ARISTOTLE's view of the moral universe entails training in a variety of virtues so that the entire organism will learn how to flourish in a particular setting. Aristotle pays little attention to abstract ethical rules and to discussions of what it takes, on the part of human beings (read, HUMAN NATURE), to act correctly. He does this because, as Martha Nussbaum argues persuasively in her Fragility of Goodness, there are two fundamentally different ways to approach ethics. One is to see ethics as a flexible business, one of finding the right habits to inculcate in a specific time and setting, so that the agent will on one hande flourish and on the other benefit his peers. Here ethics and a way of life are more or less congruent and problems come up only when there is an apparently irreconcilable conflict between two of one's good habits. This sort of conflict rather than the appearance of pure evil or sheer goodness seems to be what motivates the Greeks. One could plausibly argue that all of the extant tragic poem/plays we have( and these admittedly represet a very small percentage of their total output) take up questions surriounding conflicts of goods, or, more precisely, situations in which one is called to choose between goods with the result that some unavoidable evil ensues.
For example, consider the case of Agamemnon. He is the head 'general' or king/warlord of the 'Greek' (really, Mycenaean), forces sailing to the city of Troy to avenge the 'kidnapping', by Alexander (AKA Paris), of Agamemnon's brother's wife, the beautiful Helen, whose face famously launched a thousand ships. His huge force, which has no steady source of food and water, but which has to forage as it travels from island to island and harbor to harbor, gets becalmed by the goddess Artemis at Aulis because of some slight. (Agamemnon had bested Artemis, the goddess of the hunt, at stag-hunting and boasted that he was the better hunter).  In any event, the huge force cannot remain stuck where it is for long. They must either turn back and leave Paris' crime to their collective male honor unavenged, a BAD THING, or Agamemnon has to find a way to appease the offended god so the winds will turn in his favor. (As you can see, the Greeks were big on honor and reputation; they had a terms, 'timophilia',  which is hard to translate exactly but which means something like ' love of honor' or 'reputation-friendly'. 
The god offers Agamemnon a 'deal' -- he has, for reasons left unclear, brought his beloved daughter Iphigenia along for the war, a kind of extreme version of 'Take Your Daughter to Work Day'. The god perversely demands that Aga sacrifice this poor girl to the god. (Greek gods loved sacrifices, although human sacrifice was quite rare). Agamemnon is in a classic ethical bind. All his training as a warlord/noble urges him to avange his brother's honor in blood; all his training as a father, in a family-centered culture, urges him to protect his child. But he cannot, in this situation, have both. He must sacrifice one value in favor of the other, and there is no clear template for which value is greater.
Martha Nussbaum, mentioned above, argues thatAgamemnon's dilemma reveals something profound about life: we are often faced with such conflicts between goods, and what makes life poignant is having to accept this inherent and terrible limitation. She further argues that many Greeks saw Agamemnon as a bad guy, not because he sacrificed his daughter ( which he did) but because he tried to justify the act. Rather than admitting that whatever he did was going to be wrong, Agamemnon argued for the rightness of his decision, on the assumption that in this world there is always a better choice and that we can use reason to figure out what that choice is.
But Nussbaum writes that the Greeks disapproved of Agamemnon and morally disowned him, not for killing Iphigenia but for rationalizing it as if it were somehow the 'right' thing to do. Better to accept that one is sometimes forced to do something terrible to achieve something good, and to spend one's life agoinizing over the wrong one did,  even though one had to do it. 
This squares more with Aristotle's dog whisperer approach: he argues that each organism has to be trained to certain habits but that this training can follow only the most general, sketchy outlines, both because what is required to act right in shifting moral situations cannot be pre-determined, and because each agent is different in temperament and in what it takes for her to flourish. Thus, he could easily envision such moral quandaries as the one in which Aga finds himself because there is no in-built guarantee that virtuous training and habits will always work out neatly. The world can present us with insoluble problems; the moral key is to understand this and to act decently in the face of it, accepting that there is sometimes no good answer and that some of us are called to a life in which regret and remorse figure as important themes. Even though we all desire happiness and even know roughly what it takes to be happy, chances might not break our way and when this happens we have to know how to accept our bad luck as gracefully as possible.
The theorists we study -- Hume, Bentham and Mill, Kant -- all reject this read and argue that there is a way to make right decisions using rational principles. They do this by sshifting the focus of ethics from the given reasoning body to more abstract rules and principles that they believe are the foundations of all ethical life and decision making. In this regard they are all influenced by Descartes,  Descartes believed that philosophy needs to find absolutely certain foundations that cannot be doubted and beneath which there is nothing. Such truths or realities serve as a bedrock on which to build all less certain principles or judgments or things. This is called foundationalism. Even though all our moral philosophers rejected Descartes to one degree or another, all remained foundationalists, although they entertained incompatible beliefs about what the moral foundations were.
The utilitarians, who were really successors to Hume's moral sentiment school of thought, shared, with Hume, the fundamental belief that ethical choices are and should be guided by natural, unschooled feelings. But where Hume identified the fundamental feeling with natural sympathy the utilitarians elected to believe that the most basic human feeling was a longing for happiness and, further, that happiness consisted in living so that one exerienced a steady excess of pleasure over pain.The more pleasure one felt, the happier one was.
This is a simple equation, and 'pleasure'and 'pain' in this account can mean either physical sensations such as Freud's friction or more internal psychological states such as feelings of hope or contentment or satisfaction and the absence of anxiety and fear and anger.  Whatever the kinds and source of pleasure and pain, the happy person is she who steadily has more of one than the other. 
This position is techncially called hedonism, or the elevation of pleasure to the position of the most important human experience, and the version I am presenting is often called selfish or individualistic hedonism, and is not what the utilitarians preached.
