Do we represent peripersonal space?
Work in both animals and humans has demonstrated that the brain specifically tracks the space near the body—the so-called ‘peripersonal space’ (PPS). These representations appear to be multimodal and expressed in body-centred coordinates. They also play an important role in defence of the body from threat, manual action within PPS, and the use of tools—the latter, notably, ‘extending’ PPS to encompass the tool itself. Yet different authors disagree about important aspects of these representations, including how many there are. I suggest that the questions about the nature and number of PPS representations cannot be separated from the question of the mathematical basis of the corresponding representational spaces. I distinguish cartographic from functional bases for representation, suggesting that the latter provides both a plausible account and support a single-representation view. I conclude with reflections on functional bases and what they show about representation in cognitive science.