In 1938 Kurt Godel published the proof of a theorem which made a lot of professional mathematicians very unhappy.

He showed that any complete mathematical system will sooner or later produce statements which are inherently paradoxical; they can neither be proved true nor proved false. To some questions there can never be a satisfactory answer.

In the abstract world of mathematics such problems can be treated as no more than curiosities to be studied in the farthest reaches of academe. In politics, problems without solutions are rather more common and far more serious; they can be quite literally matters of life and death. One such problem is Tibet.

The almost universal view from the west is that the Chinese occupation of Tibet is a crime. Tibet was, and should be still, an independent and peaceful nation minding its own business and threatening no-one. The Chinese takeover was an act of naked aggression which could not be legitimised by spurious appeals to history and geography, as Beijing has attempted for at least fifty years.

Since then there has been widespread repression and violation of human rights and attacks on people and property aimed at destroying the entire Tibetan culture. While the Chinese remain, things can only get worse. Morally, there is no alternative to a free Tibet. The international community should use every legitimate means to bring this about, starting with a boycott of the Beijing Olympics.

If only it was so simple. For starters, an Olympic boycott would almost certainly do no good at all; the patchy boycott of the Moscow Olympics in 1980 did nothing to get the Russians out of Afghanistan. Indeed, given the paranoid state of Chinese politics, a boycott could be seriously counterproductive, leading to still tighter control from the Communist Party. Anyway, the Dalai Lama himself has advised against a boycott.

So it seems only sensible to rule this out. But that leaves … what? Trade bans involving the world’s largest importer of raw materials and largest exporter of consumer goods are obviously impractical; they might eventually hurt China, but they would wreck the rest of the world economy in the process. And again, there is no reason to believe that this kind of punitive action would benefit the Tibetans.

All that is left is persuasion and diplomacy, and these have not been too successful in the past either. The core fact that must be recognised is that, to Beijing, China’s territorial claim to Tibet is incontestable and non-negotiable.

In practice this has been the political reality for many years: Chinese sovereignty over Tibet is bipartisan policy in Australia, as it is in most of the world. Again, even the Dalai Lama accepts that Tibet will not regain full independence. The best that can be hoped for is a fair degree of autonomy, free of the constant authoritarian presence of the Chinese military. But this would involve an end to the protests in Lhasa, which are generally regarded by the rest of the world as entirely justified.

To Beijing, of course, they are acts of open rebellion, a threat to national security, and must be treated as such. The mainstream view in China is that the arrival of the People’s Army signalled not an invasion but a liberation (sound familiar?) by which the peasants were freed from a cruel and intolerant theocracy run by bloated monks who stole the wealth of the people to create an obscenely opulent lifestyle for themselves and whose leader fled to India to plot for his return to resume his oppressive regime.

In the years since then the material well-being of all Tibetans has increased immeasurably, particularly in the fields of health, housing and secular education. Society has been reformed and modernised, giving people from all backgrounds more choice of careers and lifestyles. The younger generation in particular now have opportunities of which their parents could not even dream. And this has been made possible by the sacrifices of their fellow Chinese, who have worked in a severe and alien environment to bring the benefits of civilisation to their benighted fellows; not many Han Chinese actually enjoy life on the plateau.

Under the circumstances, those demonstrating for a return to the bad old days must be seen as criminal reactionaries, enemies of the people. But of course they are not; they are the people, or at least the more militant representatives of the people. What the Chinese view overlooks is that the Tibetans’ hunger for independence can override any feelings of gratitude for increased material well-being, and that indeed the extra prosperity and education they have acquired will in themselves generate a desire for more control over their own lives.

This should not be surprising; the Tibetans are hardly unique. In recent times we have seen the same drive in East Timor, in former Soviet states and in the Balkans. And perhaps we are still seeing it in Iraq. The Chinese themselves have gone through similar periods in their long history. Nationalism is a force which, once unleashed, is very hard to stop. But in the case of Tibet, Beijing is determined to show that it can be done, and nothing the rest of the world says is going to change its mind – at least in the foreseeable future.

Kevin Rudd and other leaders can, and should, make the case for restraint, for a scaling down of the occupying forces, for a crackdown on profiteering and corruption among the Han Chinese, for a greater understanding and respect for Tibetan culture, for increased autonomy and more overall freedom. But they shouldn’t waste their time demanding full independence for Tibet. Not even the Dalai Lama is doing that any more.