Alone among all animal species, only humans posses a true language. But how do we know this to be the case? Can we be sure that no animals have language? And if they did, what quantitative tests could show that a vocal communication system is truly "linguistic"? The quest for a quantitative measure of language-like tendency is important, because qualitative inspection of animal vocal communication systems has so far failed to show the expected gradual evolutionary progression from non-linguistic communication to true language. Language appears to sit at a balance between information content, and cognitive tractability, and I present the results of applying relevant information theory metrics, such as entropy and Zipf's law, to corpora of animal vocal communications from a wide range of species. By comparing these metrics to artificially generated sequences (random, linguistic, and from neural models of birdsong generation), I show that a graded extent of "language-ness" does in fact exist across animal taxa, with the communication of some species (such as cetaceans) being statistically more similar to human language than the vocal systems of other species. Building on such techniques to assess the possible linguistic nature of sequences from an unknown origin, we can draw conclusions about the evolutionary processes involved in the origin of language, as well as test signals received in the search for extra terrestrial intelligence (SETI).