Aristotle's classification is often presented as a ranking that dismisses the first two kinds. It isn't. He calls all three genuine friendships; his point is that they differ in what they are based on, and therefore in how long they last and how much they can bear.
In a friendship of utility, what you value is what the person supplies — a colleague who makes work manageable, a neighbour who shares tools. In a friendship of pleasure, what you value is the enjoyment of their company. Both are real, both can be warm, and both are conditional on something that can change. When the project ends or the tastes diverge, the basis of the friendship is gone, and Aristotle thought this explains something we all observe: such friendships end without anyone doing anything wrong.
Friendship based on virtue is different in kind rather than degree. Here what you value is the person's character — who they actually are — and since character is comparatively stable, so is the friendship. Aristotle adds that this kind also contains the other two: good people are useful to each other and enjoy each other's company. It just isn't founded on either. He also thought it takes considerable time, since you cannot know someone's character quickly, and that you cannot have many such friendships, since each requires more than most people have to give.
One condition runs through all three: friendship must be mutual and mutually known. Goodwill toward someone who doesn't know it isn't friendship; neither is admiration that isn't returned. This rules out one-sided attachment, and it distinguishes friendship from the kind of connection a reader feels toward a writer they have never met.
The modern problemFriendship and impartiality.
Contemporary discussion is dominated by a tension the ancients did not press. Most moral theories demand impartiality — utilitarianism counts everyone's wellbeing equally, and Kantian ethics grounds duties in universal principles. Friendship is unashamedly partial. You help your friend move house and not the stranger who needs it more, and you would think worse of someone who treated their friends as interchangeable with strangers.
This is sometimes framed as a problem for the moral theories rather than for friendship. If a theory implies you should abandon your friend to marginally increase total welfare, many take that as evidence against the theory. Bernard Williams pressed a version of this famously: someone who pauses to calculate whether to save their drowning spouse has had, as he put it, one thought too many.
Defenders of impartial theories reply at the level of rules rather than acts — a world in which people form deep partial attachments produces more wellbeing overall, so impartial reasoning itself recommends partiality in practice. Critics find this unsatisfying, since it seems to value your friend instrumentally, as a component in a scheme, rather than for their own sake, which was the definition we began with.
What friends oweThe open questions.
Several questions remain genuinely unsettled. Does friendship require honesty even when honesty will hurt, or does it sometimes require withholding? Are you obliged to think well of a friend beyond what the evidence supports — and if so, is that a form of loyalty or a failure of judgement? Can a friendship survive one person's serious moral failure, and should it? These are not questions philosophy has answered, but naming them precisely is most of the work.