Mill’s claim: if happiness is a good to a person, then the general happiness is a good to the aggregate of all persons. There are interpretative difficulties here. Does Mill mean that if happiness is a good to me, then the general happiness is also a good to me in so far as I am part of the aggregate of all persons? Or does he mean that by adding the good of each individual person we get to the aggregate good of the whole? Probably the latter.
First pb what does it mean to say that general happiness is the sum of individual happinesses? (See Skorupski, 1989, 287; Crisp, 1997, 78ff).
Second pb: aggregation comes at the cost of equality. Cf subsequent lectures on justice for more on this.