Samantha Harvey's first novel, The Wilderness, was an ambitious study of a mind succumbing to Alzheimer's. Her second book, All Is Song, is a novel of domestic drama that also examines the place of pure philosophy in real life, considering how a middle-aged, middle-class Socrates might fare in present-day London.

Socrates established a method of probing into the eternal questions of existence and morality by relentless inquiry and debate. Taking his own ignorance as a given, his style of dogged questioning of every certainty and his huge influence over the youths of Athens led to his trial, his defiant comment that "the unexamined life is not worth living for a human being", and ultimately to his execution by hemlock. Socrates is never mentioned in this book and it's not necessary to know anything about him, but the parallels are obvious.

Leonard Deppling has spent the past year caring for his dying father in Edinburgh. Now he has returned to London to a broken relationship and a state of homelessness that forces him to move in with his older brother William. At first sight William appears to be a conventional man in his late 50s, living a comfortable life with his wife and three young sons. In fact he is a highly eccentric individual, obsessed with a "rabid seeking" after ultimate truth, a strange, driven character full of contradictions. In the past he has embraced anarchism, but is proud of his service in the Falklands war. His demeanour is gentle and slow, but his endless questioning of moral norms puts him in direct conflict with authority. Subject to trance states, William has spent time in mental institutions, and though he has very few real friends, he is elevated to near-guru status by a number of young followers who meet with him for regular discussion groups.

Leonard's arrival coincides with the arrest of Stephen, a member of the youth group and a kind of Smerdyakov to William's Ivan Karamazov. Stephen has followed his mentor's words to a literal conclusion and commited a serious crime. Should William be blamed? Quite apart from the real sense of responsibility William feels, even though he had never meant his words to be interpreted literally, the police and the parents of his youth group clearly do hold him responsible. Through Leonard's eyes we observe the family turn in on itself in crisis, thrashing out long-held tensions. A beautiful mind William may have, but it soon becomes apparent that he can be an absolute pain to live with. "Allow me a sentence free of charge sometimes," implores Leonard as he's drawn into yet another spiralling inquiry into some casual remark he made in passing.

Central to the book is the close relationship between the brothers, but William severely tests the love and patience of everyone close to him. Paparazzi are at the garden gate, headlines shout, but William refuses to compromise or defend himself, placing the quest for truth and philosophical inquiry before everything else, including his own fate and the happiness of his family. And the questions shoot up thick and fast. Just how honest is William? Does he really love the music of Carlos Puebla or is it only because he loves Puebla's politics? How far have his basic appetites and animal instincts been subsumed by critical thinking and moral theory? And how rational can a man be who tries to argue his mother out of cancer in the belief that all human illness is the result of unexamined thought?

Leonard begins to suspect that his brother's stance of humble ignorance is in fact truly arrogant. "You exempt yourself from mankind," he accuses, "you say that only your view of the world is right, your view that a man can know nothing for sure, and be certain of nothing except his own ignorance – while our view, the common view, is so patently stupid that we fail, and again we fail."

This is a novel of ideas that also creates believable characters and explores complex relationships. Harvey's prose is graceful and unhurried, full of sharp observation and moments of subtly understated pathos. It's good to read the work of a writer who refuses to compromise or fit neatly into any given category, one brave enough to tackle such uncommercial subjects as myth, religion and the nature and value of contemplation.

If Christ returned, how would he fare in today's world? Many writers have tackled this question, most speculating that, more likely than not, he'd end up in an institution. Harvey is the first to apply this approach to one of the giants of classical philosophy, and she succeeds brilliantly.

• Carol Birch's Jamrach's Menagerie is published by Canongate.