[T]he Utilitarian cannot confine himself to a single mind; he has to consider what he calls “the total happiness of a collection of minds”. Now this is an extremely odd notion. It is plain that a collection cannot literally be happy or unhappy. The oddity is clearly illustrated if we […] use the analogy of greyness. Suppose that a number of different areas, which are not adjoined to each other, all go through successive phases of greyness. What could we possibly mean by “the total whiteness of this collection of areas”?

C. D. Broad, Five Types of Ethical Theory, London, 1930, pp. 248-249