They are more rationalist than this. They did not believe that one could assess the value of acts on an individual basis. They are called utilitarians because they believe that the value of an act can be judged by its usefulness in increasing pleasure and/or in reducing pain, but with the caveat that acts are morally good(useful) to the extent that they increase pleasure and reduce pain as much as possible for all the people whom the act affects. 
Thus the ideal moral act is the one that is the most useful because it produces the greatest possible intensity and numerical spread of happiess possible in that situation. The somewhat mad genius (and possibly fatal weakness) in utilitarianism is that these guys actually believed that they could assess the relative intensity and distribution of happiness in their acts  before they did them, by developing a hedonic calculus of plus and minus pleasure and pain, using which one could mathematically calculate risk-benefit analyses that would indicate which acts were most highly useful in each situation.
Minor instances of such attachments of numerical weight to pain and pleasure happen in hospital and dental settings in which patients are routinely asked to measure their pain using a 1 - 10 scale. Other, weirder instances are the 1-10 hotness scale, used for both men and women, scoring on such shows as "Dancing With The Stars", and student evaluation forms for classes. (hmm ...).
The idea is that the act or plan that yields the highest pleasure-over-pain ratio 'wins', is most useful and is the most ehtical thing to do in the situation.
We will not discuss yet whether such a calculus makes any sense but will first note that there is another problem built into utilitarianism, which, by the way, sounds pretty cool on first glace -- as do most philosophical ideas. 
The problem is that if one argues that a simple numerical excess of pleasure over pain suffices to make an act good, then really vulgar or crass or just plain stupid acts that produce dimwit pleasure and little pain could count as ethically purer and more relevant than other acts that we identify, traditionally, as more ethical.
For example, if a bunch of folks going down to the Empire Bowl in Redlands have a grand time shooting a few frames, as they joke and drink beer and eat greasy burgers and wear weird sweaty rented shoes, and feel little pain beyond slight twinges of indigestion, then this bowling night is a very useful act, therefore highly ethical, especially since our pleasure coexists with the pleasure that the alley owners, the wait staff and  shoe renters all feel at being employed and making money. If we add in the other bowlers who are cheered by our happy, slightly goofy, presence, this act rises to heights of goodness.
By contrast when the same happy group decides to help the homeless people at the local Salvation Army facility, things go less well. First, there are no beer or burgers at the Army, and showing up with a buzz on is frowned on . No music or rental shoes or wins and losses, but a sorry crowd of weird, usually unclean, often incoherent and/or irascible people who have a hard time saying what they need, or say it over and over and over again. We do our best to feed them third-rate food, which they either wolf down because they are starving or reject or do revolting things with. Then we have to clear the tables, bussing the dirty plates and silverware; this is no more fun than slopping out the food. 
Finally, tired from serving and cleaning we help these poor people get settled for the night on cheap cots with minimal blankets and grey sheets and thin pillows. They complain and fart and cough and talk endlessly and bicker and toss and turn. There is little grace and almost nor gratitude and we end our evening's labors depleted and discouraged, telling ourselves that we have done a Good Thing. But we fell little real pleasure, knowing that they could not have enjoyed the crappy food or the minimal beds very much, although many were grateful even for small things. We did produce some pleasure but not a huge amount, and we probably experienced more pain than pleasure in serving and helping them, clichés about war inner feelings notwithstanding.
In a real sense these acts were less ethically useful, because they produced less pleasure and more pain, than going bowling and forgetting all about the poor people. Can this be correct?
Jeremy Bentham, the first self-identified utilitarian, tbought this was just right. He wrote that playing push-pin, a game of the time as mindless as any iPhone app game, was as meaningful as creating music or poetry because doing one produced as nuch overall pleasure as doing the other . As the guy at http://skeptically.org/utilitarianismtheethicaltheoryforalltimes/id3.html writes, 
Bentham wrote in The Rationale of Reward that, "Prejudice apart, the game of push-pin is of equal value with the arts and sciences of music and poetry." Mill in his still widely studied "Utilitarianism", published 20 years after the death that Bentham, wrote that Bentham held that, "Push pin equals poetry." This a particular example used to illustrate Bentham's position that all pleasures are reducible to the dimension of quantity. Mills differed. 
Following the lead of Epicurus, who held that all pleasures are reducible to quantity, Bentham wrote of seven parameters for the measurement of such quantity. However, he held that the so-called higher pleasures were reducible to quantity. He did not deny, nor did Epicurus, that certain pleasures produced in the long run, because of the development of good character, a more pleasurable life, or that other produce greater benefits for society, he simply held that these considerations were reducible to quantity. 
John Stuart Mill, as our author writes, disagreed with this because he wanted to argue that even though people naturally seek to maximize pleasure even when they calculate, in a rational sense, hiow much pleasure the act will produce not only for themselves but for everyone whom the act affects, people can be taught something more. That is they can be taught (shades of Aristotle!) to actually feel more pleasure when they do selfless acts or listen to Mozart than they do while playing 'Call of Duty'. This happens for two reasons. First, selective reinforcement in education will associate doing the good or the aesthetically advanced with good feelings: jus as when we train that famous dog, we do best when we reinforce what we like lavishly.  Second, Mill actually believes that when given the opportunity to feel what he considers more highly refined pleasure, most people will prefer those higher pleasures, because they naturally prefer such higher pleasures once they have experienced them.  Thus, once X feels what it is like to feed the homeless, she will naturally prefer the pleasure she feels when doing this to the pleasure she feels from texting her bff. Thus for Mill an act is most useful, and therefore most ethical, when it produces the maximum amount of higher pleasure for the most people possible. 

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