One of the major debates in theories of language origins is about whether human language is an extension of communication abilities which are widespread in nature, or is instead an entirely novel ability (in which case, we can call it an evolutionary discontinuity). For a special edition of Biolinguistics marking the 50th anniversary of Eric Lenneberg’s influential Biological Foundations of Language, I give some arguments in favour of discontinuity theories. This is consistent with the position in generative linguistics (the one associated with Chomsky) but I reject the generative view that what makes us unique is the syntactic structure of language and thought. I argue that that structure exists but is widespread and what distinguishes us is our ability to represent thought using socially-grounded symbols.