But why was Marx so successful? He was writing at a time of enormous social upheaval, as industrialization and urbanization were destroying an old order of ­agriculture, artisanship and village life. The changes would produce greater prosperity in the long run, but they also created a life that was, the authors note, “dismal for the new industrial class of workers laboring in the mines and factories of the early 19th century.” Gaping inequality inspired many radical writers who, like Marx, advocated the abolition of private property, the empowerment of workers and the need for a revolution.

By 1914, while still much read and quoted, Marx had been largely rejected by most of Europe’s major Socialist parties and labor movements, which had moved to practical reform and away from revolution. Then came World War I, and with it the destruction of Continental Europe’s three great multinational empires — Germany, Austria-Hungary and Russia. As Russia was crumbling, a brilliant political operator, Vladimir Lenin, seized power in what was essentially a palace coup, and institutionalized Marxism in the world’s largest country. Twenty-five years later, it had become a superpower. Without that quirk of fate, Karl Marx would have a very different place in history than he does ­today.

Montgomery and Chirot never go as far as I just did to suggest the contingent nature of the success of these ideas. Indeed, their thesis is that ideas are themselves prime movers in history. But they provide a rich and balanced account that describes the permissive environment in which ­certain notions flourish — and others founder. They also recognize that while the thinkers they concentrate on are crucial, they are usually part of a larger group of writers, all responding to their times with similar diagnoses and prescriptions.

Of the four, Charles Darwin provides the most persuasive case for the power of ideas in and of themselves. Scientific advances relate less to the political and economic conditions of the age and more to previous investigations of a particular subject. Scientists examine, affirm, refute and expand on the writings of their predecessors. In Darwin’s case, he was clearly influenced by geologists like Charles Lyell, who speculated that the Earth had been created gradually, and also by ­Georges Cuvier, who pointed to evidence that ­certain species had gone extinct. In particular, he built on the work of Jean-Baptiste ­Lamarck, who posited that all living creatures had developed from earlier forms.

But even with Darwin, perhaps especially with Darwin, society had to be ready for his theories. “We can’t really understand the force of Darwinian thought,” Montgomery and Chirot write, “without looking at this context, for it tells us why science and society were ready to seize upon certain portions of this thought.” The context was the industrial and technological revolution, new machines and processes, new ways to observe the Earth and the stars, all of which had shattered faith in religion and produced a new trust in objective, scientific laws that would uncover the way the world really worked. The search for science was itself a reflection of the age.

The last chapters of the book detail the reaction and continued opposition to Enlightenment ideas. The authors are most effective in describing the longstanding and ongoing distrust of liberal democracy that one sees today in places as diverse as Cuba, Iran, Saudi Arabia, Russia and China. They argue that forms of fascism could still be revived and that the appeal of Marxism — in response to inequality and dislocation — should not be discounted. (Though I am not convinced that anyone would again embrace Communism: It had its chance and the results were unambiguous failure.) And they point out the bizarre reality that even today, in 2015, Darwin is still controversial — especially in the nation that is a product of the Enlightenment, the United States of America. I would note, for example, that not one of the candidates running for the Republican nomination for president will straightforwardly affirm the science of evolution and advocate that it be taught in schools.

The most pressing rejection of and challenge to Enlightenment concepts today, however, is radical Islam. It certainly helps to understand the ideas behind it and the leading theorists of it — and Montgomery and Chirot do a brief, admirable job of that. But it would surely also be worth trying to understand why these ideas — many of which have been around for hundreds of years — are popular now.

It is a large question, but it’s worth recalling that the Arab world embraced many Western, Enlightenment ideas over the last century — nationalism, Pan-­Arabism, socialism. The leaders who espoused these concepts, however, produced only repression and stagnation, exacerbated by the curse of oil. The region became an arena dominated by outside powers. Radical Islam provided an off-the-shelf ideology of protest — one that now appeals to misfit Muslims everywhere. But the conditions that have made it flourish are less about the strength of abstract ideology than about the weakness of human leadership.