Since June, when he discovered he had oesophageal cancer, writer Christopher Hitchens has been interviewed by a number of senior journalists. CNN's Anderson Cooper, PBS' Charlie Rose, National Public Radio's Melissa Block and, most recently, the BBC's Jeremy Paxman have all called on Hitchens at his Washington home. They have all tried to take the measure of a man who now, after a long career as a critic of religion, confronts death.

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Compelling and sombre, the sessions have been remarkably free of sparks: the journalists are deferential in the face of Hitchens' moral courage. Does Hitchens ever dream, as he answers the same guarded questions, of an interlocutor equal to the subject? For example, James Boswell, the 18th century's greatest interviewer, who interviewed the dying philosopher David Hume.

News of the North American colonies' Declaration of Independence had not yet reached Britain when Boswell called at Hume's residence in Edinburgh. Boswell had learned shortly before that his fellow Scot had returned from London and was "just a-dying" from cancer, with a tumour "about the bigness of an egg" bulging near his gut. Although friends and doctors sought to reassure him, Hume dismissed such chatter as "very silly expectations".

Ushered into the drawing room, Boswell caught his breath: his famously plump friend was now gaunt and ghastly, his bald skull topped by a small wig. Yet his host's demeanour was cheerful. The visitor pulled up a chair and, with his usual mix of humour and intensity, went right to the heart of the matter: had the sceptical thinker and reputed atheist changed his ideas about God?

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He had not. Hume had lost his religious faith long before and did not anticipate any sudden change of heart. Besides, true morality forbade such a change. Enjoying Boswell's mixture of fascination and discomfort, Hume announced that all religions were bad for ethics: "They all make up new species of crime and bring unhappiness in their train. When I hear a man is religious, I conclude he is a rascal, though I know some instances of very good men being religious."

Boswell flinched: earlier that year, the religious but libidinous Scot had contracted his 11th case of gonorrhoea - an impressive feat even in that mercury-doused age. He grew more insistent. Surely Hume believed in the possibility of a future life where we will have to answer for our sins? Gesturing at the empty fireplace, the philosopher smiled.

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"'Tis possible that a piece of coal, put upon the fire, will not burn, but to suppose so is not at all reasonable."

Boswell would not be put off: "Does the thought of annihilation never give you any uneasiness?"

Hume shrugged: "Not at all, Mr Boswell. No more than the thought that I had not been."

As they parried, Boswell heard one of Hume's doctors being led to the drawing room. He had just moments left to prod the old sceptic into revealing a hiccup of doubt. Leaning towards his host, he cried, "If I were you, I should regret annihilation!"

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Hume replied with equanimity, "If there were a future state, Mr Boswell, I think I could give as good an account of my life as most people."

In a state of far greater distress than the dying philosopher, Boswell made his farewells. He was, he later wrote, taken "off his guard". There was, he marvelled, "no solemnity in the scene; and death for the time did not seem dismal. I left Hume with impressions that disturbed me for some time."

In many ways, Hitchens resembles Hume. There are the same heavy-lidded eyes, smooth skull, rounded face; the same "tranquillity of mind and clearness of head"; the same impatience with cant and those who believe that reason and faith can coexist. Even the backdrops are the same: fireplaces, unlit and cold, are in both men's drawing rooms.

Yet the question that for Boswell was a matter of life and death has become, for our modern Boswells, a matter of life and death interrupted by a word from our sponsor. Hume died without publishing his Dialogues Concerning Natural Religion; his friends dissuaded him from going public. Hitchens' God Is Not Great: The Case Against Religion (2007), which draws on Hume's work, is a bestseller. What could be said only privately in the 18th century is now the stuff of publicity tours. The doubt that did not dare speak its name then has its own section now at WHSmith.

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At the end of his book, Hitchens calls for a new Enlightenment. But Hume might reply that we have not done so badly by the old one. After all, the work of the earlier Enlightenment has allowed us to enjoy the fruits of Hitchens' scepticism. It has also allowed for interviewers who, unlike Boswell, do not have a dog in this philosophical fight. It is hard to imagine Rose or Cooper wrestling with Hitchens as desperately as Boswell did with Hume. In the 234 years since Boswell knocked at Hume's door, we have moved, if only in the way we talk about it, from death's centrality to its banality.

But something else more important remains centre stage: namely, the attitude of the protagonists in the face of death. When asked about his health, Hume replied that he was dying as quickly as his enemies could wish, but as cheerfully as his friends could desire. In his interviews, Hitchens has been no less wry, no less courageous. We are born, he said, "into a losing struggle and nobody can hope to come out a winner".

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We leave Hitchens, just as Boswell left Hume, disturbed. But we also leave elated upon seeing both men win the greatest prizes that can be won - dignity and lucidity - for the rest of us.