Rose's unpleasant and wealthy fiance, Cal, offers Murdoch thousands of dollars to secure him a place in the lifeboats, ahead of the women and children. Murdoch is momentarily tempted - at least, he leaves the money in his pocket for a while but, when Cal tries to close the deal, he throws the loot back in his face.
You may think it beyond dispute that Murdoch acts according to the highest standards of humanity and civilisation. Here, surely, is a moral action on which we can all agree. Not so. In the weekly, high Tory Spectator magazine, its columnist Taki argues that Murdoch is nothing more than a foolish, old-type socialist. Murdoch has absolutely no initiative, no drive. He could take the money and go for it, but, no, he dreams of paid company holidays and union get-togethers.
Even Taki perhaps does not take himself entirely seriously and it may be objected that a man once convicted of cocaine smuggling and who sometimes expresses views bordering on racism should play no part in any debate on moral values. Nevertheless, I think an important question arises from his observations, though possibly not one he intended.
What is the distinction between Cal's behaviour, which the film invites us to denounce as morally repugnant, and that of people (including, I imagine, a good many readers of this paper) who secure a privileged place in the contemporary equivalent of the lifeboat queue by paying for private hospital treatment? If there is such a distinction, I cannot immediately see it.
I raise the question to illustrate the extreme slipperiness of attempts to debate values. It is commonly said that we now live in a pluralistic society, where anything goes, whereas in the past we enjoyed a moral consensus.
I am not so sure about this. Some things, such as racism, sexism, child abuse (physical and sexual) and drunken driving, are more severely denounced and more widely deplored than they were two or three generations ago. Others, such as swearing, adultery, taking drugs and cheeking one's elders, all heinous crimes in my childhood, are now hardly regarded as moral issues at all.
The real difference between now and the past lies in attitudes to authority. When I was a child, authority was a mighty edifice, with people who expected to be obeyed piled one on top of another, like layers of a wedding cake: not just parents and teachers, but uncles, aunts, policemen, vicars, shopkeepers, employers, scoutmasters, indeed adults generally.
At the very peak of this edifice sat God the Father, the biggest stickler of all for obedience. As a moral code, Christianity may be almost entirely admirable; but the truth is that, for most of history, it has operated, not as a system of values, but as a system of authority.
So I think that Michael Barber, head of the Department for Education's standards unit, was entirely justified in his remarks at the Secondary Heads Association conference last month. Christianity, he suggested, was now a minority interest and, while children still needed to understand it for historical and cultural reasons, it no longer commanded unquestioning obedience. What we needed to do instead was to give children a highly-developed sense of ethics and of a global, as well as national, citizenship.
The trouble is that obedience is a simple matter, while ethical behaviour and citizenship are problematic. Take the desirable values listed last year by Nick Tate, chief executive of the Qualifications and Curriculum Authority: concern for others, compassion, self-discipline, restraint, concern for the truth, and also enterprise.
Most of us would hesitate over that last word, if only because we associate it with the greed and materialism of the Thatcher and Reagan years. But are the others as straightforward as they look? Are self-discipline and restraint compatible with modern injunctions to get in touch with our emotions? When does compassion become a form of featherbedding that prevents people taking charge of their own destinies? What do we mean by truth in an age when everything, from government policy to school exam results, is mediated by presentation and spin-doctoring?
We may argue that it is the duty of schools, as Professor Barber seems to suggest, to stand out against the tide of unfettered individualism, rampant consumerism, mobile phones and all the rest of it. But can schools credibly do so while accepting sponsorship in Professor Barber's own education action zones, for example, from rampantly consumerist firms? Is Professor Barber quite sure that a mobile phone company will not be involved in one of his zones?
Indeed, anybody connected with a political party (even the head of a standards and effectiveness unit) may have some difficulty putting himself or herself in the forefront of any kind of ethical renewal. We may well argue that if Britain, or the West generally, now has a central, widely-accepted set of values they are those of liberal democracy, not Christianity.
Should civics not therefore replace religious education? Should not the doctrine of parliamentary sovereignty be taught instead of the Holy Trinity?
But even liberal democracy has its ethical problems. In Britain and America, political parties of all shades, knowing that power depends on the support of what J K Galbraith calls the "contented majority", have abdicated from concern for the poor.The Christian Churches have moved into the vacant ground because they, unlike the parties, regard every human soul, even a non-voting one, as deserving of God's mercy.
My point, then, is this: values, ethics and morals are complex and difficult territory. Once, they seemed simple, not because they were simple, but because they were backed by the force of an authority that people rarely questioned.
In an age of mass communication, it is impossible to imagine restoring such authority, even if we wished to. So schools can no longer hope to hand down to their pupils a formula for the good life. The best they can do is to encourage children to think, to question, to debate, to examine critically even the most fundamental of their moral assumptions.
As Cal and Murdoch show in Titanic, and as the philosophers have known down the ages, even what seems the simplest of moral actions contains untold complexities.