The first ever non-European pope takes over at the Vatican, while Italy's economic ills and ungovernability foretell, it's argued, the wider decline of the west. First-world Catholics enmeshed in scandal in Europe and the United States have turned to a devout Argentinian to clean up their mess.

Meanwhile, there are weekly signs of the west's fall. It is not a western hi-tech company challenging Apple for global dominance of the smartphone market but South Korea's Samsung with its new Galaxy, launched with great fanfare last week. This week, our government will reportedly announce in the budget that Qatar is coming to the rescue of poverty-stricken, austerity-ridden Britain with a £10bn fund for infrastructure. And everyone knows about the rise of China. The world is turning on its axis. It is now a commonplace that the west is in irredeemable decline.

Economically, the trends are well established. If they continue, by 2015 Europe's share of world GDP will have fallen to 17% (and to 10% by 2040) from the 26% it commanded in 1980. The US's dominance in defence is also being steadily eroded; its budget is stagnating while China's is growing by double digits every year. Raw materials and oil flow to Asia rather than Europe.

Europe's population ages and its work ethic, it is claimed, is undermined by our addiction to welfare. As our economies underperform, the most exclusive parts of London, Paris, Rome and Berlin are being bought up by the newly rich from Russia, Latin America and Asia. The richest man in the world is Carlos Slim from Mexico, while the Group of Seven leading industrialised countries is no longer the locus of world economic power. That has moved to the G20.

Even western democracy, one reliable export to the rest of the world, no longer seems so admirable. The US government is deadlocked over its budget so that after the arbitrary spending sequester on 1 March, parts of government will start to close down at the end of the month. Perhaps the benign dictatorship of the Chinese Communist party offers a better model for governance.

Yet look more closely and a more subtle, more encouraging story is at work – less the decline of the west than the steady spread of its values and practices. Jorge Mario Bergoglio is pope because he embodies – at least in Catholic eyes – the best of the western Catholic tradition. He may defend core values on marriage and sexuality, however irrelevant and unjustified they now seem in secular Europe and America, but is avowedly liberal on social issues and poverty. Catholic social policy, with its commitment to justice, fulfilling work and the necessity to enfranchise every human, is one of the better components of the religion's tradition.

This social policy was an outgrowth of the church coming to terms, over the 19th century, with the Enlightenment. If it is so survive in the 21st century, it will have to come to terms with the Enlightenment's view that sex is not immoral and sexual preferences should not be stigmatised. Pope Francis might also come to regret his alleged compromises with the Argentinian junta that may dog his papacy. But nonetheless he is the best the Roman Catholic church can offer in holding an impossible line – and might prove to be one of the last who tries to do so. Soon, there will be no part of the world, not even the Catholic church, not touched by Enlightenment virtues.

The same painful process has begun in the Arab world. The Arab Spring represented a series of societies insisting on a voice, the rule of law, representative government, freedom from arbitrary imprisonment and freedom of expression. Yes, the first beneficiaries have been religious fundamentalists and Islamist zealots, but that is only to be expected in the first phase of the process. Fundamentalism is a response to being under siege; it is because western Enlightenment values are so attractive that Arab societies, concerned to preserve their identity, reaffirm their "Arabness" via religion. The attraction of the Muslim Brotherhood is much more complicated than mere religious fundamentalism - they also have a partial Enlightenment commitment to justice.

Nor is China immune. Last week saw the Sina Weibo microblogging site full of anonymous mockery of President Xi's monarchial, unopposed anointment to lead. Censorship is breaking down. The regime dares imprison fewer and fewer overt political prisoners. Meanwhile, the Communist party's upper echelons anxiously debate how legitimacy is to be won in a one-party state, but even more anxiously question how China's growth rate is to be maintained now it can no longer just copy western technology but must develop some of its own. Science, freedom of inquiry, peer review, openness to new ideas and honest statistics turn out not to be bourgeois western ideas but fundamental to innovation. They cannot be promoted in a one-party state.

Nor is it clear that the US is to be written off quite so quickly. The anti-Enlightenment American right has become locked in an anti-scientific, anti-sexual revolution and anti-justice ideology – and has lost the popular vote in five out of the last six presidential elections. Obama's victory in 2012 could be read as the great republic reasserting its commitment to Enlightenment values. Part of the rapidly escalating American economic recovery is about cheap shale gas, but part is about the rediscovery of an Enlightenment commitment to research and development, now reaching record levels, and the innovation that goes with it. As the Tea Party right's progress stalls, there is an emerging confidence that the US has not lost its way after all.

In Britain, a similar drama is playing itself out. David Cameron's modernisation project was an attempt to make his party come to terms with Enlightenment truths – on climate change, the environment, same-sex marriage, open innovation and even social justice – but he has been beaten back into the same dark laager inhabited by American conservatives. A small state and a balanced budget are everything in this theology, along with an individualism is all that is needed for capitalist success and social harmony.

These are propositions that never did work. Successful capitalism is co-created by private and public initiative, a marriage between the market and the Enlightenment – its values and its publicly created institutions. Hence Britain and the US in their different historical contexts; thus South Korea today. It is this alchemy that drove the rise of the west and is now, in varying and incomplete guises, driving the dynamism in the rest of the world. We in the west should remember what drove our success. Rather than mourn our relative decline, let's celebrate others getting as good, if not better, at what we used to practise and have allowed to atrophy. Then we must find ways to rediscover the alchemy ourselves.