Can there be a professional realm, short of politics, as divided and factionalised as that which deals with the problems of the mind? Take a sample of approaches from psychiatrists, psychologists, behavioural geneticists, cognitive neuroscientists, psychopharmacologists and psychoanalysts – and you will find factions within the factions, models of brain function competing with "psychodynamic" conceptions of the mind competing with social interpretations competing with evolutionary ones. More than a competition of ideas, it's a clash of world-views.

Darian Leader belongs to the most endangered clinical world-view of them all: that of the psychoanalyst. Though the Freudian language of childhood memory and repression still flickers through western culture, psychoanalysis as a practice has largely been excised from British public health. The wider culture has gradually followed and it's now commonplace to hear ideas that have been with us for a century being ridiculed. Leader is one of the few powerful voices left still actively – even aggressively – promoting the language of dream, libido and the oedipal formation of the mind.

One of the problems with defending psychoanalysis is that, though a relatively small faction, it is deeply divided within itself – a victim, in Freud's own term, of the narcissism of small differences. To the outsider, the rifts between Freudians, Jungians, Kleinians or the followers of Winnicott may have become obscure to the point of meaninglessness. And Leader belongs to the most obscurantist French faction of them all: that of the flamboyantly esoteric Jacques Lacan.

But where his master may be unreadable, Leader can be a good explainer of basic principles and, above all, the central purpose of the psychoanalytic project. While mainstream psychiatry is discarding the skills of the well-crafted patient history and disengaging from long-term therapeutic relationships, psychoanalysis remains a torch-bearer of careful listening and deep psychological understanding.

In the early chapters of What is Madness?, Leader spends a good deal of time attacking the approach of mainstream psychiatry, and some of his criticisms are well-aimed: flaws in the classifications of the Diagnostic and Statistical Manual of Mental Disorders (DSM), the decreasing space available in cognitive models of treatment for "the detail and value of individual lives", and the focus on surface symptoms rather than the subjective experience of madness.

So long as his focus sticks to the need to do more than address symptoms, there is helpfully provocative material here. But for every useful criticism, Leader cannot resist the temptation to flip over into shrill condemnation, suggesting at one point that the cognitive focus on symptomatology is itself "a symptom of psychosis". The suggestion that the medical mainstream is insane puts a huge burden on the author to prove the sanity of his own system – and this will not be entirely evident to the agnostic reader.

There are powerful notions in Lacanian theory, chief among them the principle that language is not merely a tool we use to describe reality, but an embodied capacity by which we (partly) create reality. Run away with that idea, however, and you can end up being able to say almost anything you like and confusing it for reality. How many readers, now, will want to follow Leader when he states that a girl in early development unconsciously reproaches her mother for not providing her with a penis and looks to her father to give her one, "not as an anatomical organ, but in the form of a child"? Is that obviously less bonkers than, say, a diagnosis of OCD based on observation of excessive hand-washing rituals?

This is a complicated and inconsistent book, brilliant in parts and silly in others, and therefore very hard to summarise. But what is most interesting in it is Leader's conception of madness as a problem of reason. All forms of madness, in Leader's psychoanalytic reading, are responses to inner conflict, and his job as a therapist becomes to "unearth the logic" in what his psychotic subjects say.

It is because he sees reason in madness that Leader can also argue that there is no such thing as "mental illness" – he views madness as a natural response to unbearable experience. And there is a great project in the ambition to unearth the logic of disorder this way. But it is also limited by its belief in the human mind as, essentially, a reasoning process. It excludes the possibility that there may not be logic, that thinking may not be central, that neurochemical or structural formation of the brain may be producing effects that are not subject to this kind of analysis.

A weakness in cognitive and neuroscientific conceptions of the mind is that they often proceed unaware of their own philosophical assumptions. To criticise the philosophical limitations of simplistically empirical psychologists, as Leader does, is essential. But if that leads you into a position in which you believe that the other fields can tell you nothing at all about the mind, then you disappear up the back end of your own factional discourse.

What Leader does best comes from the skill of close listening to patients and investigating the meaning of patient history, a skill he best displays in his chapter on Harold Shipman. This is by far the most enjoyable section of the book – partly because Leader can tell a person's story well, and partly because there is minimal Lacanian theory in it. Of course, Leader has never met Shipman, so his diagnosis – paranoia – is no more authoritative than the official report on Shipman that he derides. Nor does his view of madness provide an explanation for a serial killer that is any more satisfying than a concept of evil. But it is a reminder that psychiatric diagnosis without history is worthless.

Yet all this left me with a sense of hopelessness. Psychoanalysis needs to move on, retain its depths but discard its arcane mythologies. We need thinkers capable of bringing together the factions of mind and brain – arguing for an integrative psychiatry and a general field-theory of the mind. No one, from any of the psycho-disciplines, comes close to doing that. Perhaps it is impossible.