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Read chapters 1-3 for sure, and also chapter 5 if you have time. The book which made it possible to be a liberal in the USA without being gunned down on the sidewalk.
We shouldn't perhaps do this, but we can advise you in advance that there are insuperable problems for any such philosophy of Mind and Action. (That, in case you didn't recognise it, is a challenge).
So think about these related questions: Is there a conception of pleasure which is (a) recognisably something which all humans strive for, and yet (b) something which will function as a common currency in utilitarian calculations?
[Hint: Williams' little chapter is very good on this]Are different pleasures commensurable?
In other words, do they differ merely in the Because of these and similar problems, all modern utilitarians have abandoned pleasure as their target.
Many of the articles are pretty turgid, but the editor's introduction is excellent.
Especially if you want a working grasp of what makes Rights considerations distinctive. Second, remembering thjat Mill also wrote Utilitarianism, we wonder what light each volume throws on the other.
There are instead two different strands of thought.
Some think that what should be maximised is (weighted) as the item to be maximised. And we will expect everyone to have read everything on them.
You can access the appropriate elements of the John Stuart Mill opus online here.
Indeed, while you are there, you can check out Bentham as well.