In a previous paper on ‘fair play’ (Wigmore and Tuxill, 1995) it was suggested that one of the underlying explanations for the moral wrongness of not playing fair was that it represented a failure of respect for persons. This chapter seeks to take that idea further and explore the implications of such a claim in more depth. It will seek to do a number of things: first, to examine in more detail the idea of ‘respect for persons’ and the notions of ‘person’ to which such an injunction applies. In particular, it will explore two versions of the notion of respect: ‘recognition’ respect and ‘appraisal’ respect, (Martin, 1995, p. 143) and the different ways in which ‘persons’ can be construed as beings which demand such respect and the features of persons which make them of value and which render respect mandatory. This range will encompass, at the one extreme, the austere and attenuated definition, found in and based on Kant, which acknowledges as ‘persons’ only rational agents, and, at the other, the notion of ‘bodily’ or ‘kinaesthetic’ intelligence for which Gardner (1983) argues.