Curtis and Vehmas present an argument in support of full moral status for those with profound intellectual disabilities based on Moore's famous defence of a common-sense view of the nature and existence of the external world. According to them, the need for such an argument arises from the disturbing inferences that can, supposedly, be drawn from the standard Lockean philosophical theory of personhood. This paper develops and supports Curtis and Vehmas's central claim concerning this equality of moral status by suggesting a basis for rejecting Locke's position, based on reflections upon Wittgenstein's remarks about games and family resemblances. It also questions the validity of the disturbing inferences. It asserts that our moral duties towards and concerning people who have and people who do not have profound intellectual disability, human and non-human animals, do not derive solely from their moral status. The existence, content and strength of our moral duties towards particular people can be grounded in conditions and circumstances that pertain to us rather than to them.