A generation or so ago, Anthony Pagden's book would not have needed a sub-title.

The Enlightenment has never lacked for enemies, in church or state. It was denounced instantly for inspiring the Reign of Terror after the French Revolution, and for every revolutionary terror that followed. But for centuries Enlightenment thought held a high ground that was, in the proper sense, moral.

That was mostly because certain ideas, well understood or not, were taken for granted. Try imagining western democracy without them: human rights, international law, individual liberty, freedom of thought and speech and the rejection of superstition. Even now, most of us doubt that a decent society could function without these virtues.

We don't, for the most part, cede all power to priests and kings. We don't accept that one person is superior to another in any way, far less because of gender, title, accident of birth or skin colour. So fundamental is the Enlightenment's legacy that we cannot conceive our world without it.

That, as Pagden demonstrates, might be part of our looming problem. We might find feudalism or the divine right of kings astonishing, even comical, and wonder idly how so many societies functioned for so long without seeming to question such things. But how did they function? Some of the Enlightenment's modern enemies are keen to ask the question.

It might seem to us self-evident that honour killings, wife-burning, caste systems or female circumcision are cruel abuses. The fact remains that in parts of the world such horrors have been unchallenged, even celebrated, for centuries. They have been practised by people who believe it is crucial to abide by tradition no matter what.

Besides, who are "we"? Early in this invigorating book, Pagden paraphrases Jean-Jacques Rousseau in his seemingly crazed determination to "force people to be free" if they said they preferred their priests, kings and ignorance. In fact, Rousseau probably understood the paradox. Whether it crossed the mind of the first emissary of the west who told chaps in loin cloths to give up their headhunting is another matter.

In Pagden's previous book, Worlds At War: The 2500-Year Struggle Between East And West (2008), he wrote, disputably, of an ancient yet continuing tension, remarking that "what divided the Persians from the Greeks or the Asians from the Europeans was something more profound than petty political differences. It was a view of the world, an understanding of what it was to be, and to live, like a human being". In The Enlightenment – And Why It Still Matters he develops the theme.

The book is the history of an intellectual project written with the understanding that any history "must be a reflection of what the present owes to the past". Patently, there are vast tracts of the modern world in which Enlightenment ideas are anything but self-evident. Equally, there are growing numbers in the west who believe the efforts of David Hume, the philosophes and the rest, were wrong-headed and catastrophic.

In much of the Muslim world there are hundreds of millions of people who have no wish to contest the claims of their established religion, or to be freed of what Immanuel Kant called "the ball and chain of an everlasting permanent minority". They say they are liberated by obedience to faith, not shackled. You can find plenty of people in Europe liable to say the same as they take instruction from a man in the Vatican.

Pagden is a professor of political science and history at the University of California (Los Angeles). As such, he will be perfectly well aware that assaults on "Enlightenment values", as they are termed dismissively, are not exactly unknown in the United States. He does not labour the point, but on the American political right the old charges are being made again against the ungodly Enlightenment and its subversion of tradition and faith.

The prejudice has a history, one that Pagden lays bare with a wealth of references. Among other things, the Enlightenment gave us the idea of cosmopolitanism, the idea that, being human and equal, we are each of us "citizens of the world", not bound by tribal ties or ancient traditions. We global citizens are liberated from all of that. Thus we contemplate – even enforce? – international laws, international courts or a universal declaration of human rights.

Again, there is a problem. Unexamined, it all sounds very fine. It might even seem to hold out the long-delayed promise of rational human progress. But as the eccentric Johann Georg Hamann inquired rhetorically of Kant (I paraphrase): what is rational? Where did the words used to make "pure" reason's arguments arise unless from a local language, shaped by history and habit, into which the rationalist was born? Reason, Hamann said, is never independent of tradition, language or custom.

Nor can we simply declare ourselves citizens of the world and forget where we were made and how we were made. Ideas of justice, happiness, morality and beauty do not float in the ether but grow from specific terrains. That is why religion, nonsensical or not, still exerts its binding force. Enlightenment ideas of universalism are as vulnerable to this kind of assault from post-modernism, as Pagden shows, as they were from 19th-century reactionaries.

As has been said often enough, Enlightenment chatter over man and nature substituted idealised fictions for reality. The criticism is equivalent to Margaret Thatcher's declaration that there is no such thing as society. Enlightenment's enemies say there are plenty of humans who deserve to be treated as such, but to talk of "humankind" is to say nothing about the reality of social and cultural diversity.

In modern times, Pagden identifies the notion of "communitarianism" as a particularly powerful – he does not quite say pernicious – refinement of a familiar critique of what began on the streets of Edinburgh, Paris and elsewhere. Forget being a citizen of the world, it says, for the notion is impossible. All you can truly hope to be as a human being is what your community, at most your nation, has caused you to be, raised on the tales of your tribe, born with its assumptions, your thoughts shaped by its language.

According to this argument, there comes a point at which different communities will cease to communicate simply because their understanding of the world is at odds. A true international law, an authentic world order, a genuine respect for individual choices: these are pipe dreams. Believe in these things and you invite chaos, just as in the French Revolution. Tradition, religion and all, is to be preferred.

Pagden is not offering a polemic. He lets the history speak for itself, as much as history ever speaks. However, towards the end of his book he does invite Enlightenment's enemies, especially in the west, to ask themselves "why the world of virtue and moral authority which had apparently served our ancestors so well should have been overturned in the first place".

It is the best of questions. With religion resurgent across the world – complaining of oppression at every turn – the Enlightenment project, never completed, is at risk again. As this eloquent and thrilling book makes clear, its enemies might care to explain why it happened in the first place.

The Enlightenment – And Why It Still Matters

Anthony Pagden

Oxford University Press, £20