In her late sixties, which is when we meet her, Elizabeth is an international literary celebrity and is frequently invited to perform as such: to give a lecture, participate in a conference, receive a prize. She usually finds this exposure daunting and exhausting, but seems unable or unwilling to refuse to play the game; and in two of these episodes she is eager to speak (though she still finds the experience painful and difficult), in crusader mode, about cruelty to, and exploitation of, animals.

Like most books that can be categorised as novels of ideas, Elizabeth Costello is inhabited by characters who by profession, vocation, and nature concern themselves with the riddles and problems of existence, and periodically express these concerns in the formal settings – the learned journal, the lecture theatre, the seminar room – of intellectual life, using terms and techniques evolved and refined through the history of Western thought.

So logic and the relentlessness of logic hold a high value in their arguments, their lectures, and their disquisitions. The causal relationship, the ‘if X then Y’ formula, the crystalline mechanisms of proof, are central to Western intellectual traditions. And yet Coetzee’s heroine, not just a distinguished writer and thinker but also a tough old bat who, despite her seven decades, can still meet intellectual resistance with more resistance of her own, ‘hates sentences that hinge on because. The jaws of the trap snap shut, but the mouse, every time, has escaped.’ Logic is examined logically and found wanting; reasoned attacks are made on reason; and in the end, Elizabeth gets stuck in a sort of cosmic waiting room because she refuses, or is unable, to write a dishonest statement about what she believes to be true.

Of the nine sections into which this book is divided – for there is also an oblique postscript, which seems on first reading to be unconnected with the rest of the story – seven have already been published separately in various forms and versions, which should give some indication of how discontinuous this narrative is. In each of these episodes, some belief or position is being tested, or two modes of thought are being pitted against each other, or some classic of Western philosophy – the mind–body problem, the problem of evil – is being readdressed. Accepting an award at a college in Pennsylvania, Elizabeth makes a speech on the nature of realism; travelling on a cruise ship, she encounters an old acquaintance lecturing on ‘The Novel in Africa’; speaking at a conference in Amsterdam on the problem of evil, she finds to her horror that the fellow-novelist whose book she is passionately attacking is also present at the conference and will be in the audience.

As should by now be apparent, there’s a thread of grim comedy running through most of these intellectual encounters. At one stage, Elizabeth visits Africa for the sake of her sister Blanche, who has made it her adopted home. Long since reborn as Sister Bridget of the Marian Order, and now running a hospital for children born infected with HIV, Blanche is to have a degree conferred on her by an unnamed African university. In accepting this honorary degree in humanities, she makes an uncompromising speech about the death of the humanities. In this novel that appears at first to concern itself more with discussions of causality and personality than with the enactment of plot and character, Blanche is a superb piece of characterisation and a timely reminder that Coetzee is a great novelist and that what he is writing here is indeed a novel.

For me and probably most other readers, the heart of this book, and certainly the point at which it connects most closely with Disgrace (1999), is the section that was published separately in 1999 as The Lives of Animals. In the two guest lectures she gives at the Massachusetts college where her son teaches science, ‘The Philosophers and the Animals’ and ‘The Poets and the Animals’, Elizabeth puts an impassioned case for a rethinking of the relations between humans and animals. What’s most interesting about this is that she is neither a sentimentalist, a purist, nor a fanatic on the subject (‘I’m wearing leather shoes,’ she tells a courteous dinner companion who is avowing his respect for her convictions. ‘I wouldn’t have overmuch respect if I were you’), but rather someone who has reached the views she holds through her exploration of what it means to be human by examining the borders between the human and the non-human animal, and the moral responsibilities of the one towards the other.

During question time after the first of her lectures on animals, Elizabeth states a position that I take, albeit with the utmost caution, to be Coetzee’s own: ‘I was hoping not to have to enunciate principles,’ she says. ‘I have never been much interested in proscriptions, dietary or otherwise. Proscriptions, laws. I am more interested in what lies behind them.’

The point of convergence towards which all this discussion is moving, though from different directions and at different speeds, is the notion of embodiment that permeates the whole book: the idea of life at its most perfect as a seamless fusion of body, soul, and mind. Representations of the body recur as sticking points in the discussions of realism, of the African novel, of the competing claims of Catholicism and humanism. Power differentials and the evils arising from them are demonstrated, horribly, by what the powerful do to the bodies of the powerless. Elizabeth’s own experience of life is punctuated by occasional startling, even shocking, personal experiences of sex and violence, set in counterpoint to the events of her intellectual life.

A brief glimpse of this unity as the highest ideal of life appears at the end of ‘Lesson 7: Eros’, an oddly light-hearted meditation on the idea of sex between gods and mortals: ‘A vision, an opening up, as the heavens are opened up by a rainbow when the rain stops falling.’ Lesson 8, in which Elizabeth appears to have died and to be in some sort of antechamber to the afterlife, is a simultaneously terrifying and very funny account of a soul still apparently very much attached to its body. And the mysterious postscript can be decoded quickly enough by finding the original text to which it refers; like the rest of this book, it argues implicitly for the indivisibility of body and soul as the highest human ideal.

Elizabeth Costello is in no way the sort of novel it’s possible to read on the bus. And if you have no interest in animals, or no tolerance for the convolutions of philosophical discourse, or a preference for intricacies of plot and character as the cornerstones of fiction, then it will be a source of ongoing frustration. But otherwise, the scope and lure of its arguments and the elegance of their framing and expression are hypnotic and, in the end, irresistible.