a “special case of” framework for classifying different modes of attention manipulation. We hence describe how the attested tendencies of great ape interaction—for instance, to be dyadic rather than triadic, to be about the here-and-now rather than “displaced,” and to have a high degree of perceptual resemblance between form and meaning—are products of its Ladyginian but not Gricean character. We also reinterpret video footage of great ape gesture as Ladyginian but not Gricean, and we distinguish several varieties of meaning that are continuous with one another. We conclude that the evolutionary origins of linguistic meaning lie not in gradual changes in communication systems, but rather in gradual changes in social cognition, and specifically in what modes of attention manipulation are enabled by a species’ cognitive phenotype: first Ladyginian and in turn Gricean. The second of these shifts rendered humans, and only humans, “language ready.”