The health theories of Nordenfelt and Boorse are compared. Critical attention is focused on Nordenfelt's description of his theory as one of holistic welfare, contrasting with Boorse's analytical and statistical approach. Neither theory is found to give an entirely satisfactory account of 'health' in scientific medicine or common usage. Because Nordenfelt attenuates the ontological significance of organs and organ parts and simplifies the role of statistics, his theory is regarded as weakly holistic. Boorse underrates the importance of non-statistical evaluation. A mediating position, termed 'strong holism' is suggested as a way of integrating normative and statistical elements in a more adequate health concept.