Minimalism proposes that universal grammar (UG) is a characteristic of human thought, also known as I-language, whose main component is the operation Merge, providing for the generative and recursive properties of human thought and language. The complexity and diversity of human languages arises from a process of externalization, whereby internal thoughts are communicated and shared. A fundamental tenet of the Minimalism Program is that UG is uniquely human, emerging well after the evolution of our species, Homo sapiens. I argue instead that the essence of I-language lies in the ability to think about the non-present, as in mentally traveling in time and space, which has a long evolutionary history among animals that move. What may be special but perhaps still not unique to humans is the capacity to communicate our mental travels, as in the core linguistic property of displacement. Mental time travel, or more broadly imagination, is unbounded, and it is this that underlies the generativity of linguistic expression.