When philosophers today debate the age-old problem of the relation of mind or soul to matter or body, they tend to get involved quickly in discussing not just what actually is but also what possibly may be or by contrast what necessarily must be. No thesis in this much-disputed area has been the topic of more extended discussion than that of the "supervenience", as it is called, of the mental on the physical, according to which for any difference in the mental to have been possible, some difference in the physical would have been necessary. In this book a recognized authority on modal logic, the logic of the necessary and the possible, critically examines, from a logician's distinctive point of view, the supervenience debate in philosophy of mind and philosophical psychology, and ends up questioning not so much the truth as the significance of the supervenience thesis.