We examined how language supports the expression of temporality within sentence boundaries in English, which has a rich inventory of grammatical means to express temporality. Using a computational model that mimics how humans learn from exposure we explored what the use of different tense and aspect (TA) combinations reveals about the interaction between our experience of time and the cognitive demands that talking about time puts on the language user. Our model was trained on n-grams extracted from the BNC to select the TA combination that fits the context best. It revealed the existence of two different sub-systems within the set of TA combinations, a “simplex” one that is supported lexically and is easy to learn, and a “complex” one that is supported contextually and is hard to learn. The finding that some TA combinations are essentially lexical in nature necessitates a rethink of tense and aspect as grammatical categories that form the axes of the temporal system. We argue that the system of temporal reference may be more fruitfully thought of as the result of learning a system that is steeped in experience and organised along a number of functional principles